Chapter 4.3, Problem 47E

To determine

To find fraction in simplest form.

Answer to Problem 47E

Simplest Form of $\frac{-12}{27}=\frac{-4}{9}$ .

Simplest Form of $\frac{25}{-35}=\frac{5}{-7}$ .

Simplest Form of $\frac{-33}{-55}=\frac{-3}{-5}=\frac{3}{5}$ .

Explanation of Solution

Given information: $\frac{-12}{27},\frac{25}{-35}and\frac{-33}{-55}$

Formula Used: Factorisation

Calculation:

  $\frac{-12}{27}$ and $\frac{25}{-35}$ and $\frac{-33}{-55}$

Now, Simplify both by breaking numerator and denominator into multiplication of prime numbers

  $\frac{-12}{27}=\frac{-2\times 2\times 3}{3\times 3\times 3}$ and $\frac{25}{-35}=\frac{5\times 5}{-5\times 7}$ and $\frac{-33}{-55}=\frac{-3\times 11}{-5\times 11}$

Now, divide both the numerator by denominator to make fraction in simplest form.

  $\frac{-2\times 2\times 3}{3\times 3\times 3}=\frac{-2\times 2}{3\times 3}$ and $\frac{5\times 5}{-5\times 7}=\frac{5}{-7}$ and $\frac{-3\times 11}{-5\times 11}=\frac{3}{5}$

Hence, fraction in simplest form

  $\frac{-12}{27}=\frac{-4}{9}$ and $\frac{25}{-35}=\frac{5}{-7}$ and $\frac{-33}{-55}=\frac{3}{5}$