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 $\frac{1}{5}$.

$\frac{1}{5} + \frac{1}{5} + \frac{1}{5} + \frac{1}{5} = \frac{4}{5}$

Imagine 4 strips, each with one out of five pieces shaded:

[■][□][□][□][□]   ← 1/5
[■][□][□][□][□]   ← 1/5
[■][□][□][□][□]   ← 1/5
[■][□][□][□][□]   ← 1/5
─────────────────
4 shaded fifths   =  4/5

We added the numerators ($1+1+1+1 = 4$) and kept the denominator ($5$). Answer: $\frac{4}{5}$ ✓

⭐ 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: $5 \times 2 = 10$
• Keep the bottom: $3$
• Answer: $\frac{10}{3}$

That's it — fast and easy!

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: $3 \times 1 = 3$
• Keep the bottom: $4$
• Answer: $\frac{3}{4}$ ✓

Example 2: $6 \times \frac{2}{5}$

• Multiply the tops: $6 \times 2 = 12$
• Keep the bottom: $5$
• Answer: $\frac{12}{5}$, which is the mixed number $2\frac{2}{5}$ ✓

Example 3: $4 \times \frac{3}{8}$

• Multiply the tops: $4 \times 3 = 12$
• Keep the bottom: $8$
• That gives $\frac{12}{8}$. Now simplify: $\frac{12}{8} = \frac{3}{2} = 1\frac{1}{2}$ ✓

Another Way to See It

Any whole number can be written as a fraction over 1:

• $3 = \frac{3}{1}$
• $5 = \frac{5}{1}$
• $7 = \frac{7}{1}$

Then you multiply tops together and bottoms together.

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

• Tops: $4 \times 2 = 8$
• Bottoms: $1 \times 3 = 3$
• Answer: $\frac{8}{3} = 2\frac{2}{3}$ ✓

Same answer — just a different path!

Your Turn 🧮

Fill in each answer. Type fractions like 12/5 and whole numbers like 6.

1. $2 \times \frac{3}{7} = ?$ (write as a fraction)

2. $5 \times \frac{1}{8} = ?$ (write as a fraction)

3. $3 \times \frac{2}{9} = ?$ (write as a fraction)

🧭 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.

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

🏃 Running

You run $\frac{3}{4}$ mile each day for 5 days.

$5 \times \frac{3}{4} = \frac{15}{4} = 3\frac{3}{4} \text{ miles} ✓$

🎀 Cutting ribbon

You need 4 pieces of ribbon, each $\frac{5}{8}$ yard long.

$4 \times \frac{5}{8} = \frac{20}{8} = 2\frac{1}{2} \text{ yards} ✓$

The trick: find the whole number (how many groups) and the fraction (size of each group), then multiply!

Solve the Problems ✏️

Type fractions like 6/3 exactly as asked.

1. A recipe uses $\frac{1}{3}$ cup of flour. You make 4 batches. How much flour total? (write as a fraction)

2. A snail crawls $\frac{2}{5}$ meter each hour. How far in 3 hours? (write as a fraction)

3. Each gift needs $\frac{1}{6}$ roll of tape. How much tape for 5 gifts? (write as a fraction)

Word Problem Challenge 🎯

🏆 Review & Challenge

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

Remember:

• It's just repeated addition.
• The denominator never changes.
• If the top ends up bigger than the bottom, you can write a mixed number.

Now try these challenge questions that mix everything together!

Mixed Challenge 🎯