Multiplying Fractions by Whole Numbers

✖️ Multiplying Fractions by Whole Numbers

Multiplying a fraction by a whole number just means adding that fraction over and over again.

When you see $3 \times \frac{1}{4}$, read it as "3 groups of $\frac{1}{4}$." That is the same as:

$\frac{1}{4} + \frac{1}{4} + \frac{1}{4} = \frac{3}{4}$

So multiplying by a whole number is really just a shortcut for repeated addition. Instead of adding the fraction many times, you can multiply!

What stays the same?

• The denominator (bottom number) does not change.
• Only the numerator (top number) gets bigger.

Picture It: Repeated Addition

Let's look at $4 \times \frac{1}{5}$. That means we want 4 copies of $\frac{1}{5}$.

⭐ The Simple Rule

To multiply a whole number by a fraction:

1. Multiply the whole number by the numerator (top number).
2. Keep the denominator (bottom number) the same.
3. Simplify if you can.

Example: $5 \times \frac{2}{3}$

• Multiply the tops: $5 \times 2 = 10$

Concept Check 🎯

Make sure the big idea makes sense before we move on.

🛠️ Worked Examples

Let's walk through the rule step by step. Remember: multiply the tops, keep the bottom.

Example 1: $3 \times \frac{1}{4}$

• Multiply the tops: $3 \times 1 = 3$

🧭 Guided Practice

Choose the correct product for each one. Multiply the tops and keep the bottom!

Finish the Steps 🔍

Use what you know about the rule to complete each statement.

🌍 Real-World Word Problems

We multiply fractions by whole numbers all the time in real life!

🍪 Baking cookies

You make 3 batches of cookies. Each batch needs $\frac{2}{3}$ cup of sugar.

$3 \times \frac{2}{3} = \frac{6}{3} = 2 \text{ cups of sugar} ✓$

🏆 Review & Challenge

You've learned how to multiply a fraction by a whole number. Here's the big picture in one table:

Step	What to do	Example: $5 \times \frac{2}{3}$
1	Multiply whole number × numerator	$5\times 2=10$