Subtracting Fractions

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

Elementary25 minLesson

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:

\frac{a}{c} - \frac{b}{c} = \frac{a - b}{c}

Different Denominators (Unlike Fractions): First find a common denominator, convert both fractions, then subtract:

\frac{a}{b} - \frac{c}{d} = \frac{ad - bc}{bd}

Always simplify your answer if possible!

Try it now

What is

\frac{5}{8} - \frac{2}{8}

Worked Examples

Calculate $\frac{5}{8} - \frac{2}{8}$

Check the denominators

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

Subtract the numerators

$5 - 2 = 3$ → New numerator is 3

Keep the same denominator

$\frac{5 - 2}{8} = \frac{3}{8}$

Check if simplification is needed

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

Answer: $\frac{5}{8} - \frac{2}{8} = \frac{3}{8}$

Common Mistakes

Subtracting both numerators AND denominators

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

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

Forgetting to find a common denominator

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

Correct: Always convert to the same denominator first: $\frac{1}{2} - \frac{1}{3} = \frac{3}{6} - \frac{2}{6} = \frac{1}{6}$

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 $\frac{1}{4}$ and $\frac{1}{6}$ , use 12 instead of 24.

Forgetting to simplify the final answer

Why it's wrong: An unsimplified answer like $\frac{4}{8}$ is not wrong, but $\frac{1}{2}$ 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
Watch on YouTube

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Practice Problems

16 problems

Problem 1 of 16

Easy

What is $\frac{5}{8} - \frac{2}{8}$ ?

Why It Matters

Subtracting fractions is essential for everyday situations:

Cooking: A recipe needs $\frac{3}{4}$ cup of flour, but you only want to use $\frac{1}{4}$ cup less
Time: If you have $\frac{5}{6}$ of an hour left and spend $\frac{1}{3}$ of an hour studying, how much time remains?
Money: You had $\frac{7}{8}$ of your allowance saved and spent $\frac{3}{8}$ on a book
Sports: A runner completed $\frac{2}{3}$ of a race yesterday and $\frac{1}{6}$ 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 $\frac{3}{4}$ cup of sugar, but you want to reduce it by $\frac{1}{4}$ cup. You need $\frac{3}{4} - \frac{1}{4} = \frac{2}{4} = \frac{1}{2}$ cup.

1Try It Yourself

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

How much flour do you have left?

Step 1: Write the mathematical expression

Calculate: $\frac{7}{8} - \frac{1}{2}$

Time Management

Calculating remaining time often involves subtracting fractions of hours.

Example:

You have $\frac{3}{4}$ of an hour for homework. After $\frac{1}{3}$ hour of math, you have $\frac{3}{4} - \frac{1}{3} = \frac{9}{12} - \frac{4}{12} = \frac{5}{12}$ hour left.

2Try It Yourself

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

What fraction of the movie played between these times?

Step 1: Write the mathematical expression

Calculate: $\frac{5}{6} - \frac{1}{2}$

Key Takeaways

1For same denominators: subtract numerators, keep the denominator: $\frac{a}{c} - \frac{b}{c} = \frac{a-b}{c}$
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,

\frac{1}{4} - \frac{3}{4} = -\frac{2}{4} = -\frac{1}{2}

Glossary

Like fractions: Fractions with the same denominator, such as $\frac{2}{5}$ and $\frac{3}{5}$
Unlike fractions: Fractions with different denominators, such as $\frac{1}{3}$ and $\frac{1}{4}$
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 $\frac{2}{4}$ and $\frac{1}{2}$

Formula Card

Same Denominator

\frac{a}{c} - \frac{b}{c} = \frac{a - b}{c}

Subtract numerators, keep the denominator

Different Denominators

\frac{a}{b} - \frac{c}{d} = \frac{ad - bc}{bd}

Cross-multiply and subtract (or use LCD method)