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Multiplying a Fraction by a Whole Number

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Multiplying a Fraction by a Whole Number

Study Guide

Key Definition

To multiply a fraction by a whole number, multiply the numerator of the fraction by the whole number and keep the denominator same: $\frac{a}{b} \times n = \frac{a \times n}{b}$

Important Notes

When multiplying, only the numerator changes: $\frac{a \times n}{b}$
Think of multiplication as repeated addition: $n \times \frac{a}{b} = \frac{a}{b} + \frac{a}{b} + ... + \frac{a}{b} = \frac{a \times n}{b}$
Fractions represent division: $\frac{a}{b} = a \div b$
Whole numbers are integers: 1, 2, 3...
Decimals and mixed numbers are not integers, so this method applies to fractions (a/b form) and whole numbers.

Mathematical Notation

$\times$ represents multiplication

$\div$ or $/$ represents division

$\frac{a}{b}$ represents a fraction

$a \times n$ means multiplying a by n

Remember to use proper notation when solving problems

Why It Works

Multiplying a fraction by a whole number is like adding the fraction to itself multiple times: $5 \times \frac{1}{11} = \frac{1}{11} + \frac{1}{11} + \frac{1}{11} + \frac{1}{11} + \frac{1}{11}$

Remember

Always multiply the numerator only, keeping the denominator the same: $\frac{a \times n}{b}$

Quick Reference

Multiplying a Fraction:$\frac{a}{b} \times n = \frac{a \times n}{b}$

Understanding Multiplying a Fraction by a Whole Number

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Video explanation of this concept

Beginner

Start here! Easy to understand

Beginner Explanation

To multiply a fraction by a whole number, multiply the numerator by the whole number: $\frac{a \times n}{b}$

Practice Problems

Test your understanding with practice problems

Quick Quiz

Single Choice Quiz

Beginner

What is $5 \times \frac{1}{11}$?

Real-World Problem

Question Exercise

Intermediate

Teenager Scenario

If you eat $\frac{1}{4}$ of a pizza every day, how much pizza do you eat in 5 days?

Thinking Challenge

Thinking Exercise

Intermediate

Think About This

How do you simplify $\frac{15}{9}$ after multiplying $3 \times \frac{5}{9}$?

Challenge Quiz

Single Choice Quiz

Advanced

What is $7 \times \frac{2}{5}$?

Recap

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Review key concepts and takeaways