🎯⭐ INTERACTIVE LESSON

Multiplying and Dividing Fractions

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Multiplying and Dividing Fractions - Complete Interactive Lesson

Part 1: ✖️ Multiplying and Dividing Fractions

✖️➗ Multiplying and Dividing Fractions

Part 1 of 5 — Concept Introduction

In Grade 7 you put fractions to work. Two of the most powerful skills are multiplying and dividing them. The best part? Both come down to multiplying — once you learn one little trick for division, you are done.

Multiplying Fractions

To multiply two fractions, you do not need a common denominator. Just follow three steps:

Multiply the numerators (the tops).
Multiply the denominators (the bottoms).
Simplify the result.

In symbols:

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

Example:

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

Since $8$ and $15$ share no common factors, $\frac{8}{15}$ is already in simplest form. 🎉

The Reciprocal 🔄

The reciprocal of a fraction is what you get when you flip it upside down — the top and bottom numbers swap places.

Number	Reciprocal
$\frac{3}{4}$	$\frac{4}{3}$

Dividing Fractions

Here is the one trick you need: to divide by a fraction, multiply by its reciprocal (flip the second fraction).

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

Concept Check 🎯

Make sure you understand the division rule.

Part 2: 📝 Worked Examples

📝 Worked Examples

Part 2 of 5 — Worked Examples

Let's work two problems slowly, one step at a time.

Example 1: Multiplying Mixed Numbers

Solve $2\frac{1}{3} \times 1\frac{1}{2}$ .

Part 3: 🧭 Guided Practice

🧭 Guided Practice

Part 3 of 5 — Guided Practice

Work each problem carefully. Multiply straight across, or Keep, Change, Flip to divide. Simplify when you can.

Fill In the Steps 🔍

Complete the two steps for solving $\frac{4}{5} \div \frac{2}{3}$ .

Part 4: 🌍 Application & Word Problems

🌍 Application & Word Problems

Part 4 of 5 — Real-World Practice

Fractions show up everywhere — in recipes, in building projects, and when sharing things fairly. The tricky part of a word problem is deciding whether to multiply or divide.

Two Helpful Clues

Multiply when you want a fraction of an amount. Example: "How much is $\frac{2}{3}$ of $\frac{3}{4}$ cup?"

Part 5: Review & Challenge

🏆 Review & Challenge

Part 5 of 5 — Putting It All Together

You now have every tool for multiplying and dividing fractions. Here is the whole toolkit on one page.

Quick Reference Table

Operation	Rule	Example
Multiply	Multiply tops, multiply bottoms, simplify	$\frac{2}{3} \times \frac{4}{5} = \frac{8}{15}$

Key idea: A whole number like $5$ secretly equals $\frac{5}{1}$ , so its reciprocal is $\frac{1}{5}$ .

The reciprocal is the secret ingredient for dividing fractions, which you will use next.

$\frac{3}{4} \div \frac{2}{5} = \frac{3}{4} \times \frac{5}{2} = \frac{15}{8} = 1\frac{7}{8}$

Notice that the division turned into a multiplication the instant we flipped the second fraction. Many people remember this as "Keep, Change, Flip": keep the first fraction, change $\div$ to $\times$ , and flip the second fraction.

Step 1 — Convert to improper fractions. Always do this first with mixed numbers!

$2\frac{1}{3} = \frac{2 \times 3 + 1}{3} = \frac{7}{3}$
$1\frac{1}{2} = \frac{1 \times 2 + 1}{2} = \frac{3}{2}$

Step 2 — Multiply straight across:

$\frac{7}{3} \times \frac{3}{2} = \frac{7 \times 3}{3 \times 2} = \frac{21}{6}$

Step 3 — Simplify by dividing top and bottom by $3$ :

$\frac{21}{6} = \frac{7}{2} = 3\frac{1}{2}$

So $2\frac{1}{3} \times 1\frac{1}{2} = 3\frac{1}{2}$ . ✅

Example 2: Dividing Fractions

Solve $\frac{3}{4} \div \frac{2}{5}$ using Keep, Change, Flip.

Keep the first fraction: $\frac{3}{4}$

Change the sign: $\div$ becomes $\times$

Flip the second fraction: $\frac{2}{5}$ becomes $\frac{5}{2}$

Multiply:

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

Since $\frac{15}{8}$ is an improper fraction, rewrite it as a mixed number. $8$ goes into $15$ once with $7$ left over:

$\frac{15}{8} = 1\frac{7}{8}$

So $\frac{3}{4} \div \frac{2}{5} = 1\frac{7}{8}$ . 🎉

Your Turn 🧮

Solve $\frac{2}{3} \div \frac{4}{9}$ step by step. Type each answer in the box.

After you flip $\frac{4}{9}$ , what is the new second fraction? (Type it like $9/4$ .)
Multiply $\frac{2}{3} \times \frac{9}{4}$ simplifying. What is the result? (Type it like .)

Divide when you are splitting an amount into equal-size pieces and asking "how many fit?" Example: "How many

\frac{1}{4}

-cup scoops are in

2

cups?"

A recipe needs $\frac{3}{4}$ cup of sugar, but Maya is making only half the recipe. How much sugar does she need?

"Half of $\frac{3}{4}$ " means multiply:

$\frac{1}{2} \times \frac{3}{4} = \frac{3}{8} \text{ cup of sugar.}$

Recipe Problem 🍪

A baker has $\frac{3}{4}$ pound of chocolate. Each cookie needs $\frac{1}{8}$ pound of chocolate.

To find how many cookies the baker can make, divide: $\frac{3}{4} \div \frac{1}{8}$ .

After you flip $\frac{1}{8}$ , what is the new second fraction? (Type it like $8/1$ .)
Multiply $\frac{3}{4} \times \frac{8}{1}$ simplifying. What is the result? (Type it like .)

Word Problem Check 🎯

Remember: You never need a common denominator to multiply or divide — that rule is only for adding and subtracting! Now try the challenge questions below. 💪

Mixed Challenge 🎯

These questions blend everything you have learned.

Write the final simplified answer. (Type it like $3/2$ .)

How many whole cookies can the baker make? (Type a whole number.)