Add and Subtract Fractions | Fifth Grade

Complete Notes & Formulas

1. Estimate Sums and Differences Using Benchmarks

Definition: Use benchmark fractions (0, 1/2, 1) to quickly estimate the sum or difference of fractions before doing exact calculations.

📝 Steps to Estimate:

Step 1: Round each fraction to the nearest benchmark (0, 1/2, or 1)
Step 2: Add or subtract the benchmark fractions
Step 3: State your estimate

🔑 Rounding Rules:

Round to 0: When numerator is very small compared to denominator (Example: 1/8 ≈ 0)
Round to 1/2: When numerator is about half the denominator (Example: 4/9 ≈ 1/2)
Round to 1: When numerator nearly equals denominator (Example: 7/8 ≈ 1)

✏️ Example: Estimate 5/8 + 2/9

Step 1: Round each fraction

• 5/8: Half of 8 is 4, and 5 > 4, so 5/8 ≈ 1/2 (closer to 1)

Actually 5/8 ≈ 1 (since 5 is close to 8)

• 2/9: Half of 9 is 4.5, and 2 < 4.5, so 2/9 ≈ 0

Step 2: Add: 1 + 0 = 1

Estimate: About 1

2. Add Fractions with Unlike Denominators Using Models

Definition: Use visual models (area models, fraction bars, number lines) to understand how to add fractions with different denominators.

📐 Using Area Models:

Draw a rectangle for each fraction
Divide each rectangle according to its denominator
Shade the parts according to the numerator
Re-divide all rectangles to have the same number of parts (LCD)
Count total shaded parts over total parts

✏️ Example: Model 1/2 + 1/4

Draw two rectangles:

• First rectangle: Divide in 2, shade 1 part

• Second rectangle: Divide in 4, shade 1 part

Re-divide both into 4 parts (LCD = 4):

• 1/2 = 2/4 (2 parts shaded)

• 1/4 = 1/4 (1 part shaded)

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

3. Add Fractions with Unlike Denominators

Definition: To add fractions with different denominators, find a common denominator, convert to equivalent fractions, then add the numerators.

📝 Steps to Add Unlike Fractions:

Step 1: Find the LCD (Least Common Denominator)
Step 2: Convert each fraction to an equivalent fraction with the LCD
Step 3: Add the numerators, keep the denominator
Step 4: Simplify if needed

Formula: a/b + c/d = (ad + bc)/(bd)
(Or use LCD method)

✏️ Example: Add 2/3 + 1/4

Step 1: Find LCD of 3 and 4

LCD = 12

Step 2: Convert to equivalent fractions:

• 2/3 = (2 × 4)/(3 × 4) = 8/12

• 1/4 = (1 × 3)/(4 × 3) = 3/12

Step 3: Add: 8/12 + 3/12 = 11/12

Answer: 11/12

4. Subtract Fractions with Unlike Denominators Using Models

Definition: Use visual models to understand subtraction of fractions with different denominators by showing what remains after taking away.

✏️ Example: Model 3/4 - 1/3

Find LCD = 12

• 3/4 = 9/12 (Draw rectangle with 12 parts, shade 9)

• 1/3 = 4/12 (Take away 4 shaded parts)

Result: 5 parts remain out of 12 = 5/12

5. Subtract Fractions with Unlike Denominators

Definition: To subtract fractions with different denominators, find a common denominator, convert to equivalent fractions, then subtract the numerators.

📝 Steps to Subtract Unlike Fractions:

Step 1: Find the LCD
Step 2: Convert to equivalent fractions with LCD
Step 3: Subtract numerators, keep denominator
Step 4: Simplify if needed

Formula: a/b - c/d = (ad - bc)/(bd)
(Or use LCD method)

✏️ Example: Subtract 5/6 - 1/4

Step 1: Find LCD of 6 and 4

LCD = 12

Step 2: Convert:

• 5/6 = (5 × 2)/(6 × 2) = 10/12

• 1/4 = (1 × 3)/(4 × 3) = 3/12

Step 3: Subtract: 10/12 - 3/12 = 7/12

Answer: 7/12

6. Add and Subtract Fractions with Unlike Denominators

Definition: Combined practice of adding and subtracting fractions with different denominators in the same problem.

✏️ Example: Solve 2/5 + 1/3 - 1/15

Step 1: Find LCD of 5, 3, and 15

LCD = 15

Step 2: Convert all fractions:

• 2/5 = 6/15

• 1/3 = 5/15

• 1/15 = 1/15

Step 3: Add and subtract: 6/15 + 5/15 - 1/15 = 10/15

Step 4: Simplify: 10/15 = 2/3

Answer: 2/3

7. Add and Subtract Fractions: Word Problems

Definition: Apply fraction addition and subtraction skills to solve real-world problems.

✏️ Example 1: Pizza Problem

Sarah ate 1/4 of a pizza and Tom ate 1/3 of the same pizza. What fraction of the pizza did they eat altogether?

Solution:

Add: 1/4 + 1/3

LCD = 12

1/4 = 3/12, 1/3 = 4/12

3/12 + 4/12 = 7/12

Answer: They ate 7/12 of the pizza

✏️ Example 2: Distance Problem

Mike walked 3/4 mile to school and 1/2 mile to the library. How much farther did he walk to school than to the library?

Solution:

Subtract: 3/4 - 1/2

LCD = 4

3/4 = 3/4, 1/2 = 2/4

3/4 - 2/4 = 1/4

Answer: 1/4 mile farther

8. Add 3 or More Fractions with Unlike Denominators

Definition: Find the LCD for all fractions, convert each to an equivalent fraction, then add all numerators.

✏️ Example: Add 1/2 + 1/3 + 1/6

Step 1: Find LCD of 2, 3, and 6

LCD = 6

Step 2: Convert all:

• 1/2 = 3/6

• 1/3 = 2/6

• 1/6 = 1/6

Step 3: Add: 3/6 + 2/6 + 1/6 = 6/6 = 1

Answer: 1 whole

9. Add 3 or More Fractions: Word Problems

Definition: Real-world problems involving addition of three or more fractions.

✏️ Example: Recipe Problem

A recipe needs 1/4 cup of sugar, 1/3 cup of flour, and 1/6 cup of butter. How many cups of ingredients in total?

Solution:

Add: 1/4 + 1/3 + 1/6

LCD = 12

1/4 = 3/12, 1/3 = 4/12, 1/6 = 2/12

3/12 + 4/12 + 2/12 = 9/12 = 3/4

Answer: 3/4 cup total

10. Complete Addition and Subtraction Sentences with Fractions

Definition: Find the missing fraction in an addition or subtraction equation.

✏️ Examples:

Example 1: 1/3 + ___ = 5/6

Solution: Find the missing addend

5/6 - 1/3 = ?

LCD = 6: 5/6 - 2/6 = 3/6 = 1/2

Answer: 1/2

Example 2: ___ - 1/4 = 1/2

Solution: Find the starting number

1/2 + 1/4 = ?

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

Answer: 3/4

11. Compare Sums and Differences of Fractions

Definition: Evaluate and compare the results of two different fraction operations using <, >, or = symbols.

📝 Steps:

Solve the first expression
Solve the second expression
Compare the two results
Write the comparison using <, >, or =

✏️ Example: Compare (1/2 + 1/4) ___ (3/4 - 1/8)

Left side: 1/2 + 1/4

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

Right side: 3/4 - 1/8

LCD = 8: 6/8 - 1/8 = 5/8

Compare: 3/4 vs 5/8

Convert: 3/4 = 6/8

6/8 > 5/8

Answer: (1/2 + 1/4) > (3/4 - 1/8)

Quick Reference Chart

Operation	Steps	Formula
Addition	Find LCD → Convert → Add numerators	a/c + b/c = (a+b)/c
Subtraction	Find LCD → Convert → Subtract numerators	a/c - b/c = (a-b)/c
Estimation	Round to 0, 1/2, or 1 → Calculate	Use benchmarks

💡 Key Formulas:

LCD Method

LCM of denominators

Same Denominator

Add/subtract numerators only

Simplify

Divide by GCF

Check Work

Use estimation

🔑 Key Tips for Success: