Cancellation Math Example 4

Follow the full solution, then compare it with the other examples linked below.

Example 4

medium
Simplify \(\dfrac{30}{42}\) completely.

Solution

  1. 1
    GCF of 30 and 42: factors of 30: 1,2,3,5,6,10,15,30; factors of 42: 1,2,3,6,7,14,21,42. GCF = 6.
  2. 2
    \(\dfrac{30}{42} = \dfrac{6 \times 5}{6 \times 7} = \dfrac{5}{7}\).

Answer

\(\dfrac{5}{7}\)
Cancelling the GCF of 6: \(\frac{30}{42} = \frac{5}{7}\).

About Cancellation

Cancellation is the process of removing a common factor from the numerator and denominator of a fraction, or from both sides of an equation, to simplify. It works because dividing both parts by the same nonzero number leaves an equivalent but simpler form.

Learn more about Cancellation →

More Cancellation Examples

Example 1 easy

Simplify (dfrac{4 times 6}{4 times 3}) using cancellation.

Example 2 medium

Simplify the fraction (dfrac{18}{24}) using cancellation (find the GCF first).

Example 3 easy

Simplify (dfrac{3 times 5}{3 times 7}).

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