Multiplying Fractions

✖️ Multiplying Fractions

Multiplying fractions is one of the easiest things you can do with fractions. There is no need to find a common denominator like you do with adding or subtracting. You just follow three simple steps.

The Three Steps

1. Multiply the numerators (the top numbers)
2. Multiply the denominators (the bottom numbers)
3. Simplify the answer if you can

Here is the rule written as a formula:

$\frac{a}{b} \times \frac{c}{d} = \frac{a \times c}{b \times d}$

The top numbers go straight across, and the bottom numbers go straight across. That's it!

A Worked Example

Let's multiply $\frac{2}{3} \times \frac{4}{5}$.

• Step 1 — Numerators: $2 \times 4 = 8$
• Step 2 — Denominators: $3 \times 5 = 15$
• Step 3 — Simplify: $\frac{8}{15}$ is already in lowest terms, so we are done.

$\frac{2}{3} \times \frac{4}{5} = \frac{8}{15}$

Notice that the answer is smaller than both fractions we started with. That makes sense — when you take a "part of a part," you end up with less than you began with.

What Does It Mean? 🤔

Multiplying by a fraction means "taking a part of" something. The word "of" is a clue that you should multiply.

• $\frac{1}{2} \times 10 = 5$ → half of 10 is 5
• $\frac{1}{4} \times 12 = 3$ → one-fourth of 12 is 3

So if a problem asks for "one-third of a pizza" or "two-fifths of the class," you can multiply to find the answer.

Concept Check 🎯

📝 Worked Examples

Example 1: Two Fractions

Multiply $\frac{3}{4} \times \frac{2}{5}$.

• Numerators: $3 \times 2 = 6$
• Denominators: $4 \times 5 = 20$
• Result: $\frac{6}{20}$
• Simplify: both 6 and 20 divide by 2 → $\frac{6}{20} = \frac{3}{10}$

$\frac{3}{4} \times \frac{2}{5} = \frac{3}{10}$

Example 2: A Whole Number Times a Fraction

Multiply $5 \times \frac{2}{3}$.

A whole number can always be written as a fraction by putting it over 1. So $5 = \frac{5}{1}$.

• Numerators: $5 \times 2 = 10$
• Denominators: $1 \times 3 = 3$
• Result: $\frac{10}{3}$
• Make it a mixed number: $10 \div 3 = 3$ remainder $1$, so $\frac{10}{3} = 3\frac{1}{3}$

$5 \times \frac{2}{3} = \frac{10}{3} = 3\frac{1}{3}$

Your Turn — Multiply Across 🧮

Type each numerator and denominator. Do not simplify these answers yet.

1. $\frac{1}{2} \times \frac{3}{5} = \frac{?}{?}$ — Numerator?

2. Same problem — Denominator?

3. $\frac{4}{7} \times \frac{2}{3} = \frac{?}{?}$ — Numerator?

Guided Practice 🧭

Work each one carefully — multiply across, then simplify.

Fill in the Steps 🔍

Complete the rule for solving $4 \times \frac{3}{8}$.

🌍 Fractions in Real Life

Remember: the word "of" usually means multiply.

Recipe Time 🍪

A cookie recipe needs $\frac{2}{3}$ cup of sugar. You only want to make half the recipe. How much sugar do you need?

"Half of $\frac{2}{3}$" means $\frac{1}{2} \times \frac{2}{3}$:

$\frac{1}{2} \times \frac{2}{3} = \frac{2}{6} = \frac{1}{3} \text{ cup}$

Sharing a Garden 🌱

A garden is $\frac{3}{4}$ of an acre. You plant tomatoes in $\frac{2}{3}$ of the garden.

$\frac{2}{3} \times \frac{3}{4} = \frac{6}{12} = \frac{1}{2} \text{ acre of tomatoes}$

Solve the Word Problems 🧮

1. A pizza is cut so that each slice is $\frac{1}{8}$ of the pizza. You eat 3 slices: $3 \times \frac{1}{8} = \frac{?}{8}$ — Numerator?

2. There are 20 students in class. $\frac{1}{4}$ of them ride the bus: $\frac{1}{4} \times 20 = ?$ students — type the whole number.

3. A board is $\frac{5}{6}$ meter long. You use $\frac{1}{2}$ of it: $\frac{1}{2} \times \frac{5}{6} = \frac{5}{?}$ — Denominator?

Word Problem Check 📋

🏆 Review & Challenge

You now know everything you need to multiply fractions. Here is the whole idea in one table.

Cross-Canceling Shortcut ✂️

When a numerator and a denominator share a factor, you can cancel before multiplying to keep the numbers small:

$\frac{4}{5} \times \frac{5}{8} = \frac{4 \times \cancel{5}}{\cancel{5} \times 8} = \frac{4}{8} = \frac{1}{2}$

Remember: multiplying by a proper fraction (less than 1) always makes a number smaller.

Final Challenge 🚀

Mix everything you've learned!