Operations with Fractions - Seventh Grade

Addition, Subtraction, Multiplication & Division

1. Adding and Subtracting Fractions

Case 1: Same Denominator (Like Fractions)

When denominators are SAME:

Step 1: Add or subtract the NUMERATORS

Step 2: Keep the DENOMINATOR the same

Step 3: Simplify if possible

^a/_c ± ^b/_c = ^a±b/_c

Example: 5/8 + 2/8

5/8 + 2/8 = (5+2)/8 = 7/8

Answer: 7/8

Case 2: Different Denominators (Unlike Fractions)

When denominators are DIFFERENT:

Step 1: Find the LCD (Least Common Denominator)

Step 2: Convert both fractions to LCD

Step 3: Add or subtract numerators

Step 4: Keep the LCD as denominator

Step 5: Simplify if possible

Example: 1/4 + 1/6

Step 1: LCD of 4 and 6 = 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

2. Adding and Subtracting Mixed Numbers

Method 1: Convert to Improper Fractions

Step 1: Convert both mixed numbers to improper fractions

Step 2: Find LCD and convert

Step 3: Add or subtract numerators

Step 4: Convert back to mixed number if needed

Example: 2 1/3 + 1 1/2

Step 1: Convert to improper fractions

2 1/3 = 7/3

1 1/2 = 3/2

Step 2: LCD = 6

7/3 = 14/6

3/2 = 9/6

Step 3: 14/6 + 9/6 = 23/6

Step 4: 23/6 = 3 5/6

Answer: 3 5/6

Method 2: Add/Subtract Separately

Step 1: Add or subtract whole numbers

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

Step 3: Combine whole number and fraction

Step 4: Simplify if needed

3. Multiplying Fractions

Multiplication Rule

NO need for common denominator!

Step 1: Multiply numerators together

Step 2: Multiply denominators together

Step 3: Simplify the result

^a/_b × ^c/_d = ^a×c/_b×d

Example: 2/3 × 3/4

Step 1: Multiply numerators: 2 × 3 = 6

Step 2: Multiply denominators: 3 × 4 = 12

Step 3: Result: 6/12

Step 4: Simplify: 6/12 = 1/2

Answer: 1/2

Multiplying Mixed Numbers

Step 1: Convert mixed numbers to improper fractions

Step 2: Multiply as usual

Step 3: Convert back to mixed number if needed

Example: 2 1/2 × 1 1/3

Convert: 2 1/2 = 5/2 and 1 1/3 = 4/3

Multiply: 5/2 × 4/3 = 20/6

Simplify: 20/6 = 10/3 = 3 1/3

Answer: 3 1/3

4. Multiplicative Inverses (Reciprocals)

Definition

The reciprocal of a fraction is found by

FLIPPING the numerator and denominator

• When you multiply a number by its reciprocal, you get 1

Reciprocal of ^a/_b = ^b/_a

^a/_b × ^b/_a = 1

Examples

Number	Reciprocal	Product
3/4	4/3	3/4 × 4/3 = 1
5	1/5	5 × 1/5 = 1
2 1/2 = 5/2	2/5	5/2 × 2/5 = 1

5. Dividing Fractions

Keep-Change-Flip Method (KCF)

KEEP - CHANGE - FLIP

KEEP: Keep the first fraction the same

CHANGE: Change ÷ to ×

FLIP: Flip (take reciprocal of) the second fraction

Then multiply!

^a/_b ÷ ^c/_d = ^a/_b × ^d/_c

Example: 3/4 ÷ 2/5

KEEP: 3/4

CHANGE: ÷ becomes ×

FLIP: 2/5 becomes 5/2

3/4 × 5/2 = 15/8 = 1 7/8

Answer: 1 7/8

Dividing Mixed Numbers

Step 1: Convert mixed numbers to improper fractions

Step 2: Use Keep-Change-Flip

Step 3: Multiply and simplify

Example: 2 1/2 ÷ 1 1/4

Convert: 2 1/2 = 5/2 and 1 1/4 = 5/4

5/2 ÷ 5/4

Keep-Change-Flip: 5/2 × 4/5

Multiply: 20/10 = 2

Answer: 2

6. Estimating with Fractions and Mixed Numbers

Rounding Fractions

Round to 0 if numerator is much smaller than denominator

Round to 1/2 if numerator is about half of denominator

Round to 1 if numerator is close to denominator

Estimating Mixed Numbers

Round the fraction part to 0, 1/2, or 1

Then perform the operation with whole numbers

Example: Estimate 5 3/8 + 2 7/8

Round 5 3/8 ≈ 5 (since 3/8 is close to 1/2, round to 5 1/2)

Round 2 7/8 ≈ 3 (since 7/8 is close to 1)

Estimate: 5 1/2 + 3 = 8 1/2

Estimate: About 8 1/2

7. Evaluating Expressions with Fractions

Order of Operations (PEMDAS)

Remember: PEMDAS

Parentheses

Exponents

Multiplication & Division (left to right)

Addition & Subtraction (left to right)

Example: 1/2 + 1/3 × 2/5

Step 1: Multiply first (1/3 × 2/5 = 2/15)

Expression becomes: 1/2 + 2/15

Step 2: Find LCD (LCD = 30)

1/2 = 15/30

2/15 = 4/30

Step 3: Add: 15/30 + 4/30 = 19/30

Answer: 19/30

Quick Reference: Fraction Operations

Operation	Key Rule
Addition/Subtraction (Same Denominator)	Add/subtract numerators, keep denominator
Addition/Subtraction (Different)	Find LCD, convert, then add/subtract
Multiplication	Multiply numerators, multiply denominators
Division	Keep-Change-Flip (multiply by reciprocal)
Mixed Numbers	Convert to improper fractions first