Raju

Worksheet on Exponents | Grade 8 Powers and Exponents Worksheet

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Exponents Worksheets prevailing makes you familiar with the exponential terms, positive and negative exponents, laws of exponents, radical exponent, etc. Practice different questions to write larger numbers in the short form so that it’s convenient to read and compare. Solve Questions of Exponents provided with Solutions here and understand the approach used to solve various problems. Firstly, try to solve the Problems of Exponents on your own and assess your preparation standards.

1. Evaluate the following

(i) 3-3

(ii) (1/3)-4

(iii) (2/3)-2

(iv) (-5)-4

Solution:

(i) 3-3

= (1/3)3

= 1*1*1/3*3*3

= 1/27

(ii) (1/3)-4

= (3)4

= 3*3*3*3

= 81

(iii) (2/3)-2

= (3/2)2

= 3*3/2*2

= 9/4

(iv) (-5)-4

= (1/-5)4

= 1*1*1*1/-5*-5*-5*-5

= 1/ 625

2. Simplify the following

(i) (5/3)2 × (4/2)2

(ii) (1/6)6 × (3/4)-4

(iii) (1/3)-2× (4/3)-3

(iv) (3/8)-3 × (2/4)4

Solution:

(i) (5/3)2 × (4/2)2

= 25/9*16/4

= 25*16/9*4

= 400/36

= 100/9
(ii) (1/6)2 × (3/4)-4

= (1/6)2 * (4/3)4

= 1/36*256/81

= 1*256/36*81

= 256/2916

= 64/729
(iii) (1/3)-2× (4/3)-3

= (3/1)2*(3/4)3

= 9/1*27/64

= 9*27/1*64

= 243/64

3. Evaluate

(i) (5/3)-2 × (4/5)-3 × (2/5)0

(ii) (-2/5)-4 × ( -3/5)2

Solution:

(i) (5/3)-2 × (4/5)-3 × (2/5)0

Any number raised to power 0 is 1.

= (3/5)2*(5/4)3*1

= 9/25*125/64*1

= (9*125*1)/25*64*1

= 1125/1600

= 45/64

(ii) (-2/5)-4 × ( -3/5)2

= (5/-2)4*( -3/5)2

= 625/16*9/25

= 625*9/16*25

= 5625/400

= 225/16

4. Evaluate

(i) {(-1/3)2}-3

(ii) [{(-4/3)2}-3]-1

(iii) {(3/2)-2}1

Solution:

(i) {(-1/3)2}-3

= (-1/3)2*-3

= (-1/3)-6

= (3/-1)-6

= (-3)-6

(ii) [{(-4/3)2}-3]-1

= (-4/3)2*-3*-1
= (-4/3)6

(iii) {(3/2)-2}1

= (3/2)-2
= (2/3)2

5. Simplify the {(1/4)-3 – (1/3)-3} ÷ (1/2)-3

Solution:

= {(1/4)-3 – (1/3)-3} ÷ (1/2)-3

= {(4/1)3 – (3/1)3} ÷(2)3

= {64 – 27} ÷ 8

=37/8

6. Evaluate [6-1 × 4-1]-1 ÷ 3-1]

Solution:

= [ 1/6*1/4] ÷ 1/3]

= [1/24] ÷ 1/3

= 1/24*3/1

= 3/24

= 1/8

7. Find the value of x for which (4/3)-4 × (4/3) -5 = (4/3)3x?

Solution:

(4/3)-4 × (4/3) -5 = (4/3)3x

Since bases are equal we need to add the powers

(4/3)-4-5 = (4/3)3x

(4/3)-9 = (4/3)3x

Equating the terms we can get the value of x as follows

– 9 = 3x

x = -9/3

= -3

8. Evaluate: {(2/3)-1 – (1/2)-1}-1

Solution:

Given {(2/3)-1 – (1/2)-1}-1

= (3/2)1 -(1/2)-1*-1

= 3/2 – 1/2

= 2/2

= 1

9. By what number should (-4)-1 be multiplied so that the product becomes 36-1?

Solution:

(-4)-1*x = 36-1

1/-4*x = 1/36

x = (1/36)/(1/-4)

= 1/36*-4/1

= -4/36

= -1/9

= 9-1

10. If 52x – 1 ÷ 25 = 25, find the value of x?

Solution:

52x – 1 ÷ 25 = 25

52x – 1/25 = 25

52x – 1 = 25*25

52x – 1 = 625

52x – 1 = 54

2x -1 = 4

2x = 4+1

2x = 5

x = 5/2

Objective Questions on Rational Numbers | Rational Numbers Multiple Choice Questions and Answers

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Are you looking for Rational Numbers Multiple Choice Questions? Then you have reached the right destination where you can find Objective Questions on Rational Numbers. Try to solve problems on your own and cross-check the solutions provided. Practice MCQ Questions for Rational Numbers and increase your problem-solving skills. Have a glance at the Rational Numbers Worksheets and clear all your queries on the concepts underlying within it.

1. The sum of the rational numbers -4/19 and -2/57 is _____

(a) -14/57

(b) 5/22

(c) -20/57

(d) 14/27

Solution:

= -4/19+(-2/57)

= (-12-2)/57

= -14/57

2. The Reciprocal of a Positive Rational Numbers is

a) is a positive rational number

(b) is a negative rational number

(c) can be either a positive or a negative rational number

(d) does not exist

Solution:

a) is a positive rational number

3. The Product of Two Rational Numbers is 15/9. If one of the numbers is -3, find the other?

(a) -5/9

(b) 3/12

(c) 12/35

(d) –8/10

Solution:

(a) -5/9

-3*x= 15/9

x = (15/9)/-3/1

= 15/9*1/-3

= 15/-27

= -5/9

4. Fill in the Blanks 4/12 ÷ (_____) = -32/18

(a) -20/32

(b) -11/19

(c) -15/14

(d) -3/16

Solution:

(d) -3/16

(4/12)/x = -32/18

(4/12)/(-32/18)=x

x= 4/12*18/-32

= (4*18)/(12*-32)

= 72/-384

= -3/16

5. Which of the following forms a pair of equivalent rational numbers?

(a) 35/40 and 25/15

(b) -25/50 and 50/-77

(c) -8/16 and -24/48

(d) 9/72 and -3/24

Solution:

(c) -8/16 and -24/48

Reducing the given fractions we get the same rational number therefore, they are Equivalent Rational Numbers.

6. The Value of {-4/12 × 20/-2} is  _____

(a) -7/11

(b) -7/21

(c) -6/12

(d) 10/3

Solution:

(d) 10/3

= -4/12*20/-2

= (-4*20)/(12*-2)

= -80/-24

= 80/24

= 10/3

7. Which of the following rational numbers is in the standard form?

(a) -7/26

(b) -26/52

(c) –12/16

(d) 48/-92

Solution:

(a) -7/26

The above option is said to be in its standard form as it has no other factors in common alongside the denominator is positive.

8. Simplify 2/5 + -3/5 + 8/5 + -11/5?

(a) -1/4

(b) -12/60

(c) -4/5

(d) – 5/30

Solution:

(c) -4/5

= 2/5 + -3/5 + 8/5 + -11/5

= (2-3+8-11)/5

= (10-14)/5

= -4/5

9. Which among the following rational numbers is the greatest?

(a) 2/9

(b) -5/3

(c) -7/10

(d) 11/-22

Solution:

(a) 2/9

Among all the options since 2/9 is positive and the rest are negative numbers, it is greater.

10. What number should be added to 2/8 to get -1/12?

(a) -7/4

(b) -1/3

(c) 13/72

(d) 12/30

Solution:

(b) -1/3

2/8+x = -1/12

x = -1/12-2/8

= (-2-6)/24

= -8/24

= -1/3

Worksheet on Operations on Rational Expressions | Operations with Rational Expressions Worksheets

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Worksheet on Operations on Rational Expressions provided on our page can be a great resource for students. Rational Expressions Operations Worksheet prevailing is quite flexible and free to use. You can simply solve the various questions provided in the Worksheet to be familiar with various operations like Addition, Subtraction, Multiplication, Division, etc. For any other relevant topic worksheets, you can check our collection of Rational Numbers Worksheets and clear your concerns.

1. Simplify the following rational numbers

(i) (15/8 × 3/5) – (4/5 × -10/8) (ii) (-7/4 × 4/3) + (11/2 × 4/6)

Solution:

(i) (15/8 × 3/5) – (4/5 × -10/8)

Given (15/8 × 3/5) – (4/5 × -10/8)

= (15*3/8*5)-(4*-10/5*8)

=(45/40)-(-40/40)

= (45+40)/40

= 85/40

=17/8

(ii) (-7/4 × 4/3) + (11/2 × 4/6)

= (-7*4/4*3)+(11*4/2*6)

= -28/12+44/12

= (-28+44)/12

= 16/12

= 4/3

2. Simplify the following Rational Expressions

(i) (5/2 × 1/5) + (4/3 × 7/2) – (11/8 × 5/3)

(ii) (1/3 × 4/7) – (6/10 × -2/3) + (4/7 × 7/2)

Solution:

(i) (5/2 × 1/5) + (4/3 × 7/2) – (11/8 × 5/3)

= (5*1/2*5)+(4*7/3*2)-(11*5/8*3)

= (5/10)+(28/6)-(55/24)

= 5/10+28/6-55/24

= (5*12+28*20-55*5)/120

= (60+560-275)/120

= 345/120

= 23/8

(ii) (1/3 × 4/7) – (6/10 × -2/3) + (4/7 × 7/2)

= (1*4/3*7)-(6*-2/10*3)+(4*7/7*2)

= 4/21-(-12/30)+(28/14)

= 4/21+12/30+28/14

= (40+84+420)/210

= 544/210

= 272/105

3. Find the value of the following and express in standard form

(i) 4/5 ÷ 16/12

(ii) -5 ÷ (-7/17)

Solution:

4/5 ÷ 16/12

= 4/5*(12/16)

= 4*12/5*16

= 48/80

= 3/5

Since the rational number 3/5 has no other common factors and the denominator is positive. It is said to be in standard form.

-5 ÷ (-7/17)

= -5*17/-7

= -85/-7

= 85/7

85/7 is in standard form as it has no other common factors and the denominator is positive.

4. By what number should we multiply 14/28 to obtain the product 5/7?

Solution:

14/28*x = 5/7

x= (5/7)/(14/28)

= 5/7*28/14

= 10/7

You need to multiply 14/28 with 10/7 to obtain the product 5/7.

5. By what number should we multiply -4/13 so that the product is 24?

Solution:

-4/13*x= 24

x = 24/(-4/13)

= 24*13/-4

= 312/-4

= -78

Multiply -4/13 with -78 to obtain the product 24.

6. Cost of a rope is 5 1/3 m is $ 12 1/4. What is Cost Per Meter?

Solution:

The cost of a rope is 5 1/3 m is $12 1/4

16/3 m = $49/4

1 m =?

Divide 49/4 with 16/3

= (49/4)/(16/3)

= 49/4*3/16

= (49*3)/(4*16)

= 147/64

= 2 19/64

1 meter of rope costs $ 2 19/64.

7. If 14 trousers of equal size can be prepared from 42 meters of cloth, what is the length of the cloth required for each trouser?

Solution:

14 trousers = 42 m

1 trouser = 42/14

= 3m

Therefore, each trouser requires a length of 3m.

8. Divide the sum of 11/5 and -4/7 by the product of -21/7 and 1/-3?

Solution:

Sum = 11/5+(-4/7)

=(77-16)/35

= 61/35

Product = -21/7*1/-3

= = -21/-21

= 1

Dividing the sum with the product of given rational numbers we get

= (61/35)/1

= 61/35.

9. Divide the Sum of 45/11 and 5/3 by their difference?

Solution:

Sum = (45/11+5/3)

= (45*3+5*11)/33

= (135+55)/33

= 190/33

Difference = (45/11 – 5/3)

= (45*3 – 5*11)/33

= (135 -55)/33

= 80/33

= (190/33)/(80/33)

= 190/33*33/80

= 190/80

= 19/8

10.  By what number should -2/3 be multiplied in order to produce 3/4?

Solution:

-2/3*x= 3/4

x= (3/4)/(-2/3)

= 3/4*3/-2

= (3*3)/(4*-2)

= 9/-8

Rational Numbers Worksheets | Practice Worksheets on Rational Numbers

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Most of you might have come across Chapter Rational Numbers while studying the subject. Usually, the word rational conveys logical interpretation followed by a reason. However, when it comes to Maths it is derived from the word Ratio and has a different meaning entirely. To help students prepare effectively we have compiled Rational Numbers Worksheets all in one place.

You can use the Worksheets on Rational Numbers during your practice sessions and test your level of preparation. The Kind of Questions asked in the Worksheets covers various subtopics of Rational Numbers such as Equivalent Rational Numbers, Positive and Negative Rational Numbers, Representing Rational Numbers on the Number Line, etc.

List of Rational Numbers Worksheets to Practice

For a better user experience, we have compiled all of the Worksheets for Rational Numbers in one place. Look no further and begin your practice straight away to score well in your exams. In order to prepare a particular topic, you just need to simply tap on the quick links available to access the corresponding topic worksheet. Solve Problems on your own at first and cross-check the solutions later in order to understand where you went wrong.

Feel free to use our Online Maths Worksheets available on our Site Worksheetsbuddy.com and ace up your preparation level. You need not worry as you can make use of the worksheets categorized to solve problems that you are looking for.

Worksheet on Word Problems on Rational Numbers | Rational Numbers Word Problems Worksheet

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Are you looking everywhere to find Word Problems on Rational Numbers? Then you have come the right way we have got you Worksheet on Word Problems on Rational Numbers. You can practice using the Rational Numbers Worksheets on Word Problems and understand various questions. Try to solve the questions prevailing here on your own at first and then cross-check with the answers provided. Get an idea of where you went wrong and improvise on the corresponding areas.

1. If a Rope is 10m long two pieces of lengths 8/5m and 23/10m are cut off. What is the length of the rope left?

Solution:

Given Total Rope Length = 10m

Two pieces of lengths cut off are 8/5m and 23/10m

Therefore, to determine the rope left we need to subtract two pieces cut off i.e.

= 10 – 8/5 – 23/10

= 10-1.6-2.3

= 6.1m

Therefore, 6.1m of Rope is left.

2. A drum having paddy weights 240Kg whereas the weight of the empty drum is 50/4kg. Find the Weight of the Paddy within the drum?

Solution:

Weight of Drum and Paddy = 240Kg

Weight of Drum = 50/4Kg

Weight of Paddy = Weight of Drum and Paddy – Weight of Drum

= 240- 50/4

= 240 -12.5

= 227.5kg

The Weight of Paddy is 227.5 Kg.

3. A basket contains three types of Vegetables including 48/3kg all together. If 15/2 kg is carrot, 19/6kg is tomatoes and the rest are brinjal. What is the Weight of Brinjal?

Solution:

Total weight of three vegetables = 48/3 Kg

Weight of Carrot + Weight of Tomatoes + Weight of Brinjal = 48/3

15/2+19/6+ Weight of Brinjal = 48/3

Weight of Brinjal = 48/3-15/2-19/6

= (96-45-19)/6

= 32/6

= 16/3 Kg

Therefore, the Weight of Brinjal = 16/3 Kg.

4. Find the Cost of 7/5m of cloth if the cost of the cloth is $120/3 per m?

Solution:

Cost of 7/5m of Cloth = 7/5*(120/3)

=7/5*40

= $56

5. A truck moves at an Average Speed of 180/4 Km/hr. How much distance will it cover in 12/3 hrs?

Solution:

we know Speed = Distance/Time

180/4 = Distance/(12/3)

180/4*12/3 = Distance

Distance = 180*12/4*3

= 180 Km

6. What is the area of the rectangular park if it is 140/3m long and 50/3m broad?

Solution:

Area of rectangular park = 140/3*50/3

= 140*50/9

= 777.77m

Therefore, the area of the rectangular park is 777.77m

7. Find the area of the square plot if the side of the square measures 7/2 m?

Solution:

Area of Square Plot = S*S

= 7/2*7/2

= 49/4 Sqmt

Therefore, the Area of the Square Plot is 49/4 Sqmt.

8. One-liter diesel cost Rs. 56. How much does 35 liters of Diesel Cost?

Solution:

35 liters of Diesel = 35*56

= Rs. 1960

9. An Airplane covers 920 km in an hour. How much distance does it cover in 15/6 hours?

Solution:

1 hour = 920 km

15/6 hours = 15/6*920

= 2300Km

Therefore, the airplane covers a distance of 2300km in 15/6 hours.

10. Product of Two Rational Numbers is 42/5 and if one of them is 36/7. Find the other rational number?

Solution:

Product of Two Rational Numbers = 42/5

36/7*x= 42/5

x = (42/5)/(36/7)

= 42/5*7/36

= 42*7/5*36

= 294/180

= 49/30

The Other Rational Number is 49/30.

11. Geeta had $250 She spent 1/2 of her money on books and 1/4 of the remainder on stationery items. How much money is left with her?

Solution:

Geeta had a total money = $250

She spent 1/2 of her money on books = $250/2

= $125

Of the remaining money she spends 1/4 on Stationery Items i.e. 1/4($125)

= $ 31.25

Total money left with her = $250-( $125 – $ 31.25)

= $93.75

12. Area of a room is 214/2 m2. If the breadth is 83/4m what is its length?

Solution:

Area of a room = 214/2 m2

Breadth is 83/4 m

Length =?

Area of the Room = Length*Breadth

214/2 = 83/4*length

Length = (214/2)/(83/4)

= 214/2*4/83

= 214*4/2*83

= 856/166

= 428/83
Therefore, the Length of the Room is 428/83 m.

 

 

Worksheet on Finding Rational Numbers between Two Rational Numbers

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If you are eager to know about How to Find Rational Numbers Between Two Rational Numbers this article is definitely for you. Practice the questions from Worksheet on Finding Rational Numbers between Two Rational Numbers and test your preparation level. Concentrate on the areas you are lagging and improve your performance in the exams.

Worksheet for finding Rational Numbers between Two Rational Numbers covers the questions for finding Rational Numbers between Two Rational Numbers having either the same or different denominators. Check out Rational Numbers Worksheets to get conceptual knowledge on several concepts underlying.

1. Find out the Rational Numbers between 1/4 and 5/3?

Solution:

Check the denominators of given Rational Numbers.

If they aren’t the same firstly equate the denominators by finding the LCM.

LCM(4, 3) = 12

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

5/3 = 5*4/3*4 = 20/12

Therefore, Rational Numbers between 4/12, 5/12, 6/12, 7/12, 8/12, 9/12, 10/12, 11/12, 12/12, 13/12, 14/12, 15/12, 16/12, 17/12, 18/12, 19/12.

2. Find at least 5 Rational Numbers lying between 1/3 and 4/3?

Solution:

Since the difference between numbers is small it is hard to write rational numbers between them. So multiply the given numbers with multiples of 10.

1/3 = 1*10/3*10 = 10/30

4/3 = 4810/3810 = 40/30

Therefore, the 5 Rational Numbers between 10/30 an 40/30 is 11/30, 12/30, 13/30, 14/30, 15/30.

3. What is the Property of inserting infinitely many rational numbers between Two Rational Numbers?

Solution:

Dense Property

4. There exists always a Rational Number Between Two Distinct Rational Numbers. Is it True or False?

Solution:

True

5. Find 4 Rational Numbers between 2/5 and 7/5?

Solution:

Since the denominators are the same and numerators differ by a large value you can simply increment the numerator by 1 and keep the denominator unchanged.

3/5, 4/5, 5/5, 6/5.

6. Find a Rational Number between 4/3 and 5/4?

Solution:

You can find a Rational Number between 4/3 and 5/4 using the average.

= (4/3+5/4)/2

=(16+15) /12)/2

= (31/12)/2

= 31/12*1/2

= 31/24

7. Find out 4 Rational Number between -1/3 and 1/4?

Solution:

Since the Denominators are not the same find out the LCM first

LCM(3,4) = 12

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

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

Rational numbers between -1/3 and 1/4 are -3/12, -2/12, -1/12, 0.

8. Find Rational Numbers between 3/4 and 8/4?

Solution:

Since the denominators are the same and numerators differ by a large value you can simply increment the numerator by 1 and keep the denominator unchanged.

Rational Numbers between 3/4 and 8/4 is 4/4 5/4, 6/4, 7/4.

Worksheet on Properties of Division of Rational Numbers | Division of Rational Numbers Properties Worksheet

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To Solve Problems on Dividing Rational Numbers easily you need to be aware of the Properties of Division of Rational Numbers by which you can make your calculations simple. Practice using the Worksheet on Properties of Division of Rational Numbers and solve a variety of questions. The Questions covered here include different properties like Closure Property, Commutative Property, Associative Property, etc.

For more information regarding the Rational Numbers Properties, you can check out Rational Numbers Worksheets. Check out Solved Examples provided for a better understanding of the concept.

1.  Verify whether the given statement is true or false

3/9 ÷ 4/11 = 5/9 ÷ 5/13

Solution:

(3/9)/(4/11) = 3/9*11/4

= 3*11/9*4

= 33/36

= 11/12

5/9 ÷ 5/13 = (5/9)/(5/13)

= 5/9*13/5

= 5*13/9*5

= 65/45

= 13/9

Therefore, 3/9 ÷ 4/11 is not equal to 5/9 ÷ 5/13 and the statement is false.

2. Check whether the following statement is true or false -7 ÷ 5/4 = 5/4 ÷ (-7)

Solution:

-7 ÷ 5/4 = -7/(5/4) = -7*4/5

= -28/5

5/4 ÷ (-7) = (5/4)/(-7)

= (5/4)*(1/-7)

= 5*1/4*-7

= 5/-28

Therefore, -7 ÷ 5/4 is not equal to 5/4 ÷ (-7). Hence, the Statement is false. Commutative Property is not true for the division.

3. Check whether the following statement is true or false

{-8/5 ÷ 2/3} ÷ 4/5 = -8/5 ÷ {2/3 ÷ 4/5}

Solution:

{-8/5 ÷ 2/3} ÷ 4/5 = {(-8/5)/(2/3)}÷4/5

= (-8/5*3/2)÷4/5

= (-24/10)/(4/5)

= -24/10*5/4

= -120/40

= -3/1

-8/5 ÷ {2/3 ÷ 4/5} = -8/5÷{(2/3)/(4/5)}

= -8/5÷{(2/3)*(5/4)}

= -8/5÷{10/12}

= -8/5/(10/12)

= -8/5*12/10

= -96/50

= -48/25

Therefore, {-8/5 ÷ 2/3} ÷ 4/5is not the same as -8/5 ÷ {2/3 ÷ 4/5}. Hence, the Statement is false.

Associative Property is not true for the division.

4. Simplify 2/5 ÷ 1/4?

Solution:

= (2/5)/(1/4)

= 2/5*4/1

=2*4/5*1

= 8/5

Rational Numbers are closed under Division.

5. State whether the following statements are true or false.

1. Rational Numbers are always Closed Under Division.

2. Rational Numbers obeys the Commutative Property under Division.

3. Division of Rational Numbers obeys the Associative Property.

4. Can we divide 1 by 0

Solution:

1.  True

2. False

3. False

4. No as it is undefined

Worksheet on Division of Rational Numbers | Dividing Rational Numbers Worksheet

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Students preparing the Division of Rational Numbers can find the Worksheet on Division of Rational Numbers quite useful. Practice using the Dividing Rational Numbers Worksheet and test your preparation knowledge. We tried providing various examples on the Rational Numbers Division. Check out the step by step solution provided for solved examples and get a better idea of the concept.

For the sake of your comfort, we even provided the Word Problems on Division of Rational Numbers with Answers. Make use of them during your preparation and try to have an idea of different questions. To know more about the chapter have a look at the Rational Numbers Worksheets.

1.  Divide the Rationals

(i) 3 by 1/2

(ii) 3 by -5/7

(iii) -2/4 by 9/-8

(iv) -5/8 by -11/14

Solution:

(i) 3 by 1/2

Take the reciprocal of the second rational number and multiply it with the first rational number

= 3/(1/2)

= 3*2/1

= 6/1

(ii) 3 by -5/7

Take the reciprocal of the second rational number and multiply it with the first rational number

= 3/(-5/7)

= 3*7/-5

= 21/-5

(iii) -2/4 by 9/-8

= -2/4/(9/-8)

Take the reciprocal of the second rational number and multiply it with the first rational number

= -2/4*(-8)/9

= 16/36

= 4/9

(iv) -5/8 by -11/14

= (-5/8)/(-11/14)

Take the reciprocal of the second rational number and multiply it with the first rational number

= -5/8*14/-11

= -70/-88

= 35/44

2. Divide 7/5 by 3?

Solution:

= (7/5)/3

Take the reciprocal of the second rational number and multiply it with the first rational number

= 7/5*1/3

= 7/15

3. Divide -3 by 4/3?

Solution:

= -3/(4/3)

Take the reciprocal of the second rational number and multiply it with the first rational number

= (-3)*3/4

= -9/4

4. A Diver needs to descent to a depth of 120 feet below sea level. He wants to do it in 10 equal descents. How far he should travel in each descent?

Solution:

In order to tell how far he should travel in each descent, we need to divide 120 by 10

Firstly take the reciprocal of the divisor 10

10 reciprocal – 1/10

Multiply 120 by 1/10

= 120*1/10

= 12

Thus, he should travel 12 feet in each descent.

5. Mason made 3/4 of a pound of trail mix and if he puts 1/8 of a pound into each bag, how many bags can the mason fill?

Solution:

To find the number of bags we need to divide (3/4)/(1/8)

To divide simply find the reciprocal of the second rational number i.e. 8/1 and then multiply with first rational number

= 3/4*8/1

= 3*8/4*1

= 24/4

= 6

6. Jim bought 10 rolls of paper towel. He got 90 3/5 paper towels in all. How many rolls of paper towels were on each roll?

Solution:

To find the number of paper towels was on each roll we need to divide 90 3/5  by 10.

Firstly find the reciprocal of 10 i.e. 1/10

= (90 3/5)*1/10

=(453/5)*1/10

= (453*1)/(5*10)

= 453/50

= 9 3/50

Therefore, 9 3/50 rolls of paper towels were on each roll.

7. Simplify

(i) 4/5 ÷ -7/12

(ii) -4 ÷ (-4/15)

(iii) -12/5 ÷ (-15)

(iv) (-1/8) ÷ (-4/5)

Solution:

(i) 4/5 ÷ -7/12

= (4/5)/(-7/12)

= (4/5)*(12/-7)

= 4*12/5*-7

= 48/-35

(ii) -4 ÷ (-4/15)

= -4/(-4/15)

= -4*(15/-4)

= -60/-4

= 15/1

(iii) -12/5 ÷ (-15)

= -12/5/(-15)

= -12/5*1/(-15)

= -12*1/5*(-15)

= -12/-75

= 12/75

(iv) (-1/8) ÷ (-4/5)

= (-1/8)/(-4/5)

= 1/8*5/-4

= 1*5/(8*-4)

= 5/-32

= -5/32

8. Fill in the Blanks

(i) 8/4 ÷ (_____) = -3/2

(ii) (_____) ÷ (-7/5) = 10/19

Solution:

Let the number to be found be x

(i) 8/4 ÷ (_____) = -3/2

(8/4)÷x = 3/2

(8/4)/x/1 = 3/2

8/4*1/x = 3/2

8/4x= 3/2

12x= 16

x = 2

The number to be divided is 2.

(ii) (_____) ÷ (-7/5) = 10/19

Consider the number to be found as x

x÷ (-7/5)  = 10/19

x/(-7/5) = 10/19

x*(5/-7) = 10/19

x = (10/19)/(5/-7)

= 10/19*(-7/5)

= 10*-7/19*5

= -70/95

= -14/19

Worksheet on Properties of Multiplication of Rational Numbers

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Students looking for different properties of Multiplication of Rational Numbers can get all of them in one place. Utilize the Worksheet on Properties of Multiplication of Rational Numbers and kick start your preparation. Assess your strengths and weaknesses by solving the Rational Numbers Multiplication Properties Worksheet. Make use of the Rational Numbers Worksheets and understand different concepts underlying.

The Questions covered in the Worksheet for Properties of Multiplication of Rational Numbers include closure property, commutative property, associative property, the existence of multiplicative identity property, the existence of the multiplicative inverse property, distributive property of multiplication over addition, and multiplicative property of 0.

1. Multiply the following Rationals

(i) -5/13 by 21/(-30)

(ii) -3/10 by -15/32

(iii) -4/25 by -4/12

Solution:

(i) -5/13 by 21/(-30)

= (-5/13)/(21/-30)

= (-5/13)*(-30/21)

= (-5*-30)/13*21

= 150/273

= 50/91

(ii) -3/10 by -15/32

= (-3/10)/(-15/32)

= -3/10*32/-15

= -3*32/10*-15

= -96/-150

= 16/25

(iii) -4/25 by -4/12

= (-4/25)/(-4/12)

= -4/25*12/-4

= (-4*12)/(25*-4)

= -48/-100

= 48/100

= 12/25

2. Verify each of the following:

(i) 4/11 × (-7)/3 = (-7)/3× 4/11

(ii) (-6)/10 × 1/4 = 1/4 × (-6)/10

Solution:

(i) 4/11 × (-7)/3 = (-7)/3× 4/11

4/11 × (-7)/3 = 4*(-7)/11*3 = -28/33

(-7)/3× 4/11 = -7*4/3*11 = -28/33

Therefore, 4/11 × (-7)/3 = (-7)/3× 4/11

(ii) (-6)/10 × 1/4 = 1/4 × (-6)/10

(-6)/10 × 1/4 = -6*1/10*4 = -6/40

1/4 × (-6)/10 = 1*-6/4*10 = -6/40

(-6)/10 × 1/4 = 1/4 × (-6)/10

3. Fill in the Blanks

(i) (-13)/10 × 18/30 = 18/30 × (_____)

(ii) -32 × (-7)/11 = (-7)/11 × (_____)

(iii) {15/3 × -20/18} × (-3)/6 = (_____) × {(-20)/18 × (-3/6)}

Solution:

(i) (-13)/10

We know multiplication obeys the Commutative Property i.e. a*b = b*a

(ii) -32

We know multiplication obeys the Commutative Property i.e. a*b = b*a

(iii) 15/3

We know Multiplication of Rational Numbers is Associative i.e. a/b x (c/d x e/f)  =  (a/b x c/d) x e/f.

4. Find the Multiplicative Inverse of the following

(i) -4/5

(ii) -6/7

(iii) 11/-12

(iv) 15/8

Solution:

Multiplicative Inverse of a Rational Number is nothing but the Reciprocal of the Rational Number. Product of a Rational Number and its Multiplicative Inverse results in 1.

(i) 5/-4

(ii) 7/-6

(iii) -12/11

(iv) 8/15

5. Name the Property of Multiplication illustrated by the following statements

(i) {(-2)/5 × 3/7} × (-9)/2 = (-2)/5× {3/7 × (-9)/2}

(ii) -8/13 × -12/5 = -12/5 × -8/13

(iii) (-15)/7 × 1 = 1 × (-15)/ 7= (-15)/7

(iv) (-1)/12 × 12/-1 = 12/-1 × (-1)/12 = 1

(v) 4/5*0 = 0

(vi) (-5)/2 × {(-3)/4 + 7/5} = {(-5)/2 × (-3)/4} + {(-5)/2 × 7/5}

Solution:

(i) Associative Property

(ii) Commutative Property

(iii) Multiplicative Identity Property

(iv) Multiplicative Inverse Property

(v) Multiplicative Property of 0

(vi) Distributive Property

6. Verify the following

(3/4 × 11/5) × 7/12 = 3/4 ×(11/5 × 7/12)

Solution:

(3/4 × 11/5) × 7/12 = (3*11/4*5) × 7/12

= 33/20*7/12

= 33*7/20*12

= 241/240

3/4 ×(11/5 × 7/12) = 3/4 ×(11*7/5*12)

= 3/4 *(77/60)

= 3*77/4*60

= 241/240

Worksheet on Multiplication of Rational Numbers | 8th Class Product of Rational Numbers Worksheet

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Those who feel the concept of Multiplying Rational Numbers difficult can use the Worksheet on Multiplication of Rational Numbers here. Get to see various examples on the Rational Numbers Multiplication in the coming sections. Try to solve the questions from the Multiplication of Rational Numbers Worksheet at first and assess your preparation standards. For your comfort, we even provided solutions explained in detail. To know more you can always look up our Rational Numbers Worksheets and Clarify your doubts then and there itself.

1.  Multiply each of the following Rational Numbers

(i) 5/11 by 3/4

(ii) -2/9 by 4/11

(iii) -3/7 by -2/-5

Solution:

(i) 5/11 by 3/4

= (5/11)/(3/4)

= 5/11*4/3

= 5*4/11*3

= 20/33

(ii) -2/9 by 4/11

= (-2/9)/(4/11)

= -2/9*11/4

= -2*11/9*4

= -22/36

= -11/18

(iii) -3/7 by -2/-5

= (-3/7)/(-2/-5)

= (-3/7)/(2/5)

= -3/7*5/2

= -3*5/7*2

= -15/14

2. Find the Product of each of the following

(i) 4/5*(-7/6) (ii) (-11)/5 × 9/-3

Solution:

(i) 4/5*(-7/6)

= 4*-7/5*6

= -28/30

= -14/15

(ii) (-11)/5 × 9/-3

= -11*9/5*-3

= -99/-15

= 99/15

= 33/5

3. Find the Reciprocal of

(i) 10/22

(ii)(-5/12)

(iii) -14

Solution:

Reciprocal is nothing but the number which when multiplied by given number results in 1

(i) 22/10

(ii) 12/-5

(iii) 1/-14

4. Find the Value of

(i) (3/8)^-1

(ii) (4/5)^-1

(iii) (7/6)^-1

Solution:

(i) (3/8)^-1

= 1/(3/8)

= 8/3

(ii) (4/5)^-1

= 1/(4/5)

= 5/4

(iii) (7/6)^-1

= 1/(7/6)

= 6/7

5. Fill in the Blanks

1.  The Product of a Rational Number and its Reciprocal is  __________

2.  Reciprocal of b where b  ≠  0 is __________

3. Reciprocal of 1/b where b ≠  0 is __________

4. Rational Number 0 has its __________

5. Is Zero Reciprocal of any number __________

6. Reciprocal of Positive Rational Number remains __________

7. Reciprocal of Negative Rational Number remains __________

Solution:

1.  1

2. 1/b

3. b

4. Own Reciprocal

5. No

6. Positive

7. Negative

6. Simplify the following and express the result as a Rational Number

(i) -13/21 × 2/5

(ii) 3/4 × -5/28

Solution:

(i) -13/21 × 2/5

= (-13*2)/(21*5)

= -26/105

(ii) 3/4 × -5/28

=3*(-5)/4*28

= -15/112