Subtracting Fractions

Learn how to subtract fractions with the same and different denominators using visual models and step-by-step methods.

Elementary25 minLesson
Printable worksheet

Definition

Subtracting fractions means finding the difference between two fractional amounts.
Same Denominators (Like Fractions): When fractions have the same denominator, subtract the numerators and keep the denominator:
ac−bc=a−bc\frac{a}{c} - \frac{b}{c} = \frac{a - b}{c}
Different Denominators (Unlike Fractions): First find a common denominator, convert both fractions, then subtract:
ab−cd=ad−bcbd\frac{a}{b} - \frac{c}{d} = \frac{ad - bc}{bd}
Always simplify your answer if possible!

Try it now

What is 58−28\frac{5}{8} - \frac{2}{8}?

Worked Examples

Calculate 58−28\frac{5}{8} - \frac{2}{8}
1

Check the denominators

Both fractions have denominator 8 → Same denominator - ready to subtract
2

Subtract the numerators

5−2=35 - 2 = 3 → New numerator is 3
3

Keep the same denominator

5−28=38\frac{5 - 2}{8} = \frac{3}{8}
4

Check if simplification is needed

GCF of 3 and 8 is 1 → Already in simplest form

Common Mistakes

Subtracting both numerators AND denominators

Why it's wrong: Students sometimes apply whole number subtraction rules to fractions. 58−28≠30\frac{5}{8} - \frac{2}{8} \neq \frac{3}{0}!

Correct: Only subtract the numerators. The denominator tells us the size of the pieces and stays the same: 58−28=38\frac{5}{8} - \frac{2}{8} = \frac{3}{8}

Forgetting to find a common denominator

Why it's wrong: You cannot subtract pieces of different sizes directly. 12−13≠0−1\frac{1}{2} - \frac{1}{3} \neq \frac{0}{-1}!

Correct: Always convert to the same denominator first: 12−13=36−26=16\frac{1}{2} - \frac{1}{3} = \frac{3}{6} - \frac{2}{6} = \frac{1}{6}

Using the wrong common denominator

Why it's wrong: Multiplying denominators works but may create larger numbers than necessary.

Correct: Find the LCD (least common denominator) for easier calculations. For 14\frac{1}{4} and 16\frac{1}{6}, use 12 instead of 24.

Forgetting to simplify the final answer

Why it's wrong: An unsimplified answer like 48\frac{4}{8} is not wrong, but 12\frac{1}{2} is the standard form.

Correct: Always check if your answer can be simplified by finding the GCF of the numerator and denominator.

Watch a video explanation

The same topic explained by another teacher, if a video helps you more.

How to Add, Subtract, Multiply, and Divide Fractions (Step-by-Step)

by Understand The Math

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Interactive Visual

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Fraction Number Line

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Click on tick marks to select fractions.

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Practice Problems

16 problems
Problem 1 of 16
Easy
What is 58−28\frac{5}{8} - \frac{2}{8}?

Why It Matters

Subtracting fractions is essential for everyday situations:
  • Cooking: A recipe needs 34\frac{3}{4} cup of flour, but you only want to use 14\frac{1}{4} cup less
  • Time: If you have 56\frac{5}{6} of an hour left and spend 13\frac{1}{3} of an hour studying, how much time remains?
  • Money: You had 78\frac{7}{8} of your allowance saved and spent 38\frac{3}{8} on a book
  • Sports: A runner completed 23\frac{2}{3} of a race yesterday and 16\frac{1}{6} more today - what's the difference?
Understanding fraction subtraction helps you solve real problems involving parts of wholes!

Real World Applications

Cooking and Recipes

Cooks often need to adjust recipes by subtracting ingredient amounts.

Example:

A recipe calls for 34\frac{3}{4} cup of sugar, but you want to reduce it by 14\frac{1}{4} cup. You need 34−14=24=12\frac{3}{4} - \frac{1}{4} = \frac{2}{4} = \frac{1}{2} cup.

1Try It Yourself

You have 78\frac{7}{8} cup of flour and use 12\frac{1}{2} cup for cookies.

How much flour do you have left?

Step 1: Write the mathematical expression

Calculate: 78−12\frac{7}{8} - \frac{1}{2}

Time Management

Calculating remaining time often involves subtracting fractions of hours.

Example:

You have 34\frac{3}{4} of an hour for homework. After 13\frac{1}{3} hour of math, you have 34−13=912−412=512\frac{3}{4} - \frac{1}{3} = \frac{9}{12} - \frac{4}{12} = \frac{5}{12} hour left.

2Try It Yourself

A movie is 56\frac{5}{6} of the way through. Earlier it was 12\frac{1}{2} of the way through.

What fraction of the movie played between these times?

Step 1: Write the mathematical expression

Calculate: 56−12\frac{5}{6} - \frac{1}{2}

Key Takeaways

  • 1For same denominators: subtract numerators, keep the denominator: ac−bc=a−bc\frac{a}{c} - \frac{b}{c} = \frac{a-b}{c}
  • 2For different denominators: find the LCD, convert both fractions, then subtract
  • 3The LCD (Least Common Denominator) is the smallest number both denominators divide into evenly
  • 4Always simplify your final answer by dividing numerator and denominator by their GCF
  • 5Never subtract denominators - they represent the size of the pieces, not the quantity

Frequently Asked Questions

Yes! If you subtract a larger fraction from a smaller one, the result is negative. For example, 14−34=−24=−12\frac{1}{4} - \frac{3}{4} = -\frac{2}{4} = -\frac{1}{2}.
Yes! If you subtract a larger fraction from a smaller one, the result is negative. For example, 14−34=−24=−12\frac{1}{4} - \frac{3}{4} = -\frac{2}{4} = -\frac{1}{2}.
Your answer will still be correct, but you'll work with larger numbers. For example, using 24 instead of 12 for 14−16\frac{1}{4} - \frac{1}{6} gives 624−424=224=112\frac{6}{24} - \frac{4}{24} = \frac{2}{24} = \frac{1}{12} - same answer, more work!
Convert the whole number to a fraction first. For 2−342 - \frac{3}{4}, write 2=842 = \frac{8}{4}, then 84−34=54=114\frac{8}{4} - \frac{3}{4} = \frac{5}{4} = 1\frac{1}{4}.

Glossary

Like fractions
Fractions with the same denominator, such as 25\frac{2}{5} and 35\frac{3}{5}
Unlike fractions
Fractions with different denominators, such as 13\frac{1}{3} and 14\frac{1}{4}
LCD (Least Common Denominator)
The smallest number that both denominators divide into evenly
Simplify
Reduce a fraction to lowest terms by dividing numerator and denominator by their GCF
Equivalent fractions
Fractions that represent the same value, like 24\frac{2}{4} and 12\frac{1}{2}

Formula Card

Same Denominator

ac−bc=a−bc\frac{a}{c} - \frac{b}{c} = \frac{a - b}{c}

Subtract numerators, keep the denominator

Different Denominators

ab−cd=ad−bcbd\frac{a}{b} - \frac{c}{d} = \frac{ad - bc}{bd}

Cross-multiply and subtract (or use LCD method)

Today's challengeOne problem, three tries

More in This Topic

Adding Fractions with the Same Denominator

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Adding Fractions with Different Denominators

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Multiplying Fractions

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Dividing Fractions

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