Multiplying Fractions

To multiply fractions is as easy as following the 3 suggested steps below. It’s understood that no fraction can have a denominator of zero [latex]\color{red}0[/latex] because it will be an undefined term.

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.

  • 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.

  • 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 ac/bd 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.

(2/5) times (3/7)

Multiply the numerators of the fractions.

2 × 3 = 6

Similarly, multiply the denominators together.

5 × 7 = 35

The resulting fraction after multiplication is already in its reduced form since the Greatest Common Divisor of the numerator and denominator is [latex]\color{blue}+1[/latex]. This becomes our final answer!

our final answer is 6/35

Example 2: Multiply.

(2/10) × (5/8)

Step 1: Multiply the top numbers.

2 × 5 = 10

Step 2: Multiply the bottom numbers.

10 × 8 = 80

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

Divide the top and bottom by its Greatest Common Factor (GCF) which is [latex]10[/latex].

divide the numerator and denominator by 10

Example 3: Multiply.

(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: Calculate the product of the numerators.

2 × 6 × 1 = 12

Step 2: Compute the product of the denominators.

3 × 8 × 2 = 48

Step 3: Reduce the fraction to its simplest form.

Divide both the numerator and denominator by the greatest common divisor that is [latex]12[/latex].

simplify by dividing the top and bottom of the fraction by 12

Example 4: Multiply a whole number by a fraction.

5 × (2/15)

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

5 is the same as the fraction 5/1

Therefore, we can rewrite the original problem as [latex]{5 \over 1} \times {2 \over {15}}[/latex]. 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 [latex]5[/latex].


Example 5: Multiply.

(5/3) × (6/15)

Step 1: Multiply the numerators

5 × 6 = 30

Step 2: Multiply the denominators

3 × 15 = 45

Step 3: Reduce the answer to the lowest term by dividing the top and bottom by the Greatest Common Divisor which is [latex]15[/latex].

(5/3)(6/15) =  = 30/45 = 2/3

Example 6: Multiply.

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


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

Example 7: Multiply.

(2/12) × 9


Rewrite the whole number [latex]9[/latex] with a denominator of [latex]1[/latex]. Thus, [latex]\large{9 = {9 \over 1}}[/latex]

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

You may also be interested in these related math lessons or tutorials:

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