Adding Fractions with Like Denominators

Adding Fractions with Like Denominators 🍕

Every fraction has two parts:

• The numerator is the top number. It tells you how many pieces you have.
• The denominator is the bottom number. It tells you what size the pieces are.

Like denominators just means the bottom numbers are the same. When the bottoms match, the pieces are all the same size — so they are easy to add!

Examples of like denominators:

• $\frac{1}{4}$ and $\frac{3}{4}$ — both have a 4 on the bottom
• $\frac{2}{5}$ and $\frac{4}{5}$ — both have a 5 on the bottom
• $\frac{3}{8}$ and $\frac{5}{8}$ — both have an 8 on the bottom

Think of it like counting the same kind of pieces. If everything is cut into eighths, you can just count the eighths!

The Simple Rule ✏️

When the denominators are the same, follow these steps:

1. Add the numerators (the top numbers).
2. Keep the denominator the same (do not add the bottoms!).
3. Simplify the answer if you can.

Here it is as a picture:

$\frac{1}{8} + \frac{3}{8} = \frac{1 + 3}{8} = \frac{4}{8}$

Big idea: The denominator tells you the size of the slice. The slices don't change size when you add them — you just have more of them.

Visual Model: Pizza Slices 🍕

Problem: $\frac{1}{8} + \frac{3}{8}$

Imagine a pizza cut into 8 equal slices:

• You eat 1 slice → $\frac{1}{8}$
• Your friend eats 3 slices → $\frac{3}{8}$

You:    [■]            = 1/8
Friend: [■ ■ ■]        = 3/8
Total:  [■ ■ ■ ■]      = 4/8

All the slices are the same size (eighths), so you just count them all together: $1 + 3 = 4$ slices out of $8$.

$\frac{1}{8} + \frac{3}{8} = \frac{4}{8}$

Notice the bottom number stayed 8 the whole time. We never add the denominators!

Quick Check ✅

Let's make sure the main idea is clear.

Step-by-Step Examples 📝

Let's work through a few problems carefully, one step at a time.

Example 1: $\frac{2}{5} + \frac{1}{5}$

• Step 1 — Check the denominators: both are $5$ ✓
• Step 2 — Add the numerators: $2 + 1 = 3$
• Step 3 — Keep the denominator: $5$
• Step 4 — Write the answer: $\frac{3}{5}$

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

Example 2: $\frac{3}{10} + \frac{4}{10}$

• Step 1 — Denominators: both are $10$ ✓
• Step 2 — Add the numerators: $3 + 4 = 7$
• Step 3 — Keep the denominator: $10$
• Step 4 — Answer: $\frac{7}{10}$

$\frac{3}{10} + \frac{4}{10} = \frac{7}{10}$

Using a Number Line 📏

You can also see fraction addition on a number line. Try $\frac{1}{4} + \frac{2}{4}$.

0 ----1/4----2/4----3/4----1
       ↑              ↑
     Start          End
       └── jump +2/4 ──┘

• Start at $\frac{1}{4}$.
• Jump $2$ more fourths.
• You land on $\frac{3}{4}$.

$\frac{1}{4} + \frac{2}{4} = \frac{3}{4}$

Each jump is one fourth. You start with $1$ fourth and add $2$ more — that's $3$ fourths in all.

Your Turn — Fill in the Blanks ✍️

Solve each one and type your answer as a fraction (for example: 5/7). Keep the same denominator!

1. $\frac{2}{7} + \frac{3}{7} =$ ______

2. $\frac{4}{9} + \frac{2}{9} =$ ______

3. $\frac{5}{12} + \frac{4}{12} =$ ______

Guided Practice — Choose the Answer 🎯

Add the fractions. Remember: add the tops, keep the bottom.

Build the Answer 🧩

For the problem $\frac{2}{9} + \frac{5}{9}$, choose the correct numerator and the correct denominator for the answer.

Fractions in the Real World 🌎

Adding fractions with like denominators shows up all the time in everyday life.

🥣 Measuring Cups

A recipe needs $\frac{1}{3}$ cup of oil, and then $\frac{2}{3}$ cup more.

$\frac{1}{3} + \frac{2}{3} = \frac{3}{3} = 1 \text{ cup}$

🚶 Walking Distance

You walk $\frac{2}{10}$ mile to the park, then $\frac{3}{10}$ mile farther.

$\frac{2}{10} + \frac{3}{10} = \frac{5}{10} \text{ mile}$

⏰ Reading Time

You read $\frac{1}{4}$ hour before lunch and $\frac{2}{4}$ hour after.

$\frac{1}{4} + \frac{2}{4} = \frac{3}{4} \text{ hour}$

In each story, the denominators already match — so just add the tops and keep the bottom!

Word Problem Practice ✍️

Read each story, add the fractions, and type your answer as a fraction (for example: 5/8). Keep the denominator the same.

1. Maya colored $\frac{3}{8}$ of her picture red and $\frac{4}{8}$ blue. What fraction is colored in all?

2. A water jug was $\frac{2}{6}$ full, then you added $\frac{3}{6}$ more. How full is it now?

3. Sam ran $\frac{4}{10}$ mile, then ran $\frac{5}{10}$ mile more. How far did he run total?

One More Story 📖

Review: What You Learned 🌟

You can now add fractions that have the same denominator. Here's the whole idea in one table:

Remember the golden rule: add the numerators, keep the denominator, and simplify when you can.

• To simplify, divide the top and bottom by the same number. Example: $\frac{4}{6}$ — both $4$ and $6$ divide by $2$, giving $\frac{2}{3}$.
• An improper fraction like $\frac{9}{8}$ is greater than $1$ whole. Since $\frac{8}{8} = 1$, that leaves $\frac{1}{8}$ more, so $\frac{9}{8} = 1\frac{1}{8}$.

Challenge — Mix It All Together 🏆

These problems combine adding, simplifying, and going past one whole.