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.

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