Fractions | How to Add, Subtract, Multiply and Divide

Introduction to Fractions

• Definition of Fractions: A fraction represents a part or parts of a whole object.

• Components of a Fraction:

  • Numerator: Indicates how many parts you have.

  • Denominator: Indicates how many parts the whole is divided into.

Combining Fractions

• Rule: You must have a common denominator to add or subtract fractions.

• Example:

  • For 2/3 + 1/2:

    • Common denominator: 6

    • Convert fractions:

      • 2/3 becomes 4/6 (multiplied numerator and denominator by 2).

      • 1/2 becomes 3/6 (multiplied numerator and denominator by 3).

    • Result: 4 + 3 = 7, so 2/3 + 1/2 = 7/6.

Multiplying Fractions

• Rule: Multiply the numerators and the denominators separately.

• Example:

  • For 2/3 * 4/5:

    • Multiply: 2 * 4 = 8 and 3 * 5 = 15.

    • Result: 8/15 (no reduction needed).

Dividing Fractions

• Rule: Flip the divisor and multiply.

• Example:

  • For 2/3 ÷ 1/4:

    • Flip 1/4 to become 4/1, then multiply:

      • 2 * 4 = 8 and 3 * 1 = 3.

    • Result: 8/3 (no mixed numbers).

Cross-Canceling Fractions

• Importance: A valuable skill for simplifying before multiplication.

• Example:

  • For 2/3 * 1/4:

    • Common factor is 2.

    • Cross-cancel: 2/2 = 1 and 4/2 = 2.

    • Then compute: 1 * 1 = 1 and 3 * 2 = 6.

    • Result: 1/6.

Mixed Numbers

• Definition: A mixed number is a combination of a whole number and a fraction.

• Conversion: To convert to an improper fraction:

  • Example: Convert 2 and 1/3:

    • 2 * 3 + 1 = 7 ⇒ 7/3.

Practice Problem

• Problem: 2 and 12 * 5 and 1/3:

  • Convert to improper fractions:

    • 2 and 1/2 = 5/2 and 5 and 1/3 = 16/3.

  • Cross-cancel:

    • 2 goes into 16, 8 times and 2 goes into 2, 1 time.

  • Calculate: 5 * 8 = 40 and 1 * 3 = 3.

  • Result: 40/3 (already reduced).

Recap

• We defined fractions, combined, multiplied and divided fractions, cross-canceled, worked with mixed numbers, and solved a practice problem.