➕ Adding Fractions

Learn how to add fractions step by step • Beginner Level

1. Adding Fractions with Like Denominators

When fractions have the same denominator (the bottom number), adding them is super easy! Think of it like adding slices of the same pizza - if all slices are the same size, you just count how many slices you have in total.

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

🔑 The Golden Rule:
When denominators are the same:
• ADD the numerators (top numbers)
• KEEP the denominator (bottom number) the same
• SIMPLIFY if possible

Example 1: Pizza Slices

You eat $\frac{2}{8}$ of a pizza and your friend eats $\frac{3}{8}$. How much pizza did you eat together?

The denominators are the same (8), so we can add directly

Add the numerators: 2 + 3 = 5

Keep the denominator: 8

Answer: $\frac{5}{8}$ of the pizza

Example 2: Simplifying the Result

\frac{1}{6} + \frac{3}{6} = \frac{4}{6} = \frac{2}{3}

Since 4 and 6 can both be divided by 2, we simplify $\frac{4}{6}$ to $\frac{2}{3}$

🎯 Practice Question

What is $\frac{3}{10} + \frac{4}{10}$?

A) $\frac{7}{20}$

B) $\frac{7}{10}$

C) $\frac{12}{10}$

D) $\frac{3}{5}$

2. Adding Fractions with Unlike Denominators (Finding LCD)

When fractions have different denominators, we need to make them the same first! It's like trying to add quarters and dimes - we need to convert them to the same unit (like cents) before adding.

🔑 What is LCD?
LCD = Least Common Denominator
• It's the smallest number that both denominators can divide into evenly
• Finding the LCD helps us rewrite fractions with the same denominator

Steps to Add Fractions with Unlike Denominators:

Find the LCD (least common denominator)

Convert each fraction to have the LCD

Add the numerators

Keep the LCD as the denominator

Simplify if possible

Example 3: Finding LCD

Add: $\frac{1}{3} + \frac{1}{4}$

Find LCD of 3 and 4:
    Multiples of 3: 3, 6, 9, 12...
    Multiples of 4: 4, 8, 12...
    LCD = 12

Convert $\frac{1}{3}$ to twelfths: $\frac{1}{3} = \frac{4}{12}$ (multiply top and bottom by 4)

Convert $\frac{1}{4}$ to twelfths: $\frac{1}{4} = \frac{3}{12}$ (multiply top and bottom by 3)

Add: $\frac{4}{12} + \frac{3}{12} = \frac{7}{12}$

Check if we can simplify: 7 and 12 have no common factors, so $\frac{7}{12}$ is final

Example 4: Quick LCD Method

Add: $\frac{2}{5} + \frac{1}{3}$

Quick way: If denominators don't share factors, LCD = 5 × 3 = 15

Convert: $\frac{2}{5} = \frac{6}{15}$ (multiply by $\frac{3}{3}$)

Convert: $\frac{1}{3} = \frac{5}{15}$ (multiply by $\frac{5}{5}$)

Add: $\frac{6}{15} + \frac{5}{15} = \frac{11}{15}$

🎯 Practice Question

What is $\frac{1}{2} + \frac{1}{6}$?

A) $\frac{2}{8}$

B) $\frac{1}{3}$

C) $\frac{2}{3}$

D) $\frac{4}{6}$

3. Word Problems with Adding Fractions

Real-world problems often involve adding fractions. The key is to identify what fractions you need to add and then apply the rules we've learned!

🔑 Problem-Solving Strategy:
1. Read carefully - What are we adding?
2. Identify the fractions
3. Check if denominators are same or different
4. Add using the appropriate method
5. Simplify and check if answer makes sense

Example 5: Recipe Problem

A recipe calls for $\frac{1}{4}$ cup of sugar for the cake and $\frac{1}{2}$ cup of sugar for the frosting. How much sugar do you need in total?

Identify fractions: $\frac{1}{4}$ and $\frac{1}{2}$

Different denominators, so find LCD: LCD of 4 and 2 is 4

Convert: $\frac{1}{2} = \frac{2}{4}$

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

Answer: You need $\frac{3}{4}$ cup of sugar total

Example 6: Distance Problem

Maria walked $\frac{2}{5}$ of a mile to the store and then $\frac{3}{10}$ of a mile to the park. How far did she walk in total?

Fractions to add: $\frac{2}{5}$ and $\frac{3}{10}$

Find LCD: 10 (since 10 is a multiple of 5)

Convert: $\frac{2}{5} = \frac{4}{10}$

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

Answer: Maria walked $\frac{7}{10}$ of a mile

Example 7: Time Problem

John studied math for $\frac{3}{4}$ hour and science for $\frac{5}{6}$ hour. How long did he study in total?

Fractions: $\frac{3}{4}$ and $\frac{5}{6}$

Find LCD: Multiples of 4: 4, 8, 12... Multiples of 6: 6, 12... LCD = 12

Convert: $\frac{3}{4} = \frac{9}{12}$ and $\frac{5}{6} = \frac{10}{12}$

Add: $\frac{9}{12} + \frac{10}{12} = \frac{19}{12}$

Simplify: $\frac{19}{12} = 1\frac{7}{12}$ hours (1 hour and 35 minutes)

🎯 Practice Question

A painter used $\frac{1}{3}$ gallon of blue paint and $\frac{1}{6}$ gallon of white paint. How much paint did he use in total?

A) $\frac{2}{9}$ gallon

B) $\frac{1}{2}$ gallon

C) $\frac{1}{3}$ gallon

D) $\frac{2}{6}$ gallon

🎯 Challenge Problem

A cake recipe uses $\frac{3}{8}$ cup of oil, $\frac{1}{4}$ cup of milk, and $\frac{1}{2}$ cup of water. How many cups of liquid ingredients are used in total?

A) $\frac{5}{8}$ cups

B) 1 cup

C) $1\frac{1}{8}$ cups

D) $\frac{3}{4}$ cups

🎯 Lesson Summary

Great job! You've learned how to add fractions. Remember:

✅ Same denominators: Just add the numerators and keep the denominator
✅ Different denominators: Find the LCD first, then convert and add
✅ Always simplify: Reduce your answer to lowest terms when possible
✅ Word problems: Identify the fractions, then follow the rules

Quick Tips:

💡 LCD is often just the product of the denominators when they share no factors
💡 Always check if your answer makes sense in word problems
💡 Practice finding LCDs - it gets easier with practice!