Fractions Review: Add, Subtract, Multiply, Divide

Objective

This document provides a summary of key concepts and procedures for adding, subtracting, multiplying, and dividing fractions.

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1. Adding & Subtracting Fractions

• Common Denominator:

  • To add/subtract, the denominators must be the same.
  • Find a common denominator, usually by multiplying each fraction by the denominator of the other fraction.

• Example 1: Addition

  2/3 + 3/4
  → Get common denominators:
    - Multiply 2/3 by 4/4 => 8/12
    - Multiply 3/4 by 3/3 => 9/12
  → Add numerators:
    - 8 + 9 = 17
    - Answer: 17/12 (improper fraction)
    - As a mixed number: 1 5/12
  

• Example 2: Subtraction

  5/6 - 2/5
  → Get common denominators:
    - 5/6 × 5/5 = 25/30
    - 2/5 × 6/6 = 12/30
  → Subtract numerators:
    - 25 - 12 = 13
    - Answer: 13/30
  

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2. Multiplying Fractions

• Procedure: Multiply numerators together and denominators together.
• Example 1

  3/4 × 5/8 = 15/32
  - No simplification possible.
  

• Example 2: Simplify Before Multiplying

  21/7 × 4/32
  - Factorize: 21=7×3, 32=8×4
  - Cancel common factors (7, 4)
  - Left with 3/8
  - Easier to simplify BEFORE multiplying.
  

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3. Dividing Fractions

• Keep, Change, Flip:

  1. Keep the first fraction the same.
  2. Change the division sign to multiplication.
  3. Flip (take the reciprocal of) the second fraction.

• Example 1

  3/5 ÷ 2/7
  → 3/5 × 7/2 = 21/10
  - As a mixed number: 2 1/10
  

• Example 2: Simplify Before Multiplying

  8/15 ÷ 6/4
  → 8/15 × 4/6
  - Factorize: 8=4×2, 6=3×2, 15=5×3
  - Cancel: Five, three, two
  - Left with 1/4
  

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4. Summary/Tips

• When adding or subtracting, always get common denominators first.
• When multiplying, multiply across numerators and denominators; simplify before multiplying if possible.
• When dividing, use "keep, change, flip"; simplify before multiplying if possible.
• Always consider reducing/simplifying fractions where possible to make calculations easier.

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Key Terms

• Improper Fraction: Numerator is greater than or equal to the denominator.
• Mixed Number: Combines a whole number and a fraction.
• Reciprocal: Inverts the numerator and denominator.

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