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Multiplying Fractions

  • Basic Method for Multiplying Fractions

    • To multiply fractions, follow the steps below:

    • Step 1: Multiply the numerators to obtain the new numerator.

    • Step 2: Multiply the denominators to obtain the new denominator.

    • Resulting Fraction: The result after these steps is expressed as \frac{(numerator{1} \times numerator{2})}{(denominator{1} \times denominator{2})}.

  • Reducing Fractions

    • After obtaining the new fraction, look for a number that divides evenly into both the numerator and denominator.

    • Purpose of Reducing: By dividing both the numerator and the denominator by the same number, you reduce the fraction without changing its value.

  • Cancelling Before Multiplication

    • Cancelling refers to reducing fractions before performing the multiplication.

    • If there exists a common number that will divide evenly into both the numerator and the denominator, it is beneficial to do this prior to multiplication.

    • Advantage of Cancelling: This step reduces the size of the numbers involved, simplifying computation.

Multiplying Fractions with Whole or Mixed Numbers

  • Converting Mixed Numbers

    • When multiplying fractions that involve a whole number or mixed number, it is crucial to convert the whole or mixed number into an improper fraction first.

    • Improper Fraction Defined: An improper fraction is a fraction where the numerator is greater than or equal to the denominator. For example, the mixed number 2\frac{1}{2} becomes the improper fraction \frac{5}{2}.

  • Multiplication Process

    • After conversion, proceed to multiply as described in the basic method above.

Dividing Fractions

  • Steps for Dividing Fractions

    • To divide fractions, follow these steps:

    • Step 1: Change the sign from division to multiplication.

    • Step 2: Invert the second fraction (also known as taking the reciprocal).

      • For instance, if dividing \frac{a}{b} by \frac{c}{d}, it transforms to \frac{a}{b} \times \frac{d}{c}.

    • Step 3: Multiply using the rules of multiplication for fractions.

      • Again, multiply the numerators and multiply the denominators as per the basic multiplication method explained above.

Summary of Key Concepts

  • To multiply fractions:

    • Multiply the numerators for new numerator.

    • Multiply the denominators for new denominator.

    • Reduce the fraction if possible.

  • To multiply with whole/mixed numbers:

    • Convert to improper fractions first.

  • To divide fractions:

    • Change division to multiplication and invert the second fraction.