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Adding and Subtracting Fractions with Like Denominators

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Adding and Subtracting Fractions with Like Denominators

Study Guide

Key Definition

When we add or subtract fractions with identical denominators, we simply perform the operation on the numerators, and keep the denominator as it is. For example, $\frac{2}{3}$ + $\frac{5}{3}$ = $\frac{7}{3}$.

Important Notes

Always check if the fractions have the same denominator.
If the answer is not in lowest terms, it should be simplified.
To subtract fractions, simply subtract the numerators and keep the denominator the same.

Mathematical Notation

$\frac{a}{b}$ denotes a fraction where 'a' is the numerator and 'b' is the denominator.

Fractions are parts of a whole.

Why It Works

This works because having like denominators means we are dealing with the same sized parts. So, it's just a matter of counting how many of these equal parts we have.

Remember

The denominator does not change when adding or subtracting fractions with like denominators. It's only the numerators that are added or subtracted.

Quick Reference

Adding Fractions:$\frac{a}{c} + \frac{b}{c} = \frac{a+b}{c}$

Subtracting Fractions:$\frac{a}{c} - \frac{b}{c} = \frac{a-b}{c}$

Understanding Adding and Subtracting Fractions with Like Denominators

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Video explanation of this concept

Beginner

Start here! Easy to understand

Beginner Explanation

When we add or subtract fractions with the same denominator, we only add or subtract the numerators, while the denominator stays the same. For example, $\frac{2}{3}$ + $\frac{5}{3}$ = $\frac{7}{3}$.

Practice Problems

Test your understanding with practice problems

Quick Quiz

Single Choice Quiz

Beginner

What is $\frac{2}{7}$ + $\frac{3}{7}$?

Real-World Problem

Question Exercise

Intermediate

Pizza Scenario

You have a pizza that is cut into 8 equal slices. You eat 3 slices and your friend eats 2 slices. How much of the pizza is left?

Thinking Challenge

Thinking Exercise

Intermediate

Think About This

Can you subtract a bigger fraction from a smaller fraction if they have the same denominator? What will be the result?

Challenge Quiz

Single Choice Quiz

Advanced

What is $\frac{3}{5}$ + $\frac{-2}{5}$?

Recap

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Review key concepts and takeaways