Grade: Grade 5 Subject: Mathematics Unit: Fraction Operations SAT: Algebra ACT: Math

Adding & Subtracting Fractions

Master the art of combining and separating fractions! Learn to work with like and unlike denominators to solve real-world problems.

Understanding Fraction Addition & Subtraction

The Golden Rule of Fractions

To add or subtract fractions, the denominators (bottom numbers) MUST be the same! When denominators match, just add or subtract the numerators (top numbers).

Think of fractions like pieces of pizza. You can only combine pieces if they're the same size! If one pizza is cut into 4 pieces and another into 8 pieces, you need to make the pieces the same size before adding them together.

Remember: The denominator tells you what SIZE the pieces are. The numerator tells you HOW MANY pieces you have.

Adding Fractions with Like Denominators

When fractions have the same denominator (called "like denominators"), adding them is easy!

1 Keep the denominator the same

The pieces are already the same size, so the denominator stays the same.

2 Add the numerators

Count how many pieces you have in total.

3 Simplify if needed

Reduce the fraction to lowest terms if possible.

Example: Add 2/8 + 3/8

2 8

3 8

2 + 3 8

5 8

Visual: 2 eighths + 3 eighths = 5 eighths

Adding Fractions with Unlike Denominators

When fractions have different denominators, we need to find a common denominator first!

Finding the Least Common Denominator (LCD)

The LCD is the smallest number that both denominators divide into evenly. It's the same as the Least Common Multiple (LCM) of the denominators.

1 Find the LCD

List multiples of each denominator until you find a match.

2 Create equivalent fractions

Multiply the top and bottom of each fraction to get the LCD as the new denominator.

3 Add the numerators

Now that denominators match, add the tops!

4 Simplify

Reduce to lowest terms if possible.

Example: Add 1/3 + 1/4

Step 1: Find the LCD of 3 and 4

Multiples of 3	3	6	9	12	15
Multiples of 4	4	8	12	16	20

LCD = 12

Step 2: Create equivalent fractions

1 3

1 x 4 3 x 4

4 12

1 4

1 x 3 4 x 3

3 12

Step 3: Add the fractions

4 12

3 12

7 12

Subtracting Fractions

Subtraction works the same way as addition! Just subtract the numerators instead of adding them.

Like Denominators

5 6

2 6

3 6

1 2

Simplified: 3/6 = 1/2

Unlike Denominators

3 4

1 3

LCD = 12

9 12

4 12

5 12

Pro Tip: When subtracting, always put the larger fraction first! If you're asked to find 1/3 - 3/4, you'll get a negative answer because 1/3 is smaller than 3/4.

Fraction Calculator

Practice adding fractions! Enter two fractions and see the step-by-step solution.

Add Two Fractions

Click "Calculate" to see the step-by-step solution!

Practice Problems

Solve these problems. Click the correct answer!

Problem 1: Like Denominators

3 8 + 2 8 = ?

Problem 2: Unlike Denominators

1 2 + 1 4 = ?

Problem 3: Subtraction

7 10 - 3 10 = ?

Problem 4: Find the LCD

What is the LCD of 1/6 and 1/4?

Problem 5: Unlike Denominators Subtraction

2 3 - 1 6 = ?

Problem 6: Word Problem

Maria ate 1/4 of a pizza. Her brother ate 2/4 of the same pizza. What fraction did they eat together?

Check Your Understanding

When adding fractions, what must be the same?

What is the first step when adding fractions with unlike denominators?

Why must denominators be the same before adding?

What We Learned

🎯

Same Denominators

Just add or subtract the numerators, keep the denominator

🔄

Different Denominators

Find the LCD first, then make equivalent fractions

📐

LCD

Least Common Denominator - the smallest number both denominators divide into

✨

Simplify

Always reduce your answer to lowest terms

Key Takeaway: Adding and subtracting fractions is all about making the pieces the same size (same denominator), then counting how many pieces you have. Once you master finding the LCD, fraction operations become much easier!

Next Steps

Practice finding LCDs with different pairs of numbers
Try adding fractions with larger denominators
Work on simplifying fractions to lowest terms
Move on to learn about multiplying and dividing fractions!