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Multiplying Fractions

 

To multiply fractions is as easy as following the 3 suggested steps below.

 

Steps How To Multiply Fractions
Given two fractions with nonzero denominators a/b and c/d

Step 1: Multiply the numerators together

  • This will be the numerator of the "new" fraction.
multiply the numerators of fractions

Step 2: Multiply the denominators together

  • This will be the denominator of the "new" fraction.
multiply the denominators of fractions

Step 3: Simplify the resulting fraction by reducing it to lowest term, if needed.

(a/b) * (c/d) = [a*c]/[b*d]

 

Before we go over some examples, these are other ways to mean multiplication.

 

Dot symbol as multiplication operator. Parenthesis as multiplication operator.
dot symbol to denote multiplication of fractions parenthesis to denote multiplication of fractions

 


Example 1: Multiply the fractions (2/5) * (3/7).

Multiply the numerators of the fractions

multiply the numerators: 2 * 3 = 6

 

Similarly, multiply the denominators together.

 

multiply the denominators: 5*7=35

 

The resulting fraction after multiplication is already in its reduced form. That becomes our final answer!

 

final answer: (2/5) * (3/7) = (2*3)/(5*7)=6/35

 


Example 2: Multiply the fractions (2/10) * (5/8).

Step 1: Multiply the top numbers together product of numerators: 2*5=10
Step 2: Multiply the bottom numbers together product of denominators: 10*8=80

Step 3: Simplify the answer by reducing to lowest term.

  • Divide the top and bottom by its greatest common divisor (GCD) which is 10.
(10/80) = [10/10]/[80/10]=1/8

 


Example 3: Multiply the three fractions (2/3) * (6/8) * (1/2).

You may encounter a problem where you will be asked to multiply three fractions.

The general idea remains the same just like when you multiply two fractions, as shown in previous examples.

 

Step 1: Get the product of the numerators multiply the three numerators: 2*6*1=12
Step 2: Get the product of the denominators multiply the three denominators: 3*8*2=48

Step 3: Reduce the answer to the lowest term

  • Divide both the numerator and denominator by the greatest common divisor that is 12.
(12/48) = (12/12) / (48/12) = 1/4

 


Example 4: Multiply a whole number and a fraction 5 * (2/15).

When you multiply a whole number to a fraction, think of the whole number as fraction with a denominator of 1. Since

5 with denominator of 1

Therefore, we can rewrite the original problem as (5/1) multiplied to (2/15). With that, it should allow us to multiply the fractions as usual.

 

(5/1) * (2/15) = (5*2)/(1*15) = 10/15

 

Finally, reduce the answer by dividing the numerator and denominator by 5.

 

simplify answer to lowest term: 10/15 = 2/3

 


Example 5: Multiply (5/3) * (6/15).

Solution:

Step 1: Multiply the numerators

5 x 6 = 30

Step 2: Multiply the denominators

3 x 15 = 45

Step 3: Reduce the answer to the lowest term by dividing the top and bottom by the greatest common divisor which is 15.

 

 

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

 

 


Example 6: Multiply multiply three fractions: (3/10) * (5/4) * (8/9).

Solution:

solution: (3/10) * (5/4) * (8/9) = [3*5*8]/[10*4*9]=1/3

 


Example 7: Multiply multiply a fraction to a whole number: (2/12) * (9).

Solution:

Rewrite the whole number 9 with a denominator of 1.

(2/12) * (9/1) = [2*9]/[12*1]=3/2

 


 

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About This Topic: Multiplying Fractions

 

Practice Problems with Answers
Worksheet 1 Worksheet 2

 

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