Add and Subtract Fractions - Sixth Grade

Complete Notes & Formulas

1. Add & Subtract Fractions with Like Denominators

The Golden Rule

When denominators are the SAME:

Add or subtract NUMERATORS only

Keep the denominator the SAME

Addition Formula

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

Subtraction Formula

a/c − b/c = (a − b)/c

Example 1: Addition

Problem: 2/7 + 3/7

Step 1: Check denominators (both are 7)

Step 2: Add numerators: 2 + 3 = 5

Step 3: Keep denominator: 7

Answer: 5/7

Example 2: Subtraction

Problem: 5/8 − 3/8

Step 1: Check denominators (both are 8)

Step 2: Subtract numerators: 5 − 3 = 2

Step 3: Keep denominator: 8

Step 4: Simplify: 2/8 = 1/4

Answer: 1/4

Remember: Always simplify your answer to lowest terms!

2. Add & Subtract Fractions with Unlike Denominators

The Process

When denominators are DIFFERENT:

Find the LCD (Least Common Denominator)

Make equivalent fractions

Then add or subtract

Steps

Step 1: Find the LCD (LCM of denominators)

Step 2: Convert each fraction to equivalent fraction with LCD

Step 3: Add or subtract numerators

Step 4: Keep the LCD as denominator

Step 5: Simplify if possible

Example 1: 1/4 + 1/6

Step 1: Find LCD of 4 and 6

Multiples of 4: 4, 8, 12, 16...

Multiples of 6: 6, 12, 18...

LCD = 12

Step 2: Convert to LCD

1/4 = 3/12 (multiply by 3/3)

1/6 = 2/12 (multiply by 2/2)

Step 3: Add

3/12 + 2/12 = 5/12

Answer: 5/12

Example 2: 5/6 − 1/4

Step 1: LCD of 6 and 4 = 12

Step 2: Convert

5/6 = 10/12

1/4 = 3/12

Step 3: Subtract

10/12 − 3/12 = 7/12

Answer: 7/12

3. Add & Subtract Mixed Numbers

Method 1: Add/Subtract Parts Separately

Step 1: Add or subtract whole numbers

Step 2: Add or subtract fractions (find LCD if needed)

Step 3: Combine results and simplify

Example 1: Addition 2⅓ + 1½

Step 1: Add whole numbers: 2 + 1 = 3

Step 2: Add fractions

1/3 + 1/2

LCD = 6

2/6 + 3/6 = 5/6

Step 3: Combine

3 + 5/6 = 3⅚

Answer: 3⅚

Example 2: Subtraction with Borrowing 5¼ − 2¾

Problem: Can't subtract 3/4 from 1/4

Step 1: Borrow 1 from whole number

5¼ = 4 + 1¼ = 4⅝

Step 2: Now subtract

Whole: 4 − 2 = 2

Fraction: 5/4 − 3/4 = 2/4 = 1/2

Step 3: Combine

2 + 1/2 = 2½

Answer: 2½

Method 2: Convert to Improper Fractions

Example: 2⅓ + 1½

Step 1: Convert to improper

2⅓ = 7/3

1½ = 3/2

Step 2: Find LCD = 6

7/3 = 14/6

3/2 = 9/6

Step 3: Add

14/6 + 9/6 = 23/6 = 3⅚

Answer: 3⅚

4. Word Problems with Fractions

Keywords

Addition: Total, altogether, combined, sum, in all

Subtraction: Difference, how much more, left, remaining, less than

Example 1: Like Denominators

Problem: Sarah ate 2/8 of a pizza and John ate 3/8 of the same pizza. What fraction of the pizza did they eat altogether?

Keyword: "altogether" → Addition

2/8 + 3/8 = 5/8

Answer: 5/8 of the pizza

Example 2: Unlike Denominators

Problem: A recipe needs 1/3 cup of oil and 1/4 cup of water. How much liquid is needed in total?

LCD of 3 and 4 = 12

1/3 = 4/12

1/4 = 3/12

4/12 + 3/12 = 7/12

Answer: 7/12 cup

Example 3: Mixed Numbers

Problem: Mike walked 2¾ miles in the morning and 1½ miles in the evening. How many miles did he walk in total?

Whole numbers: 2 + 1 = 3

Fractions: 3/4 + 1/2 = 3/4 + 2/4 = 5/4 = 1¼

Total: 3 + 1¼ = 4¼

Answer: 4¼ miles

5. Inequalities with Fractions

Comparing Results

Compare the result of fraction operations using <, >, or =

Strategy

1. Calculate both expressions

2. Convert to like denominators if needed

3. Compare numerators

Example: Compare: 1/4 + 1/2 ___ 3/4

Left side: 1/4 + 1/2 = 1/4 + 2/4 = 3/4

Right side: 3/4

3/4 = 3/4

Answer: 1/4 + 1/2 = 3/4

6. Estimate Sums and Differences

Rounding Strategy

If fraction is close to 0: Round down

If fraction is close to ½: Round to ½

If fraction is close to 1: Round up

Example: Estimate 5⅞ + 3⅛

5⅞ is close to 6 (round up)

3⅛ is close to 3 (round down)

6 + 3 = 9

Estimate: About 9

(Actual: 5⅞ + 3⅛ = 9)

7. Maps with Fractional Distances

Real-World Application

Maps often show distances as fractions or mixed numbers. Add or subtract to find total distances.

Example: A map shows:

• Home to Store: 1¾ miles

• Store to Park: 2⅓ miles

Question: Total distance from home to park?

Solution:

1¾ + 2⅓

Whole: 1 + 2 = 3

Fraction: 3/4 + 1/3 = 9/12 + 4/12 = 13/12 = 1 1/12

Total: 3 + 1 1/12 = 4 1/12

Answer: 4 1/12 miles

Quick Reference: Fraction Operations

Type	Key Rule
Like Denominators	Add/subtract numerators, keep denominator
Unlike Denominators	Find LCD, convert, then add/subtract
Mixed Numbers	Add/subtract parts or convert to improper
Estimating	Round fractions to 0, ½, or 1

💡 Important Tips to Remember

✓ Same denominators: Just add/subtract numerators

✓ Different denominators: Find LCD first!

✓ Always simplify your final answer

✓ Mixed numbers: Can work with parts or convert to improper

✓ Borrowing: When subtracting, may need to borrow from whole number

✓ Check your work: Does the answer make sense?

✓ LCD = LCM of the denominators

✓ Estimate first to check reasonableness

✓ Look for keywords in word problems

✓ Practice daily to master fractions!

🧠 Memory Tricks & Strategies

Like Denominators:

"Same house, add the rooms!"

(Same denominator, add numerators)

Unlike Denominators:

"Make them match, then attach!"

(Find LCD, convert, then add/subtract)

LCD Reminder:

"LCD is LCM's twin!"

Mixed Numbers:

"Whole and part, keep them apart (or make them one)!"

Borrowing:

"When top's too small, borrow from tall!"

Simplifying:

"Divide by GCF, make it as small as can be!"

Master Fraction Addition & Subtraction! ➕ ➖ 🎯

Remember: LCD is your best friend!