Multiplying Fractions

What You’ll Learn

In this lesson you’ll learn how to multiply fractions by fractions, whole numbers by fractions, and mixed numbers, including simplifying before or after.

The Concept

Multiplying fractions is straightforward: multiply numerators together, multiply denominators together, then simplify.

Rule:

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

Example: $\frac{2}{3} \times \frac{3}{4} = \frac{6}{12} = \frac{1}{2}$

• You can simplify first (cross-cancel): 2 and 4 share 2, 3 and 3 share 3 → $\frac{1}{1} \times \frac{1}{2} = \frac{1}{2}$
• Whole number × fraction: $\frac{3}{1} \times \frac{2}{5} = \frac{6}{5} = 1 \frac{1}{5}$
• Mixed numbers: Convert to improper first, multiply, then convert back if needed.

No common denominator needed, unlike adding/subtracting.

Worked Examples

Multiply $\frac{3}{4} \times \frac{5}{6}$

1. Numerators: $3 \times 5 = 15$
2. Denominators: $4 \times 6 = 24$
3. $\frac{15}{24}$ - simplify by dividing by 3 → $\frac{5}{8}$

Now mixed: $2 \frac{1}{2} \times 1 \frac{1}{3}$

1. Convert to improper: $\frac{5}{2} \times \frac{4}{3}$
2. $\frac{5 \times 4}{2 \times 3} = \frac{20}{6} = \frac{10}{3} = 3 \frac{1}{3}$

Real-World Applications

Multiplying fractions scales recipes (half a batch: $\frac{1}{2} \times$ ingredients), calculates portions ($\frac{3}{4}$ of a pizza slice), or figures partial costs ($\frac{2}{3}$ of a 45 dollar bill for splitting). Example: A recipe calls for $\frac{3}{4}$ cup sugar for 12 cookies. For 4 cookies: $\frac{3}{4} \times \frac{1}{3} = \frac{1}{4}$ cup needed.

You’ve Got This

Multiplying fractions is one of the easier operations. Just multiply across and simplify. Think of it as “of” (like “half of” means $\times \frac{1}{2}$). Cross-cancel first to keep numbers small. Practice with simple fractions and you’ll see how quick it is.

Quiz

What is 1/2 × 3/5?

• A.3/10
• B.3/7
• C.4/10
• D.3/5

Multiply 2/3 × 3/4.

• A.6/12
• B.5/7
• C.1/2
• D.6/7

A recipe uses 3/4 cup flour for 1 batch. For 1/2 batch, how much flour?

• A.3/8 cup
• B.6/8 cup
• C.3/2 cup
• D.1/2 cup

Multiply 2 1/2 × 1 1/3.

• A.3 1/2
• B.3 1/3
• C.2 5/6
• D.4 1/6

What is 4/5 × 5/8?

• A.1/2
• B.20/40
• C.4/8
• D.9/13