Chapter 4.3, Problem 42E

To determine

To find fraction in simplest form and whether they are equivalent.

Answer to Problem 42E

Fraction is equivalent $\frac{18}{20}=\frac{45}{50}$

Simplest Form of $\frac{18}{20}=\frac{9}{10}$ .

Simplest Form of $\frac{45}{50}=\frac{9}{10}$ .

Explanation of Solution

Given information: $\frac{18}{20},\frac{45}{50}$

Formula Used: Factorisation

Calculation:

  $\frac{18}{20}$ and $\frac{45}{50}$

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

  $\frac{18}{20}=\frac{2\times 3\times 3}{2\times 2\times 5}$ and $\frac{45}{50}=\frac{3\times 3\times 5}{2\times 5\times 5}$

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

  $\frac{2\times 3\times 3}{2\times 2\times 5}=\frac{3\times 3}{2\times 5}$ and $\frac{3\times 3\times 5}{2\times 5\times 5}=\frac{3\times 3}{2\times 5}$

Hence, fraction in simplest form

  $\frac{18}{20}=\frac{9}{10}$ and $\frac{45}{50}=\frac{9}{10}$

Fraction is equivalent $\frac{18}{20}=\frac{45}{50}$