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Worksheet on Simplification of Algebraic Expressions | Simplifying Expressions and Equations Worksheet

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Detail worksheet on simplification is here. Check simplification example problems and solutions here. Refer step by step procedure to find the accurate solution on fundamental expressions and simplifications. Simplify all the algebraic expressions and rules to solve problems.

Solve many mock questions based on the simplification of algebraic expressions and integers from Simplification of Algebraic Expressions Worksheet to get perfection and crack the exam easily. Before solving the below problem, check our previous articles to know the formulae, rules, and methods. Follow the below sections to know various model questions and solutions.

Problem 1:

After striking a floor, a certain ball rebounds 4/5th of the height from which it has fallen. What is the total distance that it travels before coming to rest if it is gently dropped from a height of 120 meters?

Solution: 

As given in the question,

The height at which the ball rebounds = 4/5

The height at which the ball drops = 120 meters

Let the distance be n

The total distance it travels to come to rest position = 120 + 120 + n/1 – n

= 120 + 120 + (4/5 )/1-(4/5)

= 120 + 96/ 1-4/5

= 1080 kms

Therefore, the total distance is 1080 kms.

Problem 2:

8 years hence the sum of A’s and B’s age is 70 years. 4 years ago, the ratio between the sum of ages of A and B together and C’s age was 2:1. What is the present age of C?

Solution: 

As given in the question,

The sum of A’s and B’s age is 70 years.

A + B = 70

As given, the ratio between the sum of ages of A and B together and C ‘s age was 2:1

The equation will be A + B – 8/C-4 = 2/1

23 = C-4

C = 17

Therefore, the present age of 17 years

Problem 3:

The income of a company doubles after one every year. If the initial income was Rs. 4 lakhs. What would be the income after 5 years?

Solution: 

As given in the question,

Incomes double every year

The initial income = Rs 4 lakhs

After the first year, the income will become = 4 * 2 = 8 lakhs

After the 2 nd year, the income will become = 8 * 2 = 16 lakhs

After the 3 rd year, the income will become = 16 * 2 = 32 lakhs

After the 4th year, the income will become = 32 * 2 = 64 lakhs

After the 5th year, the income will become = 64 * 2 = 128 lakhs

Hence, the income after 5 years = 128 lakhs

Problem 4:

Man earns Rs 20 on the first day and spends Rs 15 on the next day. He again earns Rs 20 on the third day and spends Rs 15 on the next day. If he continues to save like this, how soon will he have Rs 60 in his hand?

Solution: 

As given in the question,

The amount of money man earns = Rs 20

The amount of money man spent = Rs 15

Therefore, for every 2 days, he saves Rs 5.

For the first 2 days, the amount he saves = Rs 5

For the first 4 days, the amount he saves = Rs 10

For 8 days, he saves = Rs 20

For 16 days, he saves = Rs 40

Therefore, he saves Rs 60 in 18 days

Thus, he takes 18 days to save Rs 60.

Hence, the final solution is 18 days.

Problem 5:

If Raju have 24 hamburgers and he eats half of them in one hour, then his dog eats half of what was left in one hour, how many hamburgers do he have left?

Solution: 

As given in the solution,

No of hamburgers Raju have = 24

Amount of burger he eats in one hour = 1/2

Amount of burger his dog eats = 1/2

Therefore, the no of burgers left = 24 * 1/2 * 1/2

= 24 * 1/4 = 6

Hence, Raju has 6 hamburgers left with him.

Thus, the final solution is 6 hamburgers.

Practice Questions & Worksheet on Simplification

Problem 6:

Number of working days of a school is 5 days per week and I spend 5 hours in class each day.. Boring!!! How much time do I spend in class each week?

Solution: 

As given in the question,

No of hours I spent in each day = 5

No of working days = 5

Therefore, to find the total time spend in class each week, we apply the simplification rule of multiplication.

Hence, the total time spend = 5 * 5 = 25

I attend 25 hours of class in each week.

Thus, the final solution is 25 hours.

Problem 7:

Find the three consecutive even integers such that 6 times the sum of first and the third is 24 and greater than 11 times the second.

Solution: 

As given in the question,

Let the three consecutive even integers = x, x+2,x+4

Also given, 6 times the sum of first and the third is 24 and greater than 11 times the second

Therefore, 6(x+x+4)=11(x+2)+24

6(2x+4)=11x+22+24

2x+24 = 11x + 46

On further simplification, x= 22

Then, x+2 = 24

and x+4 = 26

Therefore, the three consecutive even integers are 22,24 and 26

Hence, The final solution is 22,24 and 26

Problem 8:

Leonard found four consecutive integers such that 3 times the sum of the first and fourth was 114 less than the product of -5 and the sum of the first two. What were the integers?

Solution: 

Let the four consecutive integers be x, x+1,x+2,x+3

As given in the question,

3 times the sum of the first and fourth was 114 less than the product of -5 and the sum of the first two

=3(x+x+3) = -5(x+x+1)-144

=3(2x+3) = -5(2x+1)-144

=6x+9 = -10x-5-144

=6x+9 = -10x-119

=16x+9 = -119

=16x/16 = -128/16

= x=-8

As considered, the consecutive integers are x, x+1,x+2,x+3

Therefore, the integers are -8,-7,-6,-5

Problem 9:

The sum of 2 numbers is 36 and their product is 248. What will be the sum of their reciprocals?

Solution: 

As per the given question,

A+B=36

A * B = 248

To find the sum of their recriprocals, we have to simplify the equation 1/A+1/B

=B+A/BA = 36/248 = 9/62

Therefore the sum of their reciprocals = 9/62

Problem 10:

In a poultry farm having hens and pigs, Rohan can see 84 heads and 282 legs. How many hens are there?

Solution: 

As per the given question,

Every hen has 1 head and 2 legs

Every pig has 1 head and 4 legs

Therefore, hens + pigs = 84 is the first equation

2(Hens) + 4 (Pigs) = 282 is the second equation

On simplifying both the equations, we get

4Hens + 4Pigs – 2Hens – 4Pigs =336-282

2Hens = 54

Hens = 27

Therefore, 27 hens are present in the poultry farm.

The final solution is 27 hens.

Problem 11:

The summation of 5 consecutive numbers is found out to be 335. If we add the largest and smallest number what will we get?

Solution: 

Let the numbers be x,x+1,x+2,x+3,x+4,x+5 = 335

5x + 10 = 335

5x = 325

x = 65

Therefore, the numbers are 65,66,67,68,69

To find the sum of largest and smallest number, we have to add 65 and 69

Therefore, the solution is 134

Hence, the final solution of adding the largest and smallest number is 134.

Problem 12:

Since Raj was not paying attention in class, instead of multiplying M by 3/4, he divided by 3/4. This led to the difference of 14 between the two answers. What is the value of M?

Solution: 

As given in the question,

The number that has to be multiplied = 3/4

The number Raj divided = 3/4

The difference of two answers = 14

To find the value of M, we simplify the equation as

M*3/4 – M/3/4 = 14

3M/4 – 4M/4 = 14

9M-16M/12 = 14

-7M/12 = 14

M=-24

Hence, the final solution is -24

Problem 13:

Raman has 2 urns. Both these urns have the same pebbles. If 20 pebbles from urn B are shifted to urn A, then the number of pebbles in both urns get interchanged. But if 10 pebbles from urn A are put into urn B, then the number of pebbles in urn B is twice the number of pebbles in urn A. How many pebbles do A and B respectively have?

Solution: 

As given in the question,

No of urns Raman has = 2

Also given,

20 pebbles from urn B are shifted to urn A, then the number of pebbles in both urns get interchanged and 10 pebbles from urn A are put into urn B, which are twice the number of pebbles in urn A

On simplifying the equation, we get

B-20 = A

2(A-10) = (B+10)

2A-20 = B+10

2A-B = 30

B-A+2A-B = 20+30

A = 50

Therefore, B = A + 20 = 50 + 20 = 70

No of pebbles A and B have are 50 and 70

Therefore, the final solution is 50 and 70 respectively.

Problem 14:

On exchanging the digits in unit’s and ten’s place, the difference between original and new numbers become 27. The digits in the unit place are 2 times the digit in the hundred’s place. The digit in the ten’s place is 3 times the digit in the hundred’s place. What is 75% of the original number?

Solution: 

As given in the question,

U = 2H

H = 3H

(3*100+4*10+7*1)

(H*100+T*10+U*1)

100H +30H + 2H = 132H

100H + 10T + U

100H + 20H + 3H = 123H

132H -123H = 27

9H = 23

H = 3

Also given,

U = 6

T = 9

HTU = 396

Therefore, 75% of the original number = 396

Thus, the final solution is 396

Problem 15:

In an area 2% of families have 5 children each. But 8% have no children at all. Amongst the rest of the families 18% have 4 children and 27% have only one child. How many families live in the area, if 297 families have either 2 or 3 children each?

Solution: 

As given in the question,

Percentage of families having 5 children = 2%

Percentage of families having no children = 8%

Total percentage of families = 2% + 8% = 10%

Consider there are 100% families

Therefore, no of families with above data = 100=10 = 90 families

Percentage of families having 4 children = 18%

Percentage of families having 1 child = 27%

Total no of families in those 90 families = 45% of 90

To find the families with 2 or 3 children

100%-45% = 55% of 90

55/100* 90 = 99/2 = 44.5 families

For 100% of families, 44.5 families have children

To find the families who have either 2 or 3 children

= 297 * 100/49.5 = 600

Therefore, 600 families have either 2 or 3 children.

Problem 16:

A group wanted to renovate their club. Each member contributed an amount equal to twice the number of members in the club. But the government contributed same amount as the number of members. If each member had contributed the same amount as the number of numbers and the government had given the twice amount of the members, then they would have Rs.210 less. How many members are there?

Solution: 

M*2M+M

(2M2 + M) – (M2 + 2M)=210

M2 – M = 210

(M – 15) (M + 14) = 0

M * M = 2M

M2 + 2M

M-15 = 0

M = 15

Therefore, there were 15 members in the group who wanted to renovate their club.

The final solution is 15 members.

Worksheet on Fundamental Operations | Four Fundamental Operations Worksheet

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Worksheet on Fundamental Operations and solved examples are here. Check the practice test papers and problems involving various fundamental operations. Know the methods and applications of four fundamental properties by solving Questions on 4 Fundamental Operations. Refer to Problems on addition, subtraction, multiplication, division operations. You can find Step by Step Solutions to all the Problems in the Fundamental Operations Worksheet. Go through the below sections to know various problems involving fundamental operation methods.

Problem 1: 

Two lakh sixty-three thousand nine hundred fifty-three visitors visited the trade fair on Sunday, four lakh thirty-three thousand visited on Monday, and three lakh twenty thousand six hundred fifty-six visited on Tuesday. How many visitors in all visited the trade fair in three days?

Solution:

As per the question,

Visitors visited the trade fair on Sunday = 2,63,953

The visitors visited the trade fair on Monday = 4,33,000

Visitors visited the trade fair on Tuesday = 3,20,656

To find the no of visitors visited the trade fair in three days, we apply rule of addition

Therefore, no of visitors = 2,63,953 + 4,33,000 + 3,20,656 = 10,17,609

Hence, 10,17,609 visitors visited the trade fair in three days.

Thus, the final solution is 10,17,609

Problem 2:

The weight of 298 bags of wheat is 29204 kg. Find the weight of such 125 bags of wheat?

Solution:

As per the question,

The weight of wheat bags = 29204 kg

No of bags = 298

To find the weight of each bag, we apply the law of division rule.

Therefore, the weight of each bag = 29204/298 = 98 kgs

To find the weight of 125 bags, we apply the law of multiplication

Therefore, the weight of 125 bags = 125 * 98 = 12250

Thus, 125 bags weighs 12250 kgs.

Hence, the final solution is 12250 kgs.

Problem 3:

In a garment manufacturing unit, vests are packed in packets of 6 pieces. Ten such packets are then bundled in a carton. How many cartons are required to pack 540 vests?

Solution:

As given in the question,

Total vests = 540

Vests in a packet = 6

Packets in cartons = 10

Number of packets = 540/6 = 90

Number of cartons = 90/10 = 9

Therefore, 9 cartons are required to pack 540 vests.

Hence, the final solution is 9 cartons.

Problem 4:

A bookseller sold 56.248 copies in the first year. The sales doubled in the second year. How many copies of the books were sold in the first two years?

Solution:

As given in the question,

Sales of copies in the first year = 56, 248

Sales of copies in the second year = 56,248 * 2 = 1,12,496

Now, to find the number of copies sold in the first two years , we apply addition rule

Therefore, the number of copies in first 2 years = 56,248 + 1,12,496 = 1,68,744

Thus, the final solution is 1,68,744 copies

Problem 5:

There were 25,000 participants in a mention. One-fourth of them were above 50 years of age. How many of the participants were in the age group of 50 years or less?

Solution:

As given in the question,

Total number of participants = 25,000

Participants above the age of 50 years = 1/4 of 25,000 = 6250

To find the  participants age of 50 years or less, we apply law of subtraction

Therefore, participants age of 50 years = 25000 – 6250 = 18,750

Hence, 18,750 participants were in the age group of 50 years or less.

Thus, the final solution is 18,750 participants.

Problem 6:

The total production of natural rubber in India during three years was 49400 kgs. If the production during two years was respectively. 152870 kgs and 165850 kgs. Find the production of natural rubber during third year?

Solution:

As given in the question,

Total production in three years = 494000 kgs

Total production in two years = 152870 kg + 165850 kgs = 318720 kgs

Production during third year = Total production – Production in two years

= 494000 – 318720 = 175280 kgs

Production of natural rubber during third year = 175280 kgs

Hence, 175280 kgs is produced during third year.

Thus, the final solution is 175280 kgs.

Problem 7:

Ashok packs 580368 apples in 428 boxes. How many apples will he pack in 515 boxes?

Solution:

As per the question,

Ashok packs no of apples = 580368

No of boxes = 428

To find apples in one box = 580368 / 428 = 1356 apples

For 515 boxes = 1356 * 515 = 698340 apples

Therefore, he will pack 6,98,340 apples in 515 boxes.

Thus, the final solution is 6,98,340 apples

Problem 8:

A factory produced 1188440 bulbs in one year. How many bulbs did it produce in the month of August?

Solution:

As given in the question,

Production in one year = 1188440 bulbs

Production in one day = 1188440 / 365 = 3256 bulbs

Number of days in the month of August = 31

Production in the month of August = 3256 * 31 = 1,00,936

Therefore, 1,00,936 bulbs were produced in the month of August.

Problem 9:

Fernando opened a pizza box. Inside there was 3/4 of a pizza. Fernando ate 1/2 of what was remaining. How much of a pizza did Fernando pizza?

Solution:

As given in the question,

The amount of pizza = 3/4

Amount of pizza Fernando ate = 1/2

Therefore, the amount of pizza = 3/4 * 1/2 = 3/8

Each pizza has 6 slices, hence amount of pizza Fernando pizza

= 1/2 * 6 = 3

Thus, 3 parts of pizza Fernando ate

Hence, the final solution is 3 parts.

Problem 10:

Two brothers had a total of 24 oranges. The first brother ate 1/3 of the oranges. The second brother ate 1/4 of the oranges. How many oranges did they eat together?

Solution:

As per the question,

No of oranges both the brothers ate = 24

The amount of oranges first brother ate = 1/3

The amount of oranges second brother ate = 1/4

Amount of oranges first brother ate alone = 24 * 1/3 = 24/3 = 8

Amount of oranges second brother ate alone = 24 * 1/4 = 24/4 = 6

Therefore, two brothers ate = 8+6 = 14 oranges

Thus, the final solution is 14 oranges.

Problem 11:

The price of the cycle is Rs.5699. Find the price of 17 cycles?

Solution:

As given in the question,

The price of each cycle = Rs.5699

To find the price for 17 cycles, we have to apply the fundamental operation of multiplication.

Therefore, the price of 17 cycles = 5699 * 17 = 96883

Hence, the total price for 17 cycles is Rs. 96,883

Thus, the final solution is Rs. 96,883

Problem 12:

An employee earns Rs. 65596 in the month of March. How much is he earning in a single day?

Solution:

As given in the question,

An employee earns in March month = 65596

No of days present in March = 31

To find the earnings of each day separately, we have to apply the fundamental rule of division

Therefore, his earnings in March for each day = 65596/31 = 2116

Hence, he earns Rs. 2116 per day.

Thus, the final solution is Rs. 2116

Problem 13:

At a furniture store, I bought 2 tables and 4 chairs. If each table cost $79 and each chair cost $29. How much did I spend in all?

Solution:

As given in the question,

No of chairs I bought = 4

No of tables I bought = 2

The price of each table = $79

The price of each chair = $29

The total price of tables = 2 * 79 = 158

The total price of chairs = 4 * 29 = 116

The final amount of money spent = 158 + 116 = $274

Therefore, $274 was spent on buying chairs and tables.

Thus, the final solution is $274

Problem 14:

In an aquarium, there were 3 large fish tanks and 5 small fish tanks. Each large tank had 82 fish inside, and each small tank had 20 fish inside. How many fish does the aquarium have?

Solution:

As given in the question,

No of large fish tanks = 3

Number of small fish tanks = 5

No of fish inside the large tank = 82

Number of fish inside the small tank = 20

Total no of fishes in the large tanks = 3 * 82 = 246

Total no of fishes in the small tanks = 5 * 20 = 100

Therefore, the total number of fish in the aquarium = 346

Thus, there are 346 fish in the aquarium.

Hence, the final solution is 346 fish.

Problem 15:

At the grocery store, Meena bought 4 bags of potatoes and 3 block of cheese. Each bag of potatoes cost $17. Each block of cheese cost $14. How much did I spend in all?

Solution:

As given in the question,

No of bags of potatoes = 4

No of blocks of cheese = 3

The price of potatoes = 17

The price of cheese = 14

The total no of potatoes now available = 4 * 17 = 68

The total amount of cheese now available = 3 * 14 = 42

Therefore the total amount spent = 68 + 42 = 110

Hence, the final solution is $110

Problem 16:

Your basket team made 10 three-pointers, 8 two-point field goals, and 12 one-point foul shots. Your opponents made 8 three-pointers, 12 two-point field goals, and 11 one-point foul shots. Who won? By how many points did they win?

Solution:

As given in the question,

The basketball team makes pointers = 10

No of pointers = 3

Total points for the team = 10 * 3 = 30

No of field goals = 8

No of points = 2

Total no of field goals = 8 * 2 = 16

No of foul shots = 1

No of points = 1

Total points for the basket team = 30 + 16 + 12 = 58

The points for the opponent team is as follows.

No of three-pointers = 8

No of points = 3

Total three-pointers = 8 * 3 = 24

No of two-point field goals = 12

No of points = 2

Total two-point field goals = 12 * 2 = 24

No of foul shots = 11

No of points = 1

Total one-point foul shots = 1 * 11 = 11

Total points for opponent team = 24 + 24 + 11 = 59

Therefore, considering the total points of the team

Basketball team scored 58 points and the opponent team scored 59 points in total.

Therefore, the Opponent team has greater points and hence they win.

No of points by which the opponent team wins = 59-58 = 1

Therefore, the opponent wins by 1 point.

Hence the final solution is opponent team wins and it wins by 1 point.

Problem 17:

Latha saved Rs.16785 last year. Her father gave her Rs. 4325 more. How much money does she have now?

Solution:

The amount of money Latha saved = Rs. 16785

The amount of money her father gave her = Rs. 4325

To find the total money she saved, we apply the fundamental operation of addition

Therefore, the amount of money she saved = 16785 + 4325 = 21110

Thus, she saved Rs. 21110

Hence, the final solution is Rs. 21110

Problem 18:

Vinay has 15,180. If he spends Rs. 1690 for shopping. How much will he be left with?

Solution:

As per the solution,

The amount of money Vinay spent = Rs. 15,180

The amount of money he spends for shopping = RS. 1690

To find the amount he left with, we apply the fundamental operation of subtraction.

Therefore, the amount of money he spent with = 15,180 – 1,690 = 13,490

Thus, the final solution is Rs. 13, 490

Problem 19:

If 4095 sample copies of a book were distributed among 365 dollars. How many books did each dealer get?

Solution:

No of copies of a book = 4095

Amount of dollars = 365

To find the no of books each dealer get, we apply the fundamental law of division

Therefore, no of books dealer get = 4095/365 = 11 books

Thus, the final solution is 11 books.

Problem 20:

A company produces 19216 bikes every month. How many bikes will be produced in a year?

Solution:

As given in the question,

No of bikes company produces = 19.216

No of months in a year = 12

To find the production of bikes for a year, we apply the fundamental operation of multiplication.

Therefore, no of bikes in a year = 19216 * 12 = 230592

Thus, 230592 bikes are produced in a year.

Hence, the final solution is 230592 bikes.

Worksheet on Division of Integers | Division of Integers Worksheet

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In the given Worksheet on Division of Integers, you can find Problems on Integers Division. Find Step by Step Solutions for all the problems. Refer to all types of questions involved in the division of integers. Check solved examples and know the procedure followed to solve the problems. Go through the below sections, to know the practice tests and example problems. Try to solve as many times as possible so that your accuracy and speed will be increased. Thus, you can attempt the exam with confidence and answer the questions on Division of Integers easily.

Question 1:

If the temperature is dropping at a rate of 6 degrees per hour. How many hours will it take for the temperature to drop 30 degrees?

Solution: 

As given in the question,

The rate at which the temperature is dropping = 6 degrees per hour.

To find the hours it takes to drop the temperature to 30 degrees, we have to go for the division law of integers.

Therefore, change in temperature = -30/-6

= 5 hours

Thus, it takes 5 hours for the temperature to drop by 30 degrees per hour.

The final solution is 5 hours

Question 2:

If a stock is losing value at a rate of $8 per day. How many days before the stock has lost a value of $48?

Solution: 

The rate at which the stock is losing value = $8

To find the days that stock lost the value = $48, we have to apply the division of integers.

Therefore, no of days = -48/-8 = 6

Thus, it takes 6 days before the stock has lost the value of $48.

The final solution is $48

Question 3:

If a group of hikers is descending at a rate of 15 feet per hour down a mountain. How many hours will it take for the group of hikers to descend 105 feet?

Solution: 

The rate at which the hikers are descending = 15 feet per hour

To find time for a group of hikers to descend 105 feet, we apply the law of division.

Therefore, the time = -105/-15 = 7

Hence, the group of hikers descend 15 feet in 7 hours.

The final solution is 7 hours

Question 4:

If a bucket full of water is evaporating at a rate of 3 cm per hour. How long before the bucket has evaporated a total of 18cm?

Solution: 

The rate at which the bucket full of water is evaporated = 3 cm per hour

To find the time of the bucket evaporated a total of 18cm, we apply the division of integers.

Therefore, the total time = -18/-3 = 6

Thus, it takes 6 hours for the bucket to evaporate 18cm.

Hence, the final solution is 6 hours.

Question 5:

The product of 2 integers is 270. If one of the integers is (-18). Find the other one?

Solution: 

Let the other integer be x

As given in the question, the product of 2 integers is 270

x * (-18) = 270

x = 270/18

x = -15

Therefore, the final solution is -15

Question 6:

Find an integer which when multiplied by 4 and then divided by 9 becomes (-28)?

Solution: 

Let the integer be x

x * 4 / 9 = -28

4x / 9 = -28

4x = -28 * 9

x = -28 * 9 / 4

x = -63

Therefore, the integer which when multiplied by 4 and then divided by 9 becomes (-28) is -63

Question 7:

If the quotient obtained on dividing on integer by -9 is 8, Find the integer?

Solution: 

Let the integer be x

x / -9 = -8

x = -8 * -9

x = 72

Question 8:

A shopkeeper earns a profit of Rs 1 on selling one pen and suffers a loss of 30 paise on selling one pencil in a particular month, he incurs a lot of Rs. 5. In that month, he sold 40 pens. How many pencils did he sell in that period?

Solution: 

Let the no of pencils he sell in that month be x

No of pens he sell in that month = 40

40 * (1) + x * (-30/100) = -5

40 – 3x/10 = -5

40 + 5 = 3x/10

45 = 3x/10

x = 10 * 45/3

x = 150

Question 9:

The population of a small town is changing at rate of -255 people per year. How long will it take for the change in population to be -2040 people?

Solution: 

The rate of the population changing per year = -255

To find the change in population to be -2040 people, we have to apply division rule.

Therefore, the years for the change of population = -2040/-255 = 8

Hence, the total years = 8 years

The final solution is 8 years.

Question 10:

During a six-hour period, the temperature dropped 18 degrees. How much did the temperature change per hour?

Solution: 

Time of the period = 6 hours

Drop in the temperature = 18

To find the temperature change, apply the division rule.

Therefore, the total change = -18/6 = -3 degree

Hence, the temperature changed by 3 degrees per hour.

Question 11:

A stock decreased in value by $80 during the five days. How much did the stock decrease each day?

Solution: 

As given in the question,

The value at which the stock decreased = $80

No of days = 5

To find the stock decreased each day we apply division of integers.

Therefore, the stock decreased = -80/5 = -16

Question 12:

The outside temperature is -20degree F and rising at a rate of 5 degrees per hour. How long will it be before the temperature reaches 0 degrees F?

Solution: 

The temperature outside = -20 degree F

The rate of rising the temperature = 5 degrees per hour

To find how long will it be before the temperature reaches 0 degrees F, we apply the division of integers.

Therefore, the time taken = 20/5 = 4

Hence, it takes 4 hours to reach 0 degrees F

Question 13:

Judges in some figure skating competitions must give a mandatory 5 point deduction for each jump missed during the technical part of the competition. Marisa has participated in 5 competitions this year and has been given a total of -20 points for jumps missed. How many jumps did she miss?

Solution: 

Total no of points = -20

No of participants in the competition = 5

Therefore, total number of jumps missed = -20/(-5) = 4 jumps

The final solution is 4 jumps

Question 14:

Miranda is an excellent spinner who averages +3 points on her spins during competitions. Last year her total spin points equaled +21.

About how many spins did she successfully complete?

Solution: 

No of average spins = 3

Total spin points = 21

Therefore, no of spins she completed = 21/3 = 7 spins

Hence, the final solution is 7 spins.

Question 15:

The temperature dropped 32 degrees F in 4 hours. Suppose the temperature dropped by an equal amount each hour. What integer describes the change?

Solution: 

As given in the question,
Temperature drop = 32 degrees F
Time taken = 4 hours

Therefore, to find the integer that describes the change, we apply the division rule.

Hence, the time taken in 4 hours = -32/4 = -8 degrees F

The final solution is -8 degree F

Question 16:

A stock market fell 60 points over a period of 4 days. What was the average change in the stock market per each day?

Solution: 

As given in the question,

No of points fell in stock market = 60

Time of period = 4 days

To find the average change in the stock market per day, we apply the division method.

Therefore, the average change = 60/4 = -15

Hence, the final solution is every 15 points change in the stock market per day.

Question17:

In a lab, a substance was cooled by 36 degrees over a period of 6 hours at a constant rate. What was the change in temperature each hour?

Solution: 

As given in the question,

The temperature at which it was cooled = 36 degrees

Period of time = 6 hours

To find the change in temperature each hour, we apply the law of division rule.

Therefore, the change in temperature = 36/6 = 6

Hence, for every hour there will be a change of 6 degrees.

Thus, the final solution is 6 degrees.

Question 18:

The outside temperature is -20 degrees F and raising at the rate of 5 degrees per hour. How long will it be before the temperature reaches 0 degrees F?

Solution: 

As per the given solution,

The outside temperature = -20 degree F

The rate at which the temperature is rising = 5 degrees per hour

To find the temperature to reach 0 degrees F, we apply the division law of integers

Therefore, the change in temperature = 20/5 = 4 hours

Hence, it takes 4 hours before the temperature reaches 0 degree F

Thus, the final solution is 4 hours

Question 19:

Judges in some figure skating competitions must give a mandatory 5 point deduction for each jump missed during the technical part of the competition. Marisa has participated in 5 competitions this year and has been given a total of -20 points for jumps missed. How many jumps did she miss?

Solution: 

As given in the question,No of deduction points = 5 pointsNo of competitions Marisa participated in = 5Total points for jumps missed = -20

To find the jumps she missed, we apply the division rule.

Therefore, the jumps missed = -20/-5 = 4

Hence, Marisa missed 4 jumps in 5 competitions

Thus, the final solution is 4 jumps.

Question 20:

Mirinda is an excellent spinner who average +3 points on her spins during competitions. Last year her total spin points equaled +21. About how many spins did successfully complete?

Solution: 

As given in the question,

The average points on spin = +3

Total points equalled = +21

To find the spins that successfully completed, we apply the division law of integers.

Therefore, the spins completed = 21/3 = 7

Thus, the final solution is 7 spins.

Worksheet on Integers Multiplication | Multiplication of Integers Worksheet with Answers

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Worksheet on Multiplication of Integers is here to guide the candidates to know about the concept completely. To determine the integer multiplication method, we will follow various rules, properties, and methods. Before going to check the Multiplying Integers Worksheets, check all the rules, methods, and formulae used in multiplying the integers.

When the two integers with the same sign multiply, then the result value will always be positive. When the two integers with different signs multiply, then the value of the results will be negative. In the below sections, find the Multiplication of Integers Worksheet, practice questions, step by step procedure to solve the problems.

Question 1:

Henry made 3 withdrawals of $2 each from his savings account. What was the change in his balance?

Solution: 

As given in the question,

Henry made withdrawals = 3

The amount he withdrew = $2

As he withdrew the amount, it will be negative

Change in his balance = 3(-2) = -6

Therefore, the total change in the amount is -$6

Thus, the final solution is his savings account was declined by $6

Question 2:

Lisa plays a video game and she loses points in it. She loses 5 points 4 times?

Solution: 

As given in the question,

Lisa plays a video game and loses points = 5

Number of times she loses points = 4

Question 3:

Daniel has caddied 14 times over the past two months and earned a total of $196. How much does he earn totally in 8 months?

Solution: 

As given in the question,

No of times Daniel caddied= 14

The total amount of money he earned for 2 months = $196

For every month, he earned $196

Therefore, for every 1 month, he earned = $98

Thus, for every 8 months the amount he earned = $98*8

=$784

Hence, the final solution is $784

Question 4:

There are 63 groups at the confirmation meeting. If each group had three people, how many people were at the meeting?

Solution: 

As given in the question,

No of groups at confirmation meeting = 63

Number of people each group have = 3

No of people at the meeting = 63*3

=189

Therefore, the no of people at the meeting = 189

Thus, the final solution is 189 members were at the meeting.

Question 5:

Galapagos tortoises can nap sleep 16 hours a day. How many total hours of sleep could a group of 19 tortoises get in one day?

Solution: 

Galapagos tortoises can sleep for hours = 16

No of tortoises = 19

Total no of hours = 16*19 = 304 hours

Therefore, the total no of hours of sleep a group of 19 tortoises can get = 304 hours.

The final solution is 304 hours.

Question 6:

The stationary shop has 163 packets of pens. Each packet has 15 pens. How many pens are there?

Solution: 

No of packets of pens = 163

No of pens in each packet = 15

Total no of pens = 163*15 = 2445 pens

Therefore, the total no of pens in 163 packets = 2445 pens

Hence, the final solution is 2445 pens

Question 7:

The zookeeper wants to give each monkey 12 bananas. There are 53 monkeys. How many bananas would he need?

Solution: 

No of bananas for each monkey = 12

No of monkeys = 53

Total.no of bananas he need = 12*53

=636 bananas

Question 8:

One packet can hold 56 chocolates. How many chocolates will 17 packets hold?

Solution: 

No of chocolates a packet can hold = 56

To find the chocolates in 17 packets, we multiply 17 with 56

Therefore, no of choclates = 17*56 = 952

Thus, no of chocolates a packet can hold = 952 chocolates

Question 9:

Mother bought 8 T-Shirts at rupees 475 each. How much money did she pay in all?

Solution: 

No of t-shirts = 8

Amount of money for each shirt = Rs. 475

Total amount of money she paid = 475*8 = Rs. 3800

Therefore, the total amount of money = Rs. 3800

Hence, the final solution is 3800 rupees

Question 10:

Jay has 2140 Philippines stamps. He has 4 times as many foreign stamps as Philippine stamps. How many foreign stamps does he have?

Solution: 

No of Philippines Stamps Jay has = 2140

No of foreign stamps he has = 4 times

Total no of foreign stamps he has = 2140*4 = 8560

Hence, the final solution is 8560 stamps.

Question 11:

Manny bought 18 boxes of marbles. Each box had 555 marbles. How many marbles were there in all?

Solution: 

No of marble boxes Manny bought = 18

No of marbles each box has = 555

Total number of marbles present = 555*18

= 9990

Therefore, the final solution is 9990 marbles.

Question 12:

A baseball team has 9 players. In a tournament, there are 28 teams. How many players are there in all?

Solution: 

No of players = 9

Number of teams = 28

No of players in a team = 28*9 = 252

Therefore, the total number of players in the tournament = 252

Hence, the final solution is 252 players.

Question13:

A tray of eggs holds 12 eggs. If you have 63 full trays, how many eggs would you have?

Solution: 

No of eggs a tray holds = 12

No of full trays = 63

Total number of eggs present = 12*63 = 756

Therefore, the total number of eggs = 756 eggs

Thus, the final solution is 756 eggs.

Question 14:

A store owner was buying uniforms for his employees. If each of his three stores needed eight uniforms. How many uniforms would he need?

Solution: 

No of stores = 3

No of uniforms = 8

Total no of uniforms he need = 3*8 = 24

Therefore, the total number of uniforms = 24

Hence, the final solution is 24 uniforms.

Question 15:

John bought 2 boxes of books at a yard sale. If each box had five books. How many books did he buy?

Solution: 

No of boxes John bought = 2

No of books in each box = 5

Total books = 2*5 = 10

Therefore, the total number of books he bought = 10 books

Hence, the final solution is 10 books.

Question 16:

An employee earns eight dollars an hour at a construction site. If he works 8 hours in 1 week. How much money he would earn?

Solution: 

Amount of money employee earns at a construction site = $8

The time he works in a week = 8 hours

Amount of money he earned = 8*8 = 64

Therefore, the total amount of money he earned at the construction site = $64

Thus, the final solution is $64

Question17:

A pet store sold 5 gerbils in one week. If each of the gerbils costs 8 dollars, how much money will they have made?

Solution: 

No of gerbils a pet store sold = 5

Cost of each gerbils = $8

The total amount of money = 5*8 = 45

Therefore, the total amount of money the pet store have made = $45

Thus, the final solution is $45

Question 18:

The pupils of Mrs. Luna went on an educational tour at Manila Ocean Park. The Entrance Fee is $280 per child. There were 37 pupils in the class. How much did Mrs. Luna pay for the entrance fee if the pupils?

Solution: 

The entrance fee of Manila Ocean Park = $280

No of pupils = 37

Total amount = 280*37 = 10,360

The total amount of money Luna paid for the entrance for 37 pupils = $10,360

Thus, the final solution is $10, 360

Question 19:

In class, there are 40 children. Each child has 4 pencils. How many pencils are there in all?

Solution: 

No of children = 40

No of pencil each child has = 4

Total pencils = 40*4 = 160

Therefore, the total no of pencils = 160 pencils

Thus, the final solution is 160 pencils.

Question 20:

There are 20 oranges in each tree in an orchard. The orchard has 6 orange trees in all. How many oranges are there in an orchard?

Solution: 

No of oranges = 20

Number of trees = 6

No of oranges = 20*6 = 120

Total number of oranges for all trees = 120 oranges

Thus, the total number of oranges = 120

Hence, the final solution is 120 oranges.

Worksheet on Fraction into Percentage | Fraction to Percent Worksheet with Answers

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In this worksheet, we can see about Percentages and how to convert fractions into percentages. Here, the Percent refers to per hundred. A percent can be represented as a decimal and fraction, which will be a number between zero and one. We can represent it using the percentage formula which is defined as a number that can be represented as a fraction of 100. If we want to turn a percentage into a decimal, we can just divide by 100. In the below sections, we can see how we can convert a fraction into a percentage.

To convert a fraction into a percentage, we will divide the numerator of the fraction by the denominator of the fraction, and then we will multiply the result by 100. Then we will get the result as a percent. Here, below we can see the solved examples. Refer to Percentage Worksheets to clear further queries on the concept.

1. Express the following fractions as a percentage:

(i) 7/20
(ii) 6/25
(iii) 9/13

Solution:

(i) 7/20
Here, we will divide the numerator of the fraction by the denominator of the fraction after that we will multiply the result by 100. Then we will get the result.
= (7/20 × 100) %
= 35 %.

(ii) 6/25
Here, we will divide the numerator of the fraction by the denominator of the fraction after that we will multiply the result by 100. Then we will get the result.
= (6/25 × 100) %
= 24 %

(iii) 9/13
Here, we will divide the numerator of the fraction by the denominator of the fraction after that we will multiply the result by 100. Then we will get the result.
= (9/13 × 100) %
= 69.23 %

2. Convert 9/25 to percentage.

Solution:

9/25
To convert into a percentage, we will divide the numerator of the fraction by the denominator of the fraction after that we will multiply the result by 100. Then we will get the result.
= (9/25 × 100) %
= 36 %

3. Convert the following statements in the percentage:

(i) 10 out of 25 people are sitting.
(ii) 45 oranges in a box of 250 are bad.

Solution:

(i) 10 out of 25 people are sitting.

To convert into a percentage, we will divide the numerator of the fraction by the denominator of the fraction after that we will multiply the result by 100. Then we will get the result.
= 10/25 people are sitting
= (10/25 × 100) % people are sitting
= 40 % people are sitting.

(ii) 45 oranges in a box of 250 are bad.

To convert into a percentage, we will divide the numerator of the fraction by the denominator of the fraction after that we will multiply the result by 100. Then we will get the result.
= 45/250 oranges are bad
= (45/250 × 100) % oranges are bad
= 18 % of oranges are bad.

4. Mike ate the 2/7th part of the pizza. How much percent did Mike eat?

Solution:

Mike ate 2/7th part of the pizza,
To find the percent how much did Mike eat, we will multiply the fraction with 100
2/7 × 100
On solving we will get approx 28%.

5. The total number of students in a class is 45 and in that 27 are boys. What will be the total percentage of boys in the class?

Solution:

The total number of students is 45
Of that 27 are boys
So the percentage of boys in the class are
27/45 × 100
On solving we will get 60%.

 

Worksheet on Ratio into Percentage | Express Ratio as a Percentage

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In this Worksheet on Ratio into Percentage, we can see problems on Ratio into Percentage and know about how to convert a Ratio into Percentage. The term percent in the percentage means per hundred and the ratio refers to the comparison of values between the two numbers which shows that the size in relation to each other. Here, to find the ratio, we will multiply or divide each term in the ratio by the numbers.

So to convert the ratio into a percentage, we will add the given ratio, and then a certain number will be obtained. Then to find the percentage of the single part of the given ratio we will mention the part which we want to find as the numerator and then the total part in the denominator. And finally, to get the percentage we will multiply by 100. Then we can get the ratio converted into a percentage. To avail more information on conversion from percentage form to another form or from other forms to percentage you can refer to Percentage Worksheets.

1. Convert the following ratio into a percentage?

(i) 9 : 25

(ii) 2 : 10

(iii) 5: 20

Solution:

(i) 9: 25
We will place 9 in the numerator and 25 in the denominator
= 9/25
and then we will multiply by 100 to get the percentage
= (9/25 × 100) %
on solving we will get
= 36%

(ii) 2 : 10
We will place 2 in the numerator and 15 in the denominator
= 2/10
and then we will multiply by 100 to get the percentage
= (2/10 × 100) %
on solving we will get
= 20%.

(iii) 5: 20
We will place 5 in the numerator and 20 in the denominator
= 5/20
and then we will multiply by 100 to get the percentage
= (5/20 × 100) %
on solving we will get
= 25%

2. Convert each of the following ratios as fraction percentage?

(i) 3 : 40

(ii) 6 : 16

Solution:

(i) 3: 40
We will place 3 in the numerator and 40 in the denominator
= 3/40
and then we will multiply by 100 to get the percentage
= (3/40 × 100) %
on solving we will get
= 3/40%

(ii) 6: 16
We will place 3 in the numerator and 40 in the denominator
= 6/16
and then we will multiply by 100 to get the percentage
= (6/16 × 100) %
on solving we will get
= 75/2%

3. Express each of the following ratios into a decimal percent?

(i) 4 : 15

(ii) 3 : 20

(iii) 2: 30

Solution:

(i) 4: 15
We will place 4 in the numerator and 15 in the denominator
= 4/15
and then we will multiply by 100 to get the percentage
= (4/15 × 100) %
on solving we will get
=26.6 %

(ii) 5: 18
We will place 5 in the numerator and 18 in the denominator
= 5/18
and then we will multiply by 100 to get the percentage
= (5/18 × 100) %
on solving we will get
= 27.7 %

(iii) 2: 30
We will place 2 in the numerator and 30 in the denominator
= 2/30
and then we will multiply by 100 to get the percentage
= (2/30 × 100) %
on solving we will get
= 6.66%

4. The given angles of a triangle are in the ratio 2:2:1. Find the value of each angle and what will be the percent of each angle?

Solution:

The given angles are 2:2:1, so 2+2+1= 5 parts.

As we know that the sum of angles in a triangle is 180 degrees.
The measure of the first angle is 2/5 × 180= 72 degrees.
The measure of the second angle is 2/5 × 180= 72 degrees.
The measure of the third angle is 1/5 × 180= 36 degrees.
And to convert the given ratio to percent we will multiply by 100
The percentage for the first angle is 2/5 × 100= 40%
The percentage for the second angle is 2/5 × 100= 40%
The percentage for the third angle is 1/5 × 100= 20%

5.  In a class the total number of students in grade 8th is 50 and 26 of them are girls. Find the percentage of girl students in the class.

Solution:

The total number of students in grade 8th is 50 students.
The girl students are 26
The percentage of girl students in grade 8th is
26/50 ×100
on solving we will get
52%.

Worksheet on Percentage into Ratio | Converting Percentage to Ratio Worksheets

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Worksheet on Percentage into Ratio and we can see about how to convert a percentage to ratio. In the term percentage, percent means per hundred and this percent can be represented in decimal and in the fractions also. The term ratio refers to the comparison of values between the two numbers which indicate their sizes in relation to each other. In a simple way, the ratio is derived by comparing two qualities by division with the dividend. To find the ratio, we can multiply or divide each term in the ratio by the number.

To convert Percentage into Ratio, we will divide the percentage by 100 to remove the percent % symbol. And we will reduce the given fraction into the simplest form, and then we will write the number with a ratio sign in between the numbers. These are some steps to convert a percent into a ratio. Here below we can see some of the examples with solutions. To know more about the concept of Percentage you can always look up our Percentage Worksheets and clarify your concerns.

1. Covert each of the following percentage as the ratio in the least form:

(i) 50 %

(ii) 26 %

(iii) 160 %

Solution:

(i) 50 %

To convert Percentage into Ratio, we will divide the percentage by 100
= 50/100
and will reduce the given fraction into the simplest form
= 1/2
and then we will write the number with a ratio sign. On simplifying, we will get
= 1:2.

(ii) 26 %

To convert Percentage into Ratio, we will divide the percentage by 100 and will reduce the given fraction into the simplest form, and then we will write the number with ratio sign
= 26/100
on simplifying we will get
= 1 : 5

(iii) 160 %

To convert Percentage into Ratio, we will divide the percentage by 100 and will reduce the given fraction into the simplest form, and then we will write the number with ratio sign
= 160/100
on simplifying we will get
= 8 : 5

2.  Express each of the following rational numbers percentages into a ratio in the simplest form:

(i) 5/6 %

(ii) 25/4 %

Solution:

(i) 5/6 %
To convert a rational number Percentage into a Ratio, we will divide the percentage by 100 and will reduce the given fraction into the simplest form, and then we will write the number with a ratio sign
= 5/6 × 1/100
on simplifying we will get
= 1 : 120

(ii) 25/4 %
To convert a rational number Percentage into a Ratio, we will divide the percentage by 100 and will reduce the given fraction into the simplest form, and then we will write the number with a ratio sign
= 25/4 × 1/100
on simplifying we will get
= 1 : 16

3. Convert the following decimal percentage as ratios in the simplest form:

(i) 20.5 %

(ii) 0.5 %

Solution:

(i) 20.5 %
To convert a decimal number Percentage into Ratio. First, we will remove the decimal point by dividing with 10 and then we will divide the percentage by 100 and will reduce the given fraction into the simplest form, and then we will write the number with a ratio sign
= 205/10 %
= 205/10 × 1/100
on simplifying we will get
= 41 : 200.

(ii) 0.5 %
To convert a decimal number Percentage into Ratio First, we will remove the decimal point by dividing with 10 and then we will divide the percentage by 100 and will reduce the given fraction into the simplest form, and then we will write the number with ratio sign
= 5/10 %
= 5/10 × 1/100
on simplifying we will get
= 1 : 200.

4. In a class the total pass percentage of boys is 65%. Show the percent into ratio.

Solution:

The pass percentage of the boys are 65%, so
= 65/100
on solving we will get
= 13:20

Worksheet on Percentage into Fraction | Percentage to Fraction Worksheets with Answers

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The worksheet contains converting a Percentage into a fraction, word problems on Percentage into Fraction. These percentages and fractions can be seen in our daily life. In schools and colleges, students can see their marks in percentage. The Percent refers to per hundred and a percent can be represented as a decimal and fraction based on the need.

To convert Percentage into Fraction, we will divide the given number by 100, then we will get a decimal number. Then, if the number is not a whole number. We will multiply both numerator and denominator with 10 for every number after the decimal point. Then we will get the fraction. Practice the Percentage to Fraction Worksheet with Answers and test your preparation level. You can check out Percentage Worksheets for more information regarding the same.

1. Convert each of the following percentages into a fraction in the least terms?

(i) 20 %

(ii) 36 %

(iii) 6 %

Solution:

(i) 20 %
Here we will divide the given percent by 100, then we will get the result.
= 20/100
= 1/5.

(ii) 36 %
Here we will divide the given percent by 100, then we will get the result.
= 36/100
= 9/25.

(iii) 6 %
Here we will divide the given percent by 100, then we will get the result.
= 6/100
= 3/50.

2. Convert 35 percent to fraction.

Solution:

To convert percent to a fraction, we will divide the given percent by 100, then we will get the result.
35 %
= 35/100
= 7/20

3. Express each of the following percentages as fractions in the least terms:

(i) 32 %

(ii) 46 %

(iii) 40 %

Solution:

(i) 32 %
Here we will divide the given percent by 100, then we will get the result.
= 32/100
= 8/25.

(ii) 46 %
Here we will divide the given percent by 100, then we will get the result.
= 46/100
= 23/50.

(iii) 40 %
Here we will divide the given percent by 100, then we will get the result.
= 40/100
= 2/5.

4. Convert each of the decimal percentages as fractions in the least terms:

(i) 2.5 %

(ii) 0.2 %

(iii) 42.5%

Solution:

(i) 2.5 %
Here we will remove the decimal point by diving the decimal with 10 and then we will divide the given percent by 100, then we will get the result.
= 25/10 %
= 25/10 × 1/100
= 5/200
= 1/40.

(ii) 0.2 %
Here we will remove the decimal point by diving the decimal with 10 and then we will divide the given percent by 100, then we will get the result.
= 2/10 %
= 1/5 × 1/100
= 1/500.

(iii) 42.5%
Here we will remove the decimal point by diving the decimal with 10 and then we will divide the given percent by 100, then we will get the result.
= 425/10 %
= 425/10 × 1/100
= 17/40.

Worksheet on Increase Percentage | Percent Increase Worksheets with Solutions

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Students can use this worksheet on Increase Percentage while practicing for their examinations or any other competitive tests. This Worksheet on Percentage Increase contains the concept increase in the percentage. As we know that percentage means per hundred which is used to share the amount in terms of hundred.  In this Increase Percent Worksheet, you can find about how to solve the questions on increase percentage. In the below sections, you can find how to calculate increase percent along with solved examples and understand the concept better.

To know more such related concepts of Percentages you can refer to the Percentage Worksheets available on our site and get a good hold of the concept.

How to Calculate Percentage Increase?

To calculate Increase Percentage, First, we will find the difference between the original number and the new number.
Increase = Original number – New number.
After that, we will divide the number(increase) by the original number. And then to convert into a percentage, we will multiply the number by 100. We will calculate the %Increase by using the formula
%increase = increase / original number × 100
By this method, you can calculate the increase in the percentage. In the below, you can see some of the solved examples on Increase Percentage.

1.  Find out the Increase Percentage of the given below:

(i) 50 by 5%

(ii) 90 by 20%

(iii) 60 by 15%

(iv) 32 by 8%

Solution:

(i) 50 by 5%

The given value is 50 by 5%,
As the number 50 was increased by 5%,
So, first, we will find the new number,
As a new number= 50 + increased percentage,
which means
= 50 + (5% ×50)
on solving we will get 52.5.

(ii) 90 by 20%

The given value is 90 by 20%,
As the number 90 was increased by 20%,
So first, we will find the new number,
As a new number= 90 + increased percentage,
which means
= 90 + (20% ×90)
on solving we will get 108.

(iii) 60 by 15%

The given value is 60 by 15%,
As the number 60 was increased by 15%,
So, first, we will find the new number,
As a new number= 60 + increased percentage,
which means
= 60 + (15% ×60)
on solving we will get 69.

(iv) 32 by 8%

The given value is 32 by 8%,
As the number 32 was increased by 8%,
So, first, we will find the new number,
As a new number= 32 + increased percentage,
which means
= 32 + (8% ×32)
on solving we will get 34.56.

2. Solve out the number when increased by:

(i) 2.6% becomes 520

(ii) 25% becomes 1000

(iii) 33% becomes 1650

Solution:

(i) 2.6% becomes 2052

Here, we should find out the number,
So the number be X
as given 2.6% was increased,
So, increased number= X +(2.6% × X), on solving we will get
= 1.026X
given that the number which when increased by 2.6% becomes 2052, which means
1.026X =2052, on solving we will get
X = 2,000.

(ii) 25% becomes 1000

Here, we should find out the number,
So the number be X
as given 25% was increased,
So, increased number= X +(25% × X), on solving we will get
= 1.25X
given that the number which when increased by 25% becomes 1000, which means
1.25X =1000, on solving we will get
X = 800.

(iii) 33% becomes 6650

Here, we should find out the number,
So the number be X
as given 33% was increased,
So, increased number= X +(33% × X), on solving we will get
= 1.33X
given that the number which when increased by 1.33% becomes 6,650, which means
1.33X =6,650, on solving we will get
X = 5,000.

3. In a class the strength of the girl students increased from 30 to 42. What is the percentage increased?

Solution:

First, we will find the increased number 42-30= 12,
then we will find the % of the increased
= 12/30 ×100
on solving 40%
So, the increased percentage is 40%.

4. What number must the given number be multiplied to increase the number by 30%.

Solution:

Let the number be X,
as X is increased by 30%, which means
X + 30% × X, on solving we will get 1.3X.
So, the number to be multiplied by 1.3.

5. Mike’s salary was increased by 15% on his salary. If Mike’s new salary is Rs 65,000, find his previous salary.

Solution:

Let the previous salary be X,
Mike’s salary was increased by 15%, which means
15% of X,
To find the new salary, we will add the previous salary and the increment,
which means
New salary = Pervious salary + Increment,
X + 15% of X = 65,000, on solving we will get
= Rs 56,521.74.
So the previous salary is Rs 56,521.74.

Worksheet on Finding Value of a Percentage | Calculating Value of a Percent Worksheets

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The Worksheet on Finding the value of a Percentage helps the scholars and the individuals preparing for their examinations or for any competitive tests. In this worksheet, you can find different types of questions with answers. As we know the percent means per hundred and it is used to share the amount in terms of hundred. Here, we will discuss finding the value of the percentage in detail with solved examples below. If you have any further doubts on how to approach and all you can check our Percentage Worksheets available to get grip on the concepts.

How to Find the Value of a Percentage?

To find the value of a percentage, as we know that percent means per hundred, so first, we will multiply the given value by 100, and then we will add the percent symbol to the result that we will get. Let’s see in detail about finding the value of a percentage with some of the examples which are solved below.

1. Figure out the value of X for the following below?

(i) 15% of X is 450

(ii) 20% of X is 25 cm

(iii) 7.7% of X is 70 kg

(iv) 6% of X in 30 minutes.

Solution:

(i) 15% of X is 450

Here, we should find the value of X, so the number X,
As given 15/100 × X = 450
450/15 ×100=
on solving, we will get 3000
So the value of X is 3000.

(ii) 20% of X is 25 cm

Here, we should find the value of X, so the number X,
As given 20/100 × X = 25
25/20 ×100=
on solving, we will get 125
So the value of X is 125cm.

(iii) 7.7% of X is 70 kg

Here, we should find the value of X, so the number X,
As given 7.7/100 × X = 70
7.7/70 ×100=
on solving, we will get 11
So the value of X is 11kg.

(iv) 6% of X in 30 minutes.

Here, we should find the value of X, so the number X,
As given 6/100 × X = 30
30/6 ×100=
on solving, we will get 500
So the value of X is 500 minutes.

2. What will be the number if 3.2% of the number is 800?

Solution:

Let the number X,
As given 3.2% of the number is 800, which means
3.2/100 × X = 800
800/3.2 ×100=
on solving, we will get 25,000
So the number is 25,000.

3. Fill up the below:

(i) 60 is 12% of ________.

(ii) 350 kg is 70% of_________.

(iii) 50 hours is 25 % of ________.

Solution:

(i) 60 is 12% of ________.

Let the number X,
As given 60 is 12%, which means
12/100 × X = 60
60/12 ×100=
on solving, we will get 400
So, 60 is 12% of 400.

(ii) 350 kg is 70% of_________.

Let the number X,
As given 350 is 70%, which means
70/100 × X = 350
350/70 ×100=
on solving, we will get 500
So, 350 kg is 70% of 500 kg.

(iii) 50 hours is 25 % of ________.

Let the number X,
As given 50 is 25%, which means
25/100 × X = 50
50/25 ×100=
on solving, we will get 200
So, 50 hours is 25 % of 200 hours.

4. Solve the number whose 16 2/3% is 250?

Solution:

Let the number be X,
As given 16 2/3% is 250, which means
50/100×3 × X= 250
Therefore X is
250×3 ×100 / 50=
on solving, we will get 1,500.

5. What is the number, if 90 is 18% of a number.

Solution:

Let the number be X,
As given 90 is 18% which means,
18/100 × X = 90
Therefore X is
90×100 / 90 =
on solving, we will get 500.
So the number is 500.

6. Solve the following to find the number.

(i) 90 is 9% of which number

(ii) 6 is 10% of which number

(iii) 200 is 20% of which number

Solution: (i) 90 is 9% of which number

Let the number be X,
As given 90 is 9% which means,
9/100 × X = 90
Therefore X is
90/9 × 100 =
on solving, we will get 1000.
So the number is 1000.

(ii) $6 is 10% of which number

Let the number be X,
As given $6 is 10% which means,
10/100 × X = 6
Therefore X is
6/10 × 100 =
on solving, we will get 60.
So the number is 6.

(iii) 200 is 20% of which number

Let the number be X,
As given 200 is 20% which means,
20/100 × X = 200
Therefore X is
200/20 × 100 =
on solving, we will get 1000
So the number is 1000.

7. Mr. Mike bought 5 dozens of eggs from the store, out of that 15% was broken. How many eggs are in a stable condition?

Solution:

The total number of eggs Mike bought are 6 dozens,
As we know 1 dozen= 12, so
5 dozens= 60 eggs,
in that 15% of eggs are broken, which means
15/100 × 60=
on solving, we will get 9.
So, the number of eggs in a stable condition is 51 eggs.