Chapter 4.3, Problem 43E

To determine

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

Answer to Problem 43E

Fraction is not equivalent $\frac{9}{24}\ne \frac{15}{48}$

Simplest Form of $\frac{9}{24}=\frac{3}{8}$ .

Simplest Form of $\frac{15}{48}=\frac{5}{16}$ .

Explanation of Solution

Given information: $\frac{9}{24},\frac{15}{48}$

Formula Used: Factorisation

Calculation:

  $\frac{9}{24}$ and $\frac{15}{48}$

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

  $\frac{9}{24}=\frac{3\times 3}{2\times 2\times 2\times 3}$ and $\frac{15}{48}=\frac{3\times 5}{2\times 2\times 2\times 2\times 3}$

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

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

Hence, fraction in simplest form

  $\frac{9}{24}=\frac{3}{8}$ and $\frac{15}{48}=\frac{5}{16}$

Fraction is not equivalent $\frac{9}{24}\ne \frac{15}{48}$