How to Multiply Fractions

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

Steps in Multiplying Fractions

Given two fractions with nonzero denominators : 

the fractions a over b and c over d or written as a/b and c/d.

Step 1: Multiply the numerators together

  • This will be the numerator of the “new” fraction.
to multiply the numerators, we multiply the top numbers or the numbers above the fraction bars. that is, in (a/b)(c/d)=(a)(c) which will be our new numerator.

Step 2: Multiply the denominators together

  • This will be the denominator of the “new” fraction.
we then multiply the bottom numbers, b and d, to find the new denominator. thus, (a/b)(c/d)= where (b)(d) is our new denominator.

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

(a/b)(c/d)= where  is the resulting fraction.

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

  • Dot symbol as a multiplication operator
in (a/b)∙(c/d), the dot symbol written in between the two fractions indicate the multiplication operation. in the same manner, we can use the dot symbol when multiplying both numerators and both denominators together. we can write this as (a/b)∙(c/d) = (a∙c)/(b∙d).
  • Parenthesis as a multiplication operator
in (a/b)(c/d) = (a)(c)/(b)(d), the parentheses enclosing both fractions or variables indicate the multiplication operation.

Examples of How to Multiply Fractions

Example 1: Multiply the fractions below.

two-fifths or 2/5 multiplied by three-sevenths or 3/7

Multiply the numerators of the fractions

in our example (2/5)(3/7), we first multiply the numerators 2 and 3. that is, 2 times 3 is equal to 6 which will be our new numerator. we place 6 on top of the fraction bar.

Similarly, multiply the denominators together.

next, we multiply the denominators 5 and 7 together and place the answer at the bottom of our fraction bar. thus we have, (2/5)(3/7) =  = 6/35.

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

our final answer is 6/35

Example 2: Multiply the fractions below.

multiply 2 over 10 and 5 over 8, that is (2/10)(5/8).

Step 1: Multiply the top numbers together

we multiply 2 and 5 which are the numerators, thus we have (2/10)(5/8)=(2)(5)=10.

Step 2: Multiply the bottom numbers together

we now multiply our denominators 10 and 8. therefore, we get (2/10)(5/8)=(2)(5)/(10)(8)=10/80.

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

Divide the top and bottom by its greatest common divisor (GCD) which is 10.

we reduce 10/80 to its lowest term by dividing it by 10 which is the greatest common divisor for both numbers. that is, 10/80 = (10÷10)/(80÷10) = 1/8.

Example 3: Multiply the three fractions .

two-thirds, six-eights, and one-half multiplied together. we can write this as (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

we first multiply the numerators 2, 6, and 1 together. thus we have, (2)(6)(1) = 12.

Step 2: Get the product of the denominators

next, we multiply the denominators 3, 8, and 2 together which gives us 48. we can write this as (2/3)(6/8)(1/2) = (2)(6)(1)/(3)(8)(2) = 12/48.

Step 3: Reduce the answer to the lowest term

Divide both the numerator and denominator by the greatest common divisor that is 12.

we reduce 12/48 to its lowest form by dividing both the numerator and denominator by 12. thus we have, 12/48 = (12÷12)/(48÷12) = 1/4.

Example 4: Multiply a whole number and a fraction .

the whole number 5 times the fraction 2/15, that is (5)(2/15).

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

5 is the same as the fraction 5/1

Therefore, we can rewrite the original problem as {5 \over 1} \times {2 \over {15}}. With that, it should allow us to multiply the fractions as usual.

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

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

we divide both the numerator and denominator of the fraction 10/15 by 5 to reduce it to its lowest term. we now get 2/3 as the final answer.

Example 5: Multiply .

five-thirds multiplied by six-fifteenths or (5/3)(6/15)

Step 1: Multiply the numerators

Step 2: Multiply the denominators

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) =  = 30/45 = 2/3

Example 6: Multiply .

the fractions 3/10, 5/4, and 8/9 multiplied together.

Solution:

(3/10)(5/4)(8/9) = (3)(5)(8)/(10)(4)(9) = 120/360 = 1/3

Example 7: Multiply .

the fraction 2/12 multiplied by the whole number 9

Solution:

Rewrite the whole number 9 with a denominator of 1.

(2/12)(9/1) = (2)(9)/(12)(1) = 18/12 = 3/2

Practice with Worksheets

You might also be interested in:

Adding and Subtracting Fractions with the Same Denominator
Add and Subtract Fractions with Different Denominators
Dividing Fractions
Simplifying Fractions
Equivalent Fractions
Reciprocal of a Fraction