Chapter 4.3, Problem 7C

To determine

To write given fractions in its simplest form.

Answer to Problem 7C

  $\frac{9}{14}$

Explanation of Solution

Given Information: $\frac{27}{42}$

Formula used: Divide numerator and denominator such that they can no longer be divided by the same whole number exactly or evenly (other than the number 1).

Calculation:

  $\frac{27}{42}$

Both numerator & denominator are now written as product of its prime factors.

  $=\frac{3\times 3\times 3}{2\times 3\times 7}$

As 3 is common in both num& den, it cancels out. In the next step -

  $=\frac{3\times 3}{2\times 7}$

Final answer is-

  $=\frac{9}{14}$