## Worksheet on Ratio and Proportion | Ratio and Proportion Worksheet with Answers

Practicing from Worksheet on Ratio and Proportion helps students to think more of the concept. Solve Ratio and Proportion Question and Answers available to score better grades in the exam. The Questions in this Worksheet are based on Expressing Ratios in their Simplest Form, Simplification of Ratios, Comparison of Ratios, Arranging Ratios in Ascending and Descending Order, Mean Proportional Between Numbers, etc.

Solve as many times as possible in order to be familiar with the types of Ratio and Proportion Questions. Answering the Problems over here helps you get a good grip on the entire concept. In addition, you will learn the tips and tricks on how to solve ratio and proportion problems using different methods.  For better understanding, we even listed solutions for each and every problem making it easier for you to cross-check whether your answers are correct or not.

1. Express each of the following ratios in the simplest form

(a) 5.6 m to 28 cm

(b) 6 hours to a day

(c) 20 liters to 15 liters

(d) 170 : 240

Solution:

(a) 5.6 m to 28 cm

1 m = 100cm

5.6 m = 5.6*100 = 560 cm

Ratio of 5.6m to 20 cm = 560 cm: 20 cm

= 140:5

= 28:1

(b) 6 hours to a day

In one day there are 24 hrs

6 hrs to a day = 6 hrs: 24 hrs

= 1 :4

(c) 20 liters to 15 liters

= 20 liters :15 liters

=  4:3

(d) 170 : 240

= 170/240

= 17/24

Therefore, ratio of 170:240 in its simplified form is 17/24

2. Simplify the following ratios

(a) 1/4 : 1/3 : 1/6
(b) 3.6 : 5.4
(c) 3²/₃ : 4¹/₂

Solution:

(a) 1/4 : 1/3 : 1/6

LCM of 4, 3, 6 is 12

Expressing them in terms of a least common factor we have

1/4 = 3*3/4*3 = 9/12

1/3 = 1*4/3*4 = 4/12

1/6 = 1*2/6*2 = 2/12

Therefore 1/4:1/3:1/6 in simplified form is 9:4:2

(b) 3.6 : 5.4

Simplifying it we get the ratio as under

Dividing with GCD(3.6, 5.4) i.e. 0.9 we get the simplified form

= (3.6/0.9):(5.4/0.9)

= 4:6

(c) 3²/₃ : 4¹/₂

= 11/3:9/2

LCM of (3, 2) is 6

Expressing the given ratio in terms of LCM we get the equation as follows

11/3 = 11*2/3*2 = 22/6

9/2 = 9*3/2*3 = 27/6

Therefore, ratio 3²/₃ : 4¹/₂ in simplified form is 22:27

3. Compare the following ratios

(a) 5 : 2 and 4 : 3
(b) 1/3 : 1/5 and 1/5 ∶ 1/6

Solution:

(a) 5 : 2 and 4 : 3

Express the given ratio as fraction we get

5:2 = 5/2

4:3 = 4/3

Find the LCM(2, 3) i.e. 6

Making the denominator equal to 6 we get

5/2 = 5*3/2*3 = 15/6

4/3 = 4*2/3*2 = 8/6

5:2 > 4:3

(b) 1/3: 1/5 and 1/5 ∶ 1/6

1/3:1/5

Finding LCM of 3, 5 we get the LCM as 15

Expressing the ratios given in terms of the LCM as a common denominator

1/3 = 1*5/3*5

= 5/15

1/5 = 1*3/5*3 = 3/15

thus it becomes 5:3

1/5 ∶ 1/6

Finding LCM of 5, 6 we get the LCM as 30

Expressing the ratios given in terms of the LCM as Common Denominator

1/5 = 1*6/5*6 = 6/30

1/6 = 1*5/6*5 = 5/30

Therefore, it becomes 6:5

Therefore, 1/3: 1/5 < 1/5 ∶ 1/6

4. In the ratio 3 : 5, the consequent is 20. Find the antecedent?

Solution:

Let the Antecedent and Consequent be 3x and 5x

We know Consequent = 20

5x =20

x= 20/5

= 4

Antecedent = 3x

= 3*4

= 12

Therefore, Antecedent is 12.

5. Divide 2000 among A, B, C in the ratio 2 : 3 : 5?

Solution:

Let the numbers be 2x, 3x, 5x

Sum = 2000

2x+3x+5x = 2000

10x = 2000

x = 2000/10

x = 200

Since the sum is to be split among A, B, C in the ratio of 2:3:5

we get A’s Share = 2x

B’s Share = 3x

C’s Share = 5x

A’s Share = 2*200

= 400

B’s Share = 3*200

= 600

C’s Share = 5*200

= 1000

Therefore, A, B, C’s Share in the amount of 2000 are 400, 600, 1000 respectively.

6. Determine whether the ratios form a Proportion or not

(a) 50 cm : 1 m = \$80 : \$160

(b) 200 ml : 2.5 l = \$4 : \$20

Solution:

(a) 50 cm : 1 m = \$80 : \$160

50 cm: 1 m

We know 1m = 100 cm

= 50 cm: 100 cm

= 1:2

\$80 : \$160

= 1:2

Since both the ratios are equal they are said to be in Proportion

(b)200 ml : 2.5 l = \$4 : \$20

1 liter = 1000 ml

2.5 l = 2.5*1000

= 2500

200 ml: 2500 ml

= 2:25

\$4:\$20

= 1:5

Since both the ratios aren’t equal given values doesn’t form a Proportion.

7. Find the value of x in each of the following

(a) 4, 5, x, 48

(b) 7, 21, 30, x

(c) x, 28, 24, 4

Solution:

(a) 4, 5, x, 48

We know Product of Means = Product of Extremes

4*48 = 5*x

5x = 192

x = 192/5

(b) 7, 21, 30, x

We know Product of Means = Product of Extremes

7*x = 21*30

x = (21*30)/7

= 90

(c) x, 28, 24, 4

We know Product of Means = Product of Extremes

x*4 = 28*24

x = (28*24)/4

= 168

8. Find the fourth proportional to 54, 27, 18, x

Solution:

Product of Extremes = Product of Means

54*x = 27*18

x = (27*18)/54

= 9

9. Find the third proportional to

(a) 9, 6, x

(b) 6, 12, x

Solution:

To find third proportional we write the expression as

9:6 = 6:x

9*x = 6*6

x = 36/9

= 4

(b) 6, 12, x

6:12 = 12:x

6*x = 12*12

x = 144/6

x= 24

10. Find the mean proportional between

(a)  5 and 20

(b) 1.6 and 0.4

Solution:

Mean Proportional between two numbers is defined as the square root of the product of two numbers

(a)  5 and 20

= √(5*20)

=√100

= 10

Mean Proportional of 5 and 20 is 10

(b) 1.6 and 0.4

Mean Proportional between two numbers is defined as the square root of the product of two numbers

= √(1.6*0.4)

= v6.4

= 0.8

Mean Proportional of 1.6 and 0.4 is 0.8

## Free Printable Percentage Worksheets | Percentages Word Problems Worksheets for Practice

Percentage is a concept that children often difficulty with while solving related problems. There are several areas in percentages that you need to master in order to get grip on the concept. Our Percentage Worksheets include finding Percentage of a Number, Calculating Percentage Increase, Decrease, changing decimals to and from percents, etc. You will learn percentage is nothing but a fraction over 100. Learn useful tricks, converting between fractions to percentages, percentages, and parts of a whole expressed as a percent value.

Solve the Problems in the Percentage Worksheets with Solutions and cross-check where you went wrong. You will no longer feel the concept of percentage difficult once you start practicing these plethora of percent worksheets regularly. In fact, you can find different methods of solving the percentage related problems in no time along with a clear and straight forward description.

### Quick Links for Percentage Concepts

Below is the list of Percentage Worksheets available for several underlying concepts. In order to access them, you just need to click on the quick links available and solve the related problems easily. Worksheets on Percentages will make students of different grades familiar with various concepts of Percentages such as Percentage Increase, Percentage Decrease, Conversion from Percentage to Decimal, Fraction, Ratio, and Vice Versa. Percentage Worksheets are free to download, easy to use, and flexible.

### Final Words

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## Worksheet on Probability | Free Printable Probability Worksheets to Practice

Are you looking for help on the concepts of Probability? Don’t Panic as we have curated the Probability Worksheets with Solutions explaining in detail. Utilize the Worksheet on Probability during your practice sessions and test your knowledge of the concept. Firstly, attempt the Probability Questions in our Worksheets on your own and then cross-check your Answers with the Solutions provided. With consistent practice, you can score better grades in your exams.

Worksheets for Probability can be great for learning and practicing the concept. Students of different Grades can utilize these Practice Sheet for Probability and get acquainted with various model questions. Probability Worksheets include concepts like Probability Theory, Applications of Probability, Probability Statistics, etc. Solve more Problems from this Worksheet and attempt the exam with confidence.

1. A coin is tossed 110 times and the tail is obtained 60 times. Now, if a coin is tossed at random, what is the probability of getting a tail?

Solution:

Probability of an Event to happen = No. of Favourable Outcomes/ Total Number of Outcomes

Probability of getting tail when tossed a coin = 60/110

= 6/11

Therefore, the probability of getting tails is 6/11 when tossed a coin.

2. A coin is tossed 200 times and heads are obtained 120 times. Now, if a coin is tossed at random, what is the probability of getting a head?

Solution:

Probability of an Event to happen = No. of Favourable Outcomes/ Total Number of Outcomes

Probability of getting a head = 120/200

= 12/20

= 3/5

Therefore, the probability of getting a head is 3/5.

3. In 120 throws of a dice, 4 is obtained 42 times. In a random throw of a dice, what is the probability of getting 4?

Solution:

Probability of an Event to happen = No. of Favourable Outcomes/ Total Number of Outcomes

Probability of getting 4 = 42/120

= 21/60

= 7/20

The probability of getting 4 is 7/20.

4. What is the Probability of showing neither head nor tail when a coin is tossed?

Solution:

When a coin is tossed the only possible outcomes are head and tail i.e. 2

Probability of neither head nor tail = 0/2

= 0

Therefore, the Probability of showing neither head nor tail is 0.

5. In 2005, there was a survey of 100 people, it was found that 68 like orange juice while 32 dislike it. From these people, one is chosen at random. What is the probability that the chosen people dislike orange juice?

Solution:

Probability of people disliking orange juice = number of people disliking orange juice/total number of people

= 32/100

= 8/25

Therefore, the Probability of chosen people disliking orange juice is 8/25.

6. In a box there are 20 non-defective and some defective bulbs. If the probability that a bulb selected at random from the box to be defective is 3/4 then find the number of defective bulbs?

Solution:

Let the number of defective bulbs be x

Therefore the total number of bulbs = 20+x

Given Probability of Defective Bulbs = 3/4

x/(20+x) = 3/4

4x = 3(20+x)

4x = 60+3x

4x-3x = 60

x = 60

Therefore, the number of defective bulbs is 60.

7. A bag contains 7 white balls and some black balls. If the probability of drawing a black ball from the bag is thrice the probability of drawing a white ball then find the number of black balls?

Solution:

Let the number of black balls be n

Given Number of White Balls = 7

Total Number of Balls = 7+n

Probability of Drawing Black Balls = n/7+n

Probability of Drawing White Balls = 7/7+n

Given Condition is Probability of Drawing Black Ball = 3(Probability of Drawing White Ball)

n/(7+n) = 3(7/(7+n))

n/7+n = 21/7+n

n = 21

Therefore, the number of black balls is 21.

8. A bag contains 7 red balls, 5 green balls, and some white balls. If the probability of not drawing a white ball in one draw be 2/3 then find the number of white balls?

Solution:

Let the number of white balls be n

Total number of balls in the bag = 7+5+n

= 12+n

Probability of drawing red ball = 7/12+n

Probability of drawing green ball = 5/12+n

Probability of drawing white ball = n/12+n

Given Probability of not drawing a white ball = 2/3

Thus, the probability of drawing a white ball = 1- 2/3

= 1/3

Therefore, n/12+n =1/3

solving this equation we get the value of n

12+n = 3n

12 = 2n

n = 6

Therefore, the number of white balls is 6.

9. One card is drawn at random from a well-shuffled deck of 52 cards. Find the probability that the card is drawn is either a red card or king?

Solution:

Total Number of Cards = 52

Number of Cards = 26

No. of Kings in Red Cards = 2

Favorable Outcomes for either red card or king = 26+2

Probability of Red Card or King = Favorable Outcomes/Total number of Cards

= 28/52

= 7/13

The probability that the card drawn is red or king is 7/13.

10. A die is thrown once, find the probability of getting an odd number and a multiple of 3?

Solution:

Given a die is thrown once

Probability of getting an odd number = {1, 3, 5}

Probability of getting an odd number or multiple of 3 is = {1, 3, 5} = 3

Required Probability = 3/6

= 1/2

## Worksheet on Inverse Variation | Inverse Variation Worksheet with Answers

Worksheet on Inverse Variation includes various questions to practice. Learn how to Solve Inverse Variation Problems by checking out the Sample Problems covering different models. Practice using the Inverse Variation Worksheet as much as possible and get a good grip on the concept. Test your preparation standard using the Worksheet for Inverse Variation and plan your preparation accordingly. Improve your scores in the exam by consistently practicing from the Word Problems on Inverse Variation.

1. If 30 men can reap a field in 12 days, in how many days can 8 men reap the same field?

Solution:

30 men – 12 days

8 men – ?

Since it is an inverse variation we need to apply the straight multiplication

30*12 = 8*m

m = (30*12)/8

= 45 days

Therefore, 8 men can reap the same field in 45 days.

2. 10 men can dig a pond in 6 days. How many men can dig it in 5 days?

Solution:

10 men – 6 days

? – 5 days

Since it is inverse variation apply the straight multiplication

10*6 = m*5

60/5 = m

m = 12

Therefore, 12 men can dig the pond in 5 days.

3. A truck covers a particular distance in 2 hours with a speed of 40 miles per hour. If the speed is increased by 10 miles per hour, find the time taken by the truck to cover the same distance?

Solution:

This is the case of Inverse Variation

Because More Speed  Less Time

Given Speed is 40 miles if it is increased by 10 miles then Speed is 50 miles

No. of Hours   Speed

2                        40

m                       50

2*40 = m*50

80 =50m

80/50 = m

m = 1.6 hours

The truck takes 1.6 hours to cover the same distance.

4. If y varies inversely as x, and y = 16 when x = 3, find x when y = 12?

Solution:

let y = k/x

16 = k/3

Thus, k = 48

y = k/x

12 = 48/x

x = 48/12

x = 4

Therefore, x = 4.

5. The frequency of a vibrating guitar string varies inversely with its length. Suppose a guitar string 0.80 meters long vibrates 4 times per second. What frequency would a string 0.5 meters long have?

Solution:

We know y = k/x

from the given data we can rearrange the equation as

f = k/l

4 = k/0.80

k = 0.80*4

=3.2

f = 3.2/l

= 3.2/0.5

= 6.4 times per second.

6. Amar takes 15 days to reduce 20 kilograms of his weight by doing 20 minutes of exercise per day. If he does exercise for 1 hour per day, how many days will he take to reduce the same weight?

Solution:

More minutes Per Day = Less Days to Reduce Weight

Let m be the number of days to reduce weight

No. of Days   No. of Minutes

15                   20

m                    60

Since it is Inverse Variation go with straightforward multiplication

15*20  = m*60

m = (15*20)/60

= 5 days

Therefore, Amar takes 5 days to reduce weight if he does 1 hour of exercise per day.

7. 12 taps having the same rate of flow, fill a tank in 24 minutes. If three taps go out of order, how long will the remaining taps take to fill the tank?

Solution:

12 taps – 24 minutes

since three taps went out of order number of taps = 12 -3 =9

12 taps – 24 minutes

9 taps – ?

Therefore, applying the inverse variation shortcut we have the equation

12*24 = 9*m

(12*24)/9 = m

m = 32

Therefore, 9 taps take 32 minutes to fill the tank.

8. 60 patients in a hospital consume 1200 liters of milk in 30 days. At the same rate, how many patients will consume 1440 liters in 28 days?

Solution:

Given, 60 patients consume 1200 lt of milk in 30 days and say x patients consume 1440 lt of milk in 28 days.

60*30/1200 = x*28/1440

1800/1200 = 28x/1440

18/12 = 28x/1440

3/2 = 28x/1440

3*1440/2*28 = x

x = 77 patients(Approx)

Therefore, 77 Patients can consume 1440 liters of milk in 28 days.

## Worksheet on Direct Variation | Word Problems on Direct Variation with Solutions

Worksheet on Direct Variation includes different questions to practice. Learn how to solve Word Problems on Direct Variation by referring to the Solved Examples available. We have provided Step by Step Solutions for all the Problems explained in the Direct Variation Worksheet. Practice using them and learn different methods used to approach. Assess your strengths and weaknesses using the Worksheet for Direct Variation and plan your preparation accordingly.

1. If 10 oranges cost \$ 14, how many oranges can be bought for \$ 32?

Solution:

Given 10 oranges = \$14

? = \$32

Let the number of oranges that can be bought using the \$32 is x

rearranging we get the value of x as

x*14 = 10*32

x = 320/14

x = 22 Oranges(Approx)

Therefore, 22 Oranges can be bought for \$32.

Solution:

From the given data

Let the cost of 20 basketballs be m

Cross multiplying we get

m = (20*1140)/70

= \$325.71

3. 7 men can complete a work in 42 days. In how many days will 5 men finish the same work?

Solution:

From given data

Men  Days

7        42

5        ?

Cross multiply to get the no. of days 5 men finish the work

no. of days = (5*42)/7

= 30

Therefore, 5 men take 30 days to finish the work.

4. If a car covers 90 km in 6 liters of petrol, how much distance will it cover in 24 liters of petrol?

Solution:

90 Km – 6 Liters

? – 24 Liters

distance be d

cross multiply to obtain the value of d we have

d = (90*24)/6

= 360 Km

Car Covers 360 Km in 24 Liters of Petrol.

5. If 3 Persons weave 210 Shawls? How many shawls will be Weaven by 7 Persons?

Solution:

3 Persons – 210 Shawls

7 Persons – ?

Cross multiplying we get

No. of Shawls = (210*7)/3

= 490

7 Persons can weave 490 Shawls.

6. In 24 Weeks, Michael raised \$240,000 for cancer research. How much money will he raise 36 weeks?

Solution:

24 Weeks – \$2,40,000

36 Weeks – ?

Money raised by Michael = (2,40,000*36)/24

= \$3,60,000

Michael raises \$3,60,000 in 36 Weeks.

7. If 5 men can paint a house in 12 hours, how many men will be able to paint it in 36 hours?

Solution:

5 men – 12 hours

? – 36 hours

No. of Men = (5*36)/12

= 15

15 Men can Paint a House in 36 Hours.

8. If the cost of transporting 60 kg of goods for 100 km is Rs 120, what will be the cost of transporting 160 kg of goods for 200 km?

Solution:

The cost of transporting 60kg of goods for 100 km is 120

cost of 1 kg for 1 km = 120/60*100 = Rs. 1/50

cost of 160kg for 200 km = 1/50*160*200

= Rs. 640

Cost of transporting 160kg of goods for 200km is Rs. 640

## Ratio and Proportion Worksheets with Answers | Worksheet on Ratio and Proportion

Ratio and Proportion Worksheet available here makes it easy for you to grasp the related concepts. Questions covered in the Worksheet on Ratio and Proportion includes Simplifying Ratios, Arranging Ratios in Ascending or Descending Order, Expressing Ratio in Simplest Form, etc. Practice as many times as possible using the Ratio and Proportion Worksheets and test your preparation standard. To make it convenient for you we have provided detailed solutions for all the Problems provided.

1. Express each of the following Ratios in Simplest Form?

a) 2.4 m to 20 cm

b) 4 hours to half day

c) 10 liters to 7 liters

d)144 to 108

Solution:

a) 2.4 m to 20 cm

We know 1m = 100 cm

2.4 m = 240 cm

express it in the form of Ratio

= 240: 20

Divide the ratios with their GCF to obtain the simplest form

GCF(240, 20) = 20

Dividing with GCF we obtain the simplified ratio as 12:1

Therefore, 2.4 m to 20 cm expressed in simplest form is 12:1

b) 4 hours to half day

We know half-day has 12 hours

Expressing 4 hours to half-day we have the ratio as 4:12

Divide the ratio with their GCF(4, 12) i.e. 4

= 1:3

4 hours to half-day expressed in simplest form is 1:3

c) 10 liters to 7 liters

= 10:7

Given Ratio is in its simplest form since their GCF is 1 and it can’t be simplified further.

d) 144 to 108

= 144:108

To obtain the simplified form of the given ratio Divide it with their GCF

GCF(144, 108) = 36

= 4:3

2. Simplify the following ratios

(a) 1/3: 1/5: 1/8

(b) 5.4: 6.3

Solution:

(a) 1/3: 1/5: 1/8

Find the LCM of the Denominators

LCM(3, 5, 8) = 120

Express the given ratios with a common denominator

= 40/120: 24/120: 15/120

= 40: 24: 15

Therefore, 1/3: 1/5: 1/8 in simplest form is 40:24:15

(b) 5.4: 6.3

Convert the decimals to integers firstly.

Multiply with 10 i.e. 5.4*10 = 54

6.3*10 = 63

Expressing the integers in terms of ratio we have 54:63

GCF(54, 63) =9

Divide the ratio with GCF to get the simplified form

= 6: 7

Therefore, 5.4:6.3 in simplified form is 6:7

3. Determine whether the following Ratios form a Proportion or not

a) 4:5 and 8:10

b) 6:7 and 5:3

Solution:

a) 4:5 and 8:10

4:5 = 4/5

8:10 = 8/10

= 4/5

Since both the ratios are in the same proportion they are said to be in proportion

Therefore, 4:5 and 8:10 are equal.

b)6:7 and 5:3

6:7 = 6/7

5:3 = 5/3

Since both proportions aren’t equal they are not in proportion.

4. Compare Ratio 5: 10 and 3: 6

Solution:

5:10 = 5/10

3:6 = 3/6

LCM of 10, 6 is 30

Expressing given ratios as Equivalent Ratios we have

5/10 = 5*3/10*3 = 15/30

3/6 = 3*5/6*5 = 15/30

Since both the ratio are having same fractions they are equal.

5. Find the Mean Proportional between 9 and 16?

Solution:

Let the Mean Proportional be x

x2= 9*16

x2 = 144
x = 12

6. If 10, x, x, 10 are in proportion, then find the value of x?

Solution:

Product of Means= Product of Extremes

x*x = 10*10

x2 = 100
x= 10

7. From the total strength of the class, if the no of boys in the class is 10 and no of girls in the class is 20, then find the ratio between girls and boys?

Solution:

Given Strength of Boys = 10

Strength of Girls = 20

The ratio of Girls and Boys = 20:10

Simplifying the ratio we get 2:1

8. Suppose 2 numbers are in the ratio 4:3. If the sum of two numbers is 70. Find the numbers?

Solution:

Given Ratio of Two Numbers is 4:3

As per the given data

4x+3x = 70

7x = 70

x = 10

Numbers are 4x, 3x

4x = 4*10 = 40

3x = 3*10 = 30

## List of Essay Topics for K-12 Students | English Essay Writing Topics for Thoughtful Learning

English Essays can be way more formulaic than you think. Essays are quite common in your elementary school or mid-school as a part of your curriculum. An Essay is a Short Piece of Information to express your views on a particular topic. To help you out we have listed the Most Common Essay Topics for Students of Different Grades all in One Place. You name it and we have it! Make the most out of the Essay Writing Topics and Ideas provided and become a champ in your competitions or speeches.

## Essay Writing Topics & Ideas for Grades Kindergarten, 1, 2, 3, 4,5, 6, 7,8,9, 10, 11, 12 & Competitive Exams

Keeping in mind the Students Point of View we have jotted the frequently asked Essay Topics from Different Categories. We have a large collection of Essay Topics right from Kids to College Students. You can use these Sample Essays as a part of the preparation for Competitive Tests or School Speeches. Read and Practice the Long & Short Essays of different word length as per your requirement and bring out the imaginative side in you.

### How to Write an Essay?

It’s not as simple as you sit and write down an Essay. A Lot more planning goes into writing an essay successfully. If you are struggling with and want to improve your skills refer to the tips for essay writing. They are as under

• Decide what kind of essay you want to write
• Brainstorm the Topic and Research on it.
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• Develop a Thesis Statement and Outline your Essay.
• Write down the Essay and Proof Read for any Grammar Mistakes.

If you follow the aforementioned steps you can always write a Clear and Simple Essay. Use the Tips for Writing Essays and get yourself right on the path of a Well Written Essay.

### Essay Structure | How to Structure an Essay?

An essay needs to be written in the following manner and each sentence needs to be logical and there has to be connectivity between the previous statement.

1. Introduction
2. Main Body
3. Conclusion

Introduction: Introduction plays an important role to grab the user’s attention as well to inform them of what will be covered. Provide background information on the topic supporting your argument. After that, Formulate a Thesis Statement.

Main Body: In the Body, you can make arguments supporting your thesis statement and develop ideas accordingly. Interpret and analyze the information you have gathered from various sources and frame sentences on your own. The Length of the Body Text depends on the Type of Essay you are writing. Give your essay a clear structure and try to use paragraphs.

Conclusion: Conclusion will be the Final Paragraph in the Essay. It shouldn’t take too much text in your essay. A Great Conclusion is necessary to create a strong impact on the user.

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1. Where do I get Simple & Creative Essay Writing Topics for K-12 Grades Students?

You can get Simple & Creative Essay Writing Topics for K-12 Grades Students on our page.

2. What are some of the General Essay Writing Tips?

Pick up a topic and prepare an overview of your ideas. Write an effective Introduction followed by Thesis Statement. After that write the Body and Conclusion supporting your views.

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## Worksheet on Functions or Mapping | Functions Worksheet with Answers

Those seeking help on Functions or Mapping can make the most out of the Worksheet on Functions or Mapping. Most of the questions prevailing here are based on domain, codomain, and range of a function, identifying functions from Mapping Diagrams, determining whether a set of ordered pairs form a function or not, etc. Attempt all the questions in the Identifying Functions from Mappin Diagrams Worksheets and get a better idea of the concepts within.

For the sake of your convenience, we even listed the step by step solutions to all the sample provided. Solve the  Mapping and Functions Problems on your own and verify with the Answers Provided and test your preparation level.

1. State whether each set of ordered pair represent a function or not?

{(1, 9), (-4, –6), (-6, 5), (3, 8), (7, –16), (–10, 7)}

Solution:

Given Set of Ordered Pairs {(1, 9), (-4, –6), (-6, 5), (3, 8), (7, –16), (–10, 7)}

It is a function since any of the first components aren’t repeated and have unique images in the other set.

2. State whether each set of ordered pair represent a function or not?

{(-4, 3), (5, -7), (10, 5), (9, 6), (6, -3), (5, 8), (1, 3)}

Solution:

Given Set of Ordered Pairs {(-4, 3), (5, -7), (10, 5), (9, 6), (6, -3), (5, 8), (1, 3)}

It is not function since the first components are repeated.

3. State whether the following relation represents a function or not?

Solution:

The above arrow diagram represents a function since each element in the set is associated with one element in the other set. Thus it represents a function.

4. A function is given by f(x) = 3x+3. Find the values of

(a) f(1)

(b) f(0)

(c) f(-2)

Solution:

Given f(x) = 3x+3

To find f(1) substitute 1 in place of x in the given function

f(1) = 3*1+3 = 3+3 = 6

To find f(0) substitute 0 in place of x in the given function

f(0) = 3*0+3 = 0+3 = 3

To find f(-2) substitute -2 in place of x in the given function

f(-2) = 3*(-2)+3 = -6+3 = -3

5. Determine whether each set of ordered pairs on the graph represents a function or not?

Solution:

Ordered Pairs = {(-2, 6) (2, 3) (4, -12) (8, 6) (10, 15) (12, -6) (16, 9)}

The above graph represents a function since it has first components unique.

6. Determine whether the following Mapping Diagram represents a function or not?

Solution:

The above mapping diagram represents a function since each element in the set is mapped with only one element in the other set.

7. Which of the following represents mapping?

a) {(3, 2); (7, 3); (6, 5); (8, 7)}

b) {(4, 8); (5, 12); (4, 14)}

Solution:

a) {(3, 2); (7, 3); (6, 5); (8, 7)}

The Set of Ordered Pairs represent Mapping since all of them have unique images.

b) {(4, 8); (5, 12); (4, 14)}

Set of Ordered Pairs doesn’t represent Mapping Since doesn’t have unique images and the first components are repeated.

8. Determine whether the relationship given in the Mapping Diagram is a function or not?

Solution:

Since 4 is mapped with more than one element as output i.e. 0, 9 the relationship given in the above mapping diagram is not a function.

9. Draw Mapping Diagram for the Relation R = {(1, 7) (2, 8) (8, 3)}?

Solution:

Place all the domain values in the left column and write the range value in the right column and draw arrows between them indicating the relationship.

## Worksheet on Math Relation | Math Relation Questions with Answers

Students can practice various questions from Relation to get grip on the concepts. This Worksheet on Math Relation covers various topics like Mapping for Relations, Representing Relations using a set of ordered pairs, arrow diagrams, etc. Solve the Ample Problems provided in the Math Relation Worksheet and get a better idea of the concepts within it. Practice the problems on your own and cross-check your solutions with the step by step solutions provided to understand where you went wrong.

1. If A= {3, 4, 5, 6, 7, 8}, B = {9, 10, 11, 12}. What is the number of elements in AxB?

Solution:

Given n(A) = 6

n(B) = 4

n(AxB) = 24

2. Determine the domain and range of the given function

{11, -5), (8, -3), (5, 2), (7, 6), (6, -10)}

Range =_____

Domain = _____

Solution:

Given Function is {11, -5), (8, -3), (5, 2), (7, 6), (6, -10)}

Domain is the first component of the ordered pairs and second component in the ordered pairs is the Range.

Domain = {11, 8, 5, 7, 6}

Range = {-5, -3, 2, 6, -10}

3. Represent Relation {(-3, 3) (0, -5) (2, 0) (6, 0)} using an Arrow Diagram?

Solution:

Take the Domain Values on the left column and Range Values in the Right Column and mark the relation between them using arrows.

4. Let A = {10, 15, 18, 21, 24} B = { 3, 5, 6, 7} be two sets and let R be a relation from A to B ‘is multiple of’. Represent in the Set of Ordered Pairs?

Solution:

R = {(10, 5) (15, 3) (18, 3) (18, 6) (21, 3) (21, 7) (24, 6)}

5. Given the relation R = {(3,4), (7,-1), (x,7), (-3,-4)}. Which of the following values for x will make relation R a function?
(a) 8
(b) 7
(c) -3
(d) 3

Solution:

(a) 8

To make relation R a Function we need to have a value that doesn’t repeat with the first components of the ordered pairs. Therefore, among all the options 8 is the value that is unique.

6. State whether the following statements are true or false

(i) All Functions are Relations

(ii) All Relations are Functions

(iii) A relation is a set of input and output values that are related in some way

Solution:

(i) True

(ii) False

(iii) True

7. Express the Relation as a Set of Ordered Pairs?

Solution:

Expressing the above Relation as a Set of Ordered Pairs we get

R = {(-4, 0) (-4, 9) (-4, 11)}

8. If A = {u, v, w} and B = {x, y}, find A × B and B × A. Check whether the two products equal or not?

Solution:

Given A = {u, v, w} and B = {x, y}

AxB = {(u,x) (u, y) (v,x) (v,y) (w, x) (w, y)}

BxA = {(x,u) (y, u) (x, v) (y, v) (x, w) (y, w)}

AxB and BxA don’t have the same ordered pairs.

Therefore,  AxB ≠ BxA.

9. If (u/2 + 1, v+2) = (1, 2/5), find the values of u and v?

Solution:

Given (u/2 + 3, v+2) = (1, 2/5)

As per the Equality of Ordered Pairs we have

u/2+3 = 1

u/2 = 1-3

u/2 = -2

u = -2*2

u = -4

v+2 = 2/5

v = 2/5-2

v =(2-4) /5

v = -2/5

Therefore, values of u and v are -4, -2/5.

10. Range is the Set of _____ when it comes to Relations in Math?

Solution:

The range is the set of y-values when it comes to Relations in Math.

## Relations and Mapping Worksheets | Worksheet on Relations and Functions with Solutions

If you need help on Relations and Mapping solve different questions from Relations and Mapping Worksheets. Try to solve various questions on Relations and Mapping and get the concepts underlying easily. The following sections include questions on Ordered Pairs, Cartesian Product of Two Sets, Identifying whether a Mapping Diagram is function or not, Representation of Math Relation, Domain, and Range, etc.

The Worksheets on Relations and Mapping include both complex and sample problems. Students can practice them and get step by step solutions to several example problems. The worksheet over here explains how to interpret and present relations as graphs, ordered pairs, arrow diagrams, etc.

1. Express the Relation as a Set of Ordered Pairs?

Solution:

Ordered Pairs for the given relation

{(-2,2), (-2, 6), (-1,1) (0, 2) (4, 6)}

2. Function g(x) = 6x2+2x-2 find the value of g(-1)?

Solution:

g(x) = 6x2+2x-2

g(-1) = 6.(-1)2+2(-1)-2

= 6.1-2-2

= 6-4

= 2

3. Function f(x) is given by x3. Find the value of f(2)-f(1)/2-1?

Solution:

f(x) = x3

f(2) = 23
= 8
f(1) = 13
= 1
(f(2)-f(1))/2-1 = (8-1)/2-1

= 7/1

= 7

4. If If (4x + 2, 2y – 3) = (4, 3) find the values of x, y?

Solution:

Given (4x + 2, 2y – 3) = (4, 3)

As per equality of ordered pairs the first components and second components needs to be equal.

4x+2 = 4,  2y-3 = 3

4x= 4-2,  2y = 3+3

4x = 2,    2y = 6

x = 2/4,    y = 6/2

x = 1/2,   y = 3

Therefore, values of x, y are 1/2 and 3.

5. From the set of Ordered Pairs {(2, 8); (3, 9); (3, 5); (1, 7)} find the Domain and Range?

Solution:

From the set of ordered pairs given duplicates are not allowed for domain and range.

Domain = {2, 3, 1}

Range = {8, 9, 5, 7}

6. Following Figure Shows a Relationship from Set A to B. Write the Relation in Roster Form and also provide the Domain and Range?

Solution:

From the above arrow diagram, we can write the relation from Set A to Set B in Roster Form as

R = {(-2, 4) (2, 4) (4, 16) (5, 25) (6, 36)}

Domain = { -2, 2, 4, 5, 6}

Range = {4, 16, 25, 36}

Repetitions are not allowed in the domain and range.

7. For the Relation given in Tabular Form draw the mapping diagram?

Solution:

The above tabular form relation can be expressed in Mapping as such

8. Let A = {3, 4, 5, 6} B = {x, y, z} find the Cartesian Product of AxB?

Solution:

Given A = {3, 4, 5, 6} B = {x, y, z}

AxB = {(3,x) (3, y) (3, z) (4, x) (4, y) (4, z) (5, x) (5, y) (5, z) (6, x) (6, y) (6, z)}

9. Write the Domain and Range for the following Relations?

(a) R₁ = {(6, 2); (6, 5); (3, 5); (0, 8); (7, 3)}
(b) R₂ = {(x, 2); (y, 3); (z, 2); (u, 6)}

Solution:

The domain is the first component of the ordered pairs and range is the second component of the ordered pairs. Repetitions are not allowed in both Domain and Range.

(a) R₁ = {(6, 2); (6, 5); (3, 5); (0, 8); (7, 3)}

Domain = { 6, 3, 0, 7}

Range = { 2, 5, 8, 3}

(b) R₂ = {(x, 2); (y, 3); (z, 2); (u, 6)}

Domain = { x, y, z, u}

Range = { 2, 3, 6}

10. If AxB = {(x, 3); (x, 4); (x, 5); (y, 3); (y, 4); (y, 5)}. Find BxA?

Solution:

AxB = {(x, 3); (x, 4); (x, 5); (y, 3); (y, 4); (y, 5)}

BxA = {(3, x) (4, x) (5, x) (3, y) (4, y) (5, y)}