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Multiplying a Fraction by a Fraction

Master multiplying a fraction by a fraction with interactive lessons and practice problems! Designed for students like you!

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Multiplying a Fraction by a Fraction

Study Guide

Key Definition

To multiply fractions, multiply the numerators to get the new numerator and multiply the denominators to get the new denominator: $\frac{a}{b} \times \frac{c}{d} = \frac{a \times c}{b \times d}$, where b ≠ 0 and d ≠ 0.

Important Notes

Always multiply numerators with numerators and denominators with denominators: $\frac{a}{b} \times \frac{c}{d} = \frac{a \times c}{b \times d}$
Ensure denominators are non-zero (b ≠ 0, d ≠ 0).
Simplify your result if possible.
Visualize with diagrams to understand the concept better.
Multiplying by a fraction is like scaling by a part of a whole.
Remember that the order of multiplication doesn't affect the result.

Mathematical Notation

$\frac{a}{b}$ means a divided by b

$\times$ represents multiplication

$=$ represents equality

Remember to use proper notation when solving problems

Why It Works

By multiplying the numerators and denominators separately, you are effectively scaling the fractions together, combining their parts into a new fraction: $\frac{a \times c}{b \times d}$

Remember

Always simplify fractions when possible and visualize the process with diagrams for better understanding.

Quick Reference

Multiplication of Fractions:$\frac{a}{b} \times \frac{c}{d} = \frac{a \times c}{b \times d}$ (simplify if possible)

Understanding Multiplying a Fraction by a Fraction

Choose your learning level

Watch & Learn

Video explanation of this concept

Beginner

Start here! Easy to understand

Beginner Explanation

Simple explanation with $\frac{2}{3} \times \frac{5}{7} = \frac{10}{21}$

Practice Problems

Test your understanding with practice problems

Quick Quiz

Single Choice Quiz

Beginner

What is $\frac{2}{3} \times \frac{5}{7}$?

Real-World Problem

Question Exercise

Intermediate

Teenager Scenario

If you eat $\frac{2}{3}$ of a pizza and then $\frac{5}{7}$ of that portion, how much of the whole pizza did you eat?

Thinking Challenge

Thinking Exercise

Intermediate

Think About This

If $\frac{3}{4}$ of a group is boys, and $\frac{2}{5}$ of the boys play soccer, what fraction of the group plays soccer?

Challenge Quiz

Single Choice Quiz

Advanced

What is $\frac{7}{8} \times \frac{4}{9}$?

Recap

Watch & Learn

Review key concepts and takeaways