Adding and Subtracting Fractions

For Elementary Students

Adding Fractions with the Same Bottom Number

When fractions have the same denominator (bottom number), it's easy!

Just add the top numbers. Keep the bottom number the same.

Example: 2/5 + 1/5 = ?

Think about it like this: You have 2 slices of pizza cut into fifths, and your friend has 1 slice. How many fifths do you have together?

You: ▢▢
Friend: ▢
Together: ▢▢▢ = 3/5

Answer: 2/5 + 1/5 = 3/5

More Examples with Same Denominator

Example 1: 1/8 + 3/8 = ?

• Top numbers: 1 + 3 = 4
• Bottom stays: 8
• Answer: 4/8 (which simplifies to 1/2)

Example 2: 4/7 + 2/7 = ?

• Top: 4 + 2 = 6
• Bottom stays: 7
• Answer: 6/7

Subtracting Fractions with Same Bottom Number

Same rule: Just subtract the top numbers. Keep the bottom the same.

Example: 5/8 − 3/8 = ?

Think: You have 5 slices, you eat 3. How many left?

• Top: 5 − 3 = 2
• Bottom stays: 8
• Answer: 2/8 = 1/4 (simplified)

Why Can't We Add Different Denominators?

You can't add 1/2 + 1/3 directly because they're different-sized pieces!

Think about it like this: You can't add 2 apples and 3 oranges to get "5 apples" — they're different things!

Same with fractions — halves and thirds are different sizes.

We will learn later how to make them the same size.

For Junior High Students

Review: Same Denominator

When fractions have the same denominator, add or subtract the numerators only. Keep the denominator.

Addition: a/c + b/c = (a + b)/c

Subtraction: a/c − b/c = (a − b)/c

Example: 3/9 + 4/9 = 7/9

Example: 7/10 − 2/10 = 5/10 = 1/2 (simplified)

Think of it like: Adding slices of the same pizza.

Different Denominators: The Challenge

When denominators are different, you cannot add them directly.

❌ Wrong: 1/2 + 1/3 = 2/5 (This is incorrect!)

✓ Right: Convert to same denominator first!

Finding a Common Denominator

Common denominator: A number both denominators divide into evenly.

Least Common Denominator (LCD): The smallest common denominator.

Example: Find LCD for 1/4 and 1/6

List multiples:

• Multiples of 4: 4, 8, 12, 16, 20, 24...
• Multiples of 6: 6, 12, 18, 24...

LCD = 12 (first number in both lists)

Step-by-Step: Adding with Different Denominators

Example: 1/3 + 1/4 = ?

Step 1: Find the LCD

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

Step 2: Convert both fractions to denominator 12

• 1/3 = ?/12 → 3 × 4 = 12, so multiply top by 4: 1/3 = 4/12
• 1/4 = ?/12 → 4 × 3 = 12, so multiply top by 3: 1/4 = 3/12

Step 3: Add the numerators

• 4/12 + 3/12 = 7/12

Step 4: Simplify if possible

• 7/12 is already simplest

Answer: 7/12

More Addition Examples

Example: 2/5 + 1/3

• LCD: 15
• Convert: 2/5 = 6/15 and 1/3 = 5/15
• Add: 6/15 + 5/15 = 11/15

Example: 3/4 + 1/8

• LCD: 8 (4 divides into 8)
• Convert: 3/4 = 6/8 and 1/8 stays same
• Add: 6/8 + 1/8 = 7/8

Step-by-Step: Subtracting with Different Denominators

Example: 3/4 − 1/3 = ?

Step 1: Find LCD

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

Step 2: Convert both

• 3/4 = 9/12
• 1/3 = 4/12

Step 3: Subtract

• 9/12 − 4/12 = 5/12

Answer: 5/12

More Subtraction Examples

Example: 5/6 − 1/4

• LCD: 12
• Convert: 5/6 = 10/12 and 1/4 = 3/12
• Subtract: 10/12 − 3/12 = 7/12

Example: 2/3 − 1/6

• LCD: 6
• Convert: 2/3 = 4/6 and 1/6 stays same
• Subtract: 4/6 − 1/6 = 3/6 = 1/2

Always Simplify Your Answer!

After adding or subtracting, check if you can simplify.

Example: 1/4 + 1/4 = 2/4 = 1/2

Example: 3/8 + 1/8 = 4/8 = 1/2

Checking Your Work

Use estimation! Does your answer make sense?

Example: 1/2 + 1/3

• Think: A half and a third should be less than 1
• Our answer: 5/6 ✓ (less than 1, makes sense!)

Use subtraction to check addition:

If 1/4 + 3/4 = 1, then 1 − 1/4 = 3/4 ✓

Real-Life Uses

Cooking: "Recipe needs 1/3 cup flour and 1/4 cup sugar. How much total?"

• 1/3 + 1/4 = 7/12 cup

Measurement: "Walked 3/4 mile, then 1/2 mile. Total?"

• 3/4 + 1/2 = 3/4 + 2/4 = 5/4 = 1 1/4 miles

Time: "Studied 1/2 hour, then 1/4 hour. Total?"

• 1/2 + 1/4 = 2/4 + 1/4 = 3/4 hour (45 minutes)

Practice