Multiplying fractions is one of the easiest operations you can do with fractions once you know the rule. This guide walks you through how to multiply fractions step by step, with simple examples and common questions people search for online.

# The Basic Rule for Multiplying Fractions

To multiply two fractions:

  1. Multiply the numerators (top numbers).
  2. Multiply the denominators (bottom numbers).
  3. Simplify the result if possible by reducing the fraction.

If you have two fractions:

  • First fraction: ( \frac{a}{b} )
  • Second fraction: ( \frac{c}{d} )

Then:

  • Product: ( \frac{a}{b} \times \frac{c}{d} = \frac{a \times c}{b \times d} )

# Example: Simple Fraction Multiplication

Example 1:
Multiply ( \frac{2}{3} \times \frac{4}{5} )

  1. Multiply numerators: ( 2 \times 4 = 8 )
  2. Multiply denominators: ( 3 \times 5 = 15 )
  3. Result: ( \frac{8}{15} )

Can we simplify ( \frac{8}{15} )?

  • 8 factors: 1, 2, 4, 8
  • 15 factors: 1, 3, 5, 15
    They share only 1, so it is already in simplest form.

Answer: ( \frac{2}{3} \times \frac{4}{5} = \frac{8}{15} )

# How to Multiply Fractions and Simplify (Reduce) the Answer

Often the result can be simplified.

Example 2:
Multiply ( \frac{3}{4} \times \frac{2}{6} )

  1. Numerators: ( 3 \times 2 = 6 )
  2. Denominators: ( 4 \times 6 = 24 )
  3. Result: ( \frac{6}{24} )

Now simplify:

  • Greatest common divisor (GCD) of 6 and 24 is 6.
  • Divide top and bottom by 6:
    • ( 6 \div 6 = 1 )
    • ( 24 \div 6 = 4 )

Simplified answer: ( \frac{1}{4} )

So ( \frac{3}{4} \times \frac{2}{6} = \frac{1}{4} ).

# Faster Method: Cross-Simplifying Before Multiplying

To keep numbers small, you can simplify before multiplying using cross-cancellation.

Example 3:
Multiply ( \frac{3}{4} \times \frac{2}{6} ) again, but with cross-simplifying.

Fractions: ( \frac{3}{\mathbf{4}} \times \frac{2}{\mathbf{6}} )

  • Look diagonally:
    • 3 (top left) with 6 (bottom right)
    • 2 (top right) with 4 (bottom left)

Simplify diagonals:

  1. 3 and 6:

    • GCD is 3
    • ( 3 \div 3 = 1 ), ( 6 \div 3 = 2 )

  2. 2 and 4:

    • GCD is 2
    • ( 2 \div 2 = 1 ), ( 4 \div 2 = 2 )

Now the problem becomes:

  • ( \frac{1}{2} \times \frac{1}{2} = \frac{1 \times 1}{2 \times 2} = \frac{1}{4} )

Same answer as before, but with smaller numbers and less work.

# How to Multiply a Fraction by a Whole Number

To multiply a fraction by a whole number, convert the whole number to a fraction.

  • Whole number ( n = \frac{n}{1} )

Example 4:
Multiply ( \frac{5}{8} \times 3 )

  1. Rewrite 3 as ( \frac{3}{1} ):
    ( \frac{5}{8} \times \frac{3}{1} )

  2. Multiply numerators: ( 5 \times 3 = 15 )

  3. Multiply denominators: ( 8 \times 1 = 8 )

Result: ( \frac{15}{8} ) (an improper fraction)

If you want a mixed number:

  • ( 15 \div 8 = 1 ) remainder 7
  • So ( \frac{15}{8} = 1 \frac{7}{8} )

# How to Multiply Mixed Numbers (e.g., 1 1/2 × 2 2/3)

Mixed numbers must first be converted to improper fractions.

Steps:

  1. Convert each mixed number to an improper fraction.
  2. Multiply the fractions (numerators together, denominators together).
  3. Simplify.
  4. (Optional) Convert back to a mixed number.

Example 5:
Multiply ( 1 \frac{1}{2} \times 2 \frac{2}{3} )

  1. Convert to improper fractions:

    • ( 1 \frac{1}{2} = \frac{1 \times 2 + 1}{2} = \frac{3}{2} )
    • ( 2 \frac{2}{3} = \frac{2 \times 3 + 2}{3} = \frac{8}{3} )

  2. Multiply fractions:

    ( \frac{3}{2} \times \frac{8}{3} = \frac{3 \times 8}{2 \times 3} = \frac{24}{6} )

  3. Simplify ( \frac{24}{6} = 4 ) (a whole number)

Answer: ( 1 \frac{1}{2} \times 2 \frac{2}{3} = 4 )

# Why Multiplying Fractions Feels Easier Than Adding Them

Many learners struggle with adding and subtracting fractions because you need a common denominator. With multiplication:

  • You do not need a common denominator.
  • You only multiply straight across: top with top, bottom with bottom.

This is why many students find multiplying fractions simpler than adding or subtracting them.

If you’re curious about adding fractions, look up resources on “how to add fractions with unlike denominators” or online tutorials from educational sites like Khan Academy or BBC Bitesize.

# Common Questions About Multiplying Fractions

# 1. Do I need the same denominator to multiply fractions?

No. Unlike addition and subtraction, you do not need the same denominator. Just multiply:

  • Numerators together
  • Denominators together

# 2. What if one number is a whole number?

Rewrite the whole number as a fraction over 1, like ( 5 = \frac{5}{1} ), then multiply.

# 3. Do I always have to simplify?

In schoolwork and most real-world applications, it’s best practice to simplify your answer so the fraction is in lowest terms. That usually means:

  • Divide numerator and denominator by their greatest common divisor (GCD).

# 4. Can the answer to multiplying fractions be bigger than both starting fractions?

Yes. For example:

  • ( \frac{3}{2} \times \frac{3}{2} = \frac{9}{4} = 2 \frac{1}{4} ), which is greater than 1.

But if you multiply two proper fractions (both less than 1), the answer will be smaller than either of them:

  • ( \frac{1}{2} \times \frac{1}{3} = \frac{1}{6} )

# Real-Life Examples of Multiplying Fractions

Understanding where this shows up in real life can make it stick.

  1. Cooking and baking

    • If a recipe uses ( \frac{3}{4} ) cup of sugar, and you make half the recipe:
      ( \frac{1}{2} \times \frac{3}{4} = \frac{3}{8} ) cup of sugar.

  2. Discounts and sales

    • If an item is already 50% off (multiply by ( \frac{1}{2} )), and there is an extra 20% off (multiply by ( \frac{1}{5} )), the overall effect involves multiplying fractions representing the remaining portions or discount portions.

  3. Area problems

    • If a rectangle is ( \frac{3}{5} ) meter long and ( \frac{2}{3} ) meter wide, its area is:
      ( \frac{3}{5} \times \frac{2}{3} = \frac{6}{15} = \frac{2}{5} ) square meters.

For visual explanations, you can find helpful fraction-area diagrams on sites like Math is Fun.

# Quick Practice Problems

Try these on your own:

  1. ( \frac{1}{2} \times \frac{4}{5} = ? )
  2. ( \frac{7}{8} \times \frac{3}{7} = ? )
  3. ( \frac{2}{3} \times 6 = ? )
  4. ( 1 \frac{3}{4} \times \frac{2}{5} = ? )

Answers:

  1. ( \frac{1 \times 4}{2 \times 5} = \frac{4}{10} = \frac{2}{5} )
  2. ( \frac{7 \times 3}{8 \times 7} = \frac{21}{56} = \frac{3}{8} )
  3. Rewrite 6 as ( \frac{6}{1} ):
    ( \frac{2}{3} \times \frac{6}{1} = \frac{12}{3} = 4 )
  4. Convert ( 1 \frac{3}{4} = \frac{7}{4} ):
    ( \frac{7}{4} \times \frac{2}{5} = \frac{14}{20} = \frac{7}{10} )

# Summary: How to Multiply Fractions

To multiply fractions:

  • Multiply the numerators.
  • Multiply the denominators.
  • Simplify the resulting fraction.

Whether you’re working with simple fractions, whole numbers, or mixed numbers, the core idea stays the same: top × top, bottom × bottom, then reduce.

If you’d like, you can ask for:

  • More practice questions with answers
  • A visual explanation
  • A comparison of multiplying vs adding fractions