MULTIPLY AND DIVIDE RATIONAL NUMBERS WORKSHEET

Problem 1 :

Multiply 2/3 and 5/7.

Problem 2 :

Evaluate : 

(4/-11) ⋅ (-22/8)

Problem 3 :

Simplify :

(2/5) ÷ (7/9)

Problem 4 :

Simplify : 

(-4/9) ÷ (9/-4)

Problem 5 :

Multiply 2¼ and 3½.

Problem 6 :

Simplify : 

-9¾ ÷  1⅞

Problem 7 :

Find the product of -11/2 and 4/5.

Problem 8 :

What is three-seventh of 14/15 ?

Problem 9 :

Lorraine wants to divide three-fifth of a pizza equally to 5 of her friends. How much pizza will each friend get ?

Problem 10 :

Last month, Jacob gave two-fifth of his earning to his friend. If Jacob had earned $12000 last month, how much money did he give his friend ?

Detailed Answer Key

Problem 1 :

Multiply 2/3 and 5/7.

Solution :

=  (2/3) ⋅ (5/7)

Multiply numerators and denominators. 

=  (2 ⋅ 5) / (3 ⋅ 7)

=  10/21

Problem 2 :

Evaluate : 

(4/-11) ⋅ (-22/8)

Solution :

=  (4/-11) ⋅ (-22/8)

Before we multiply numerators and denominators, we can simplify as shown below.

=  (-2) / (-2)

=  1

Problem 3 :

Simplify :

(2/5) ÷ (7/9)

Solution :

  =  (2/5) ÷ (7/9)

To divide by 7/9, multiply by 9/7.

=  (2/5) ⋅ (9/7)

Multiply the numerators and denominators. 

=  (2 ⋅ 9) / (5 ⋅ 7)

=  18/35

Problem 4 :

Simplify : 

(-4/9) ÷ (9/-4)

Solution :

  =  (-4/9) ÷ (9/-4)

To divide by 9/-4, multiply by -4/9.

=  (-4/9) ⋅ (-4/9)

Multiply the numerators and denominators. 

=  [(-4)(-4)] / (9 ⋅ 9)

=  16/81

Problem 5 :

Multiply 2¼ and 3½.

Solution :

=  (2¼) ⋅ (3½)

Converting the mixed fractions to improper fractions.

=  (9/4) ⋅ (7/2)

=  (9 ⋅ 7) / (4 ⋅ 2)

=  63/8

=  7⅞

Problem 6 :

Simplify : 

-9¾ ÷  1⅞

Solution :

=  -9¾ ÷  1⅞

Converting the mixed numbers to improper fractions

=  (-39/4) ÷ (15/8)

To divide by 15/8, multiply by 8/15.

=  (-39/4) ⋅ (8/15)

Simplify 39 and 15 using 3 times table, 4 and 8 using 4 times table. 

=  (-13/1) ⋅ (2/5)

=  (-13 ⋅ 2) / (1 ⋅ 5)

=  -26/5

=  -5⅕

Problem 7 :

Find the product of -11/2 and 4/5.

Solution :

  =  (-11/2) ⋅ (4/5)

Multiplying the numerators and denominators.

=  (-11 ⋅ 4) / (2 ⋅ 5)

=  -44/10

=  -22/5

Converting the improper fraction into mixed fraction.

  =  -4⅖

Problem 8 :

What is three-seventh of 14/15 ?

Solution :

Three-seventh of 14/15 :

=  (3/7) ⋅ (14/15)

Simplify 3 and 15 using 3 times table, 7 and 14 using 7 times table. 

=  (1/1) ⋅ (2/5)

Multiply numerators and denominators. 

=  (1 ⋅ 2) / (1 ⋅ 5)

=  2/5

Problem 9 :

Lorraine wants to divide three-fifth of a pizza equally to 5 of her friends. How much pizza will each friend get ?

Solution :

Amount of pizza each friend will get :

=  (3/5) ÷ 5

=  (3/5) ÷ (5/1)

To divide by 5/1, multiply by 1/5.

=  (3/5) ⋅ (1/5)

Multiply numerators and denominators. 

=  (3 ⋅ 1) / (5 ⋅ 5)

=  3/25

Each friend will get 3/25 of a pizza.  

Problem 10 :

Last month, Jacob gave two-fifth of his earning to his friend. If Jacob had earned $12000 last month, how much money did he give his friend ?

Solution :

Money given to friend :

=  (2/5) ⋅ 12000

=  (2/5) ⋅ (12000/1)

Simplify 5 and 12000 using 5 times table.

=  (2/1) ⋅ (2400/1)

Multiply numerators and denominators. 

=  (2 ⋅ 2400) / (1 ⋅ 1)

=  4800/1

=  4800

John gave $4800 to his friend. 

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