MULTIPLICATIVE INVERSE WORKSHEET

1. Find the multiplicative inverse of 9/11.

2. Find the multiplicative inverse of -5.

3. Find the multiplicative inverse of 2⅗.

4. What is the multiplicative inverse of the sum of 3/4 and 5/6?

5. What is the multiplicative inverse of (5/21) x (7/20)?

6. What is the multiplicative inverse of (24/7 ÷ 32/35)?

7. What is the multiplicative inverse of 0.32?

8. What is the multiplicative inverse of 1.25?

9. If y/3 and 4/5 are multiplicative inverse to each other, then find the value of y.

10. If 2/5 and 7/z are multiplicative inverse to each other, then find the value of z.

11. Identity element for multiplication of rational numbers is ______________.

(a) 1   (b) 0    (c) -1     (d) does not exist

12.  9/4 x ___ = 1

13.  Sum of a number and its additive inverse is equal to _________.

14. What is the multiplicative inverse of -2  1/3 ?

15.  The product of two rational numbers is -9. If one of the number is -12, find the other number.

16. Find x, if -9/8 + x = -3/2

17. With what number should we multiply -36/35, so that the product be -6/5.

18. How many pieces, each of length 3  3/4 can be cut from the rope of length 30 m ?

19. The car is moving at an average speed of 54 4/5 km/h .how much distance will it cover in 7 1/2 hours?

20. 9/8 ÷ (________) = -3/2

1. Answer :

Multiplicative inverse of 9/11 = 11/9

2. Answer :

Multiplicative inverse of -5 = -1/5

3. Answer :

Convert the given mixed number to an improper fraction.

2⅗ = 13/5

Reciprocal of 13/5 is 5/13.

Multiplicative inverse of 2⅗ = 5/13

4. Answer :

Two fractions 3/4 and 5/6 have different denominators.

Least common multiple of (4, 6) = 12.

Make the denominator of each fraction as 12 using multiplication.

3/4 = (3 x 3)/(4 x 3) = 9/12

5/6 = (5 x 2)/(6 x 5) = 10/12

3/4 + 5/6 :

= 9/12 + 10/12

= (9 + 10)/12

= 19/12

Reciprocal of 19/12 is 12/19.

Multiplicative inverse of (3/4 + 5/6) = 12/19

5. Answer :

= (5/21) x (7/20)

Simplify.

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

= 1/12

Reciprocal of 1/12 is 12.

Multiplicative inverse of (5/21) x (7/20) = 12

6. Answer :

= 24/7 ÷ 32/35

Simplify.

= 24/7 x 35/32

= 3/1 x 5/4

= 15/4

Reciprocal of 15/4 is 4/15.

Multiplicative inverse of (24/7 ÷ 32/35) = 4/15

7. Answer :

0.32 = 32/100

= 8/25

Reciprocal of 8/25 is 25/8.

25/8 = 3.125

Multiplicative inverse of 0.32 = 3.125

8. Answer :

1.25 = 125/100

= 5/4

Reciprocal of 5/4 is 4/5.

4/5 = 0.8

Multiplicative inverse of 1.25 = 0.8

9. Answer :

Since y/3 and 4/5 are multiplicative inverse to each other, their product is equal to 1.

y/3 x 4/5 = 1

4y/15 = 1

Multiply each side by 15/4.

y = 15/4

10. Answer :

Since 2/5 and 7/z are multiplicative inverse to each other, their product is equal to 1.

2/5 x 7/z = 1

14/5z = 1

Take reciprocal on each side.

5z/14 = 1

Multiply each side by 14/5.

z = 14/5

11. Answer :

The element for multiplication of rational numbers is 1.

12. Answer :

Given that, 9/4 x ___ = 1

To identityfy the rational number to be multiplied to get 1, we have to find the reciprocal of 9/4, which is 4/9

Then,

= (9/4) x (4/9)

= 1

So, the required number be 4/9.

13. Answer :

Sum of a number and its additive inverse is equal to 0.

14. Answer :

Given number is = -2  1/3

converting into improper fraction, we get

= -7/3

Its reciprocal is -3/7

15. Answer :

The product of two rational numbers = -9

One of the number = -12

Let x be the other number

x(-12) = -9

x = -9/(-12)

x = 3/4

16. Answer :

-9/8 + x = -3/2

Adding the additive inverse of -9/8, we get 

x = -3/2 + 9/8

LCM (2, 8) = 8

x = -6/8 + 9/9

x = (-6 + 9)/8

x = 3/8

So, the required number is 3/8.

17. Answer :

Let x be the required number.

One number = -36/35

Product of these two numbers = -6/5

x (-36/35) = -6/5

x = (-6/5) (-35/36)

x = 7/6

So, the required number is 7/6.

With what number should we multiply -36/35, so that the product be -6/5.

18. Answer :

How many pieces, each of length 3  3/4 can be cut from the rope of length 30 m ?

Length of rope = 30 m

Length of each piece = 3  3/4 m

Converting into improper fraction, we get

= 15/4

number of pieces to be cut = 30/(15/4)

= 30 (4/15)

= 2(4)

= 8

So, the required number of pieces is 8.

19. Answer :

Average speed = 54  4/5 km/h ==> 274/5

Time taken = 7   1/2 hours ==> 15/2

Time = distance / speed

15/2 = distance / (274/5)

15/2 = distance (5/274)

(15/2) (274/5) = distance 

Distance = 411

20. Answer :

Let x be the required number.

9/8 ÷ x = -3/2

9/8 ⋅ (1/x) = -3/2

1/x = (-3/2) ⋅ (8/9)

1/x = -4/3

x = -3/4

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