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Subtraction: Mixed Numbers

Master subtraction of mixed numbers with clear explanations, practical tips, and interactive practice problems. Learn to (1) convert mixed numbers to improper fractions, (2) find a common denominator, (3) subtract the numerators, (4) simplify or convert back to a mixed number, and (5) check your work by adding the difference back.

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Subtraction: Mixed Numbers

Study Guide

Key Definition

A mixed number is a combination of a whole number and a fraction, such as $4 \frac{2}{3}$.

Important Notes

Convert mixed numbers to improper fractions before subtracting.
Ensure fractions have a common denominator.
Simplify your answer.
Borrow from the whole number if necessary.
Check your work by adding the subtracted amount back.

Mathematical Notation

$-$ represents subtraction

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

$\times$ or $*$ represents multiplication

$\div$ or $/$ represents division

Remember to use proper notation when solving problems

Why It Works

Changing mixed numbers into improper fractions lets you work with a single operation (subtraction of fractions) instead of juggling whole-number and fractional parts separately.

Remember

Always convert to improper fractions: $5 \frac{3}{4}$ becomes $\frac{23}{4}$.

Quick Reference

Improper Fraction:$\frac{a \times b + c}{b}$

Understanding Subtraction: Mixed Numbers

Choose your learning level

Watch & Learn

Video explanation of this concept

Beginner

Start here! Easy to understand

Beginner Explanation

Step 1: Convert each mixed number to an improper fraction.
Step 2: Rewrite the fractions with a common denominator.
Step 3: Subtract the numerators and keep the common denominator.
Step 4: Simplify and, if you like, turn the answer back into a mixed number.

Practice Problems

Test your understanding with practice problems

Quick Quiz

Single Choice Quiz

Beginner

What is $5 \frac{3}{4} - 3 \frac{1}{4}$?

Real-World Problem

Question Exercise

Intermediate

Teenager Scenario

If you have $7 \frac{3}{8}$ meters of rope and cut off $2 \frac{5}{8}$ meters, how much rope is left?

Thinking Challenge

Thinking Exercise

Intermediate

Think About This

Subtract $6 \frac{1}{2} - 4 \frac{3}{4}$ using improper fractions.

Challenge Quiz

Single Choice Quiz

Advanced

What is $8 \frac{5}{6} - 5 \frac{7}{12}$?

Recap

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Review key concepts and takeaways