Adding and Subtracting Fractions

➕ Adding & Subtracting Fractions

A fraction is just a way to talk about parts of a whole. The bottom number, called the denominator, tells you how many equal pieces the whole is cut into. The top number, called the numerator, tells you how many of those pieces you have.

When two fractions have the same denominator, the pieces are all the same size. That makes them super easy to combine!

The Big Rule

When the denominators match (we call these like denominators), you simply add or subtract the numerators and keep the denominator the same:

$\frac{a}{c} + \frac{b}{c} = \frac{a + b}{c}$

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

Think of it like pizza slices: if every slice is one-fifth of a pizza, then 2 slices plus 1 slice = 3 slices. The size of each slice never changes!

Two Quick Examples 🍕

Adding:

$\frac{2}{5} + \frac{1}{5} = \frac{2 + 1}{5} = \frac{3}{5}$

We added the numerators ($2 + 1 = 3$) and kept the denominator $5$.

Subtracting:

$\frac{7}{8} - \frac{3}{8} = \frac{7 - 3}{8} = \frac{4}{8} = \frac{1}{2}$

We subtracted the numerators ($7 - 3 = 4$) and kept the denominator $8$. Then we simplified $\frac{4}{8}$ to $\frac{1}{2}$ because both $4$ and $8$ can be divided by $4$.

⭐ Always simplify your answer when you can! A simplified fraction uses the smallest numbers possible.

The #1 Mistake to Avoid 🚫

The most common mistake is adding the denominators. Don't do it!

For example, $\frac{2}{5} + \frac{1}{5}$ is not $\frac{3}{10}$. The denominator stays $5$, so the answer is $\frac{3}{5}$.

Remember: the denominator is the size of the slice. Combining slices never changes their size!

Concept Check 🎯

Let's make sure the big idea is locked in.

🧮 Worked Examples

Let's slow down and work through problems one step at a time.

Example 1: Adding

$\frac{3}{7} + \frac{2}{7}$

Step 1 — Check the denominators. Both are $7$, so they match. We're good to go!

Step 2 — Add the numerators. $3 + 2 = 5$.

Step 3 — Keep the denominator. It stays $7$.

$\frac{3}{7} + \frac{2}{7} = \frac{5}{7}$

Step 4 — Simplify if possible. $5$ and $7$ share no common factor, so $\frac{5}{7}$ is already in simplest form. ✅

Example 2: Subtracting and Simplifying

$\frac{9}{10} - \frac{3}{10}$

Step 1 — Check the denominators. Both are $10$. They match!

Step 2 — Subtract the numerators. $9 - 3 = 6$.

Step 3 — Keep the denominator. It stays $10$.

$\frac{9}{10} - \frac{3}{10} = \frac{6}{10}$

Step 4 — Simplify. Both $6$ and $10$ can be divided by $2$:

$\frac{6}{10} = \frac{6 \div 2}{10 \div 2} = \frac{3}{5}$

So the final answer is $\frac{3}{5}$. 🎉

Your Turn ✏️

Type just the numerator of each answer (the bottom number is given for you).

1. $\frac{1}{6} + \frac{4}{6} = \frac{?}{6}$

2. $\frac{5}{9} + \frac{2}{9} = \frac{?}{9}$

3. $\frac{8}{11} - \frac{3}{11} = \frac{?}{11}$

🤝 Guided Practice

Work through these two questions. Take your time and remember the steps!

Fill in the Blanks 🔍

Choose the correct value for each blank.

• $\frac{3}{10} + \frac{4}{10} = \frac{?}{10}$
• $\frac{7}{12} - \frac{2}{12} = \frac{?}{12}$

🌍 Fractions in Real Life

Fractions show up everywhere — in pizza, pies, measuring cups, and even how far you've walked!

Pizza Party 🍕

Imagine a pizza cut into 8 equal slices. Each slice is $\frac{1}{8}$ of the pizza.

• Maria eats $\frac{3}{8}$ of the pizza.
• Her brother eats $\frac{2}{8}$ of the pizza.

How much did they eat together?

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

Together they ate $\frac{5}{8}$ of the pizza.

How much is left over? The whole pizza is $\frac{8}{8}$, so:

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

There's $\frac{3}{8}$ of the pizza left for later! 😋

Word Problem Workout ✏️

A water bottle is marked in fourths. Type just the numerator for each answer.

1. Sam drinks $\frac{1}{4}$ of his bottle in the morning and $\frac{2}{4}$ at lunch. How much has he drunk in all? $\frac{?}{4}$

2. A ribbon is $\frac{7}{12}$ of a meter. You cut off $\frac{4}{12}$ of a meter. How much ribbon is left? $\frac{?}{12}$

3. Lily reads $\frac{2}{6}$ of her book on Monday and $\frac{3}{6}$ on Tuesday. How much has she read total? $\frac{?}{6}$

Story Check 📖

🏆 Review & Challenge

You've learned how to add and subtract fractions with like denominators. Here's everything in one quick table:

Bonus idea — fractions greater than 1. Sometimes the answer is more than a whole. For example, $\frac{5}{3}$ means $5 \div 3 = 1$ remainder $2$, so $\frac{5}{3} = 1\frac{2}{3}$.

📌 Remember the rule: You can only add or subtract fractions that have the same denominator. In Grade 5, you'll learn how to handle different denominators!

Final Challenge 🚀

Mix it all together!