Chapter 4.3, Problem 41E

To determine

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

Answer to Problem 41E

Fraction is not equivalent $\frac{12}{15}\ne \frac{26}{30}$

Simplest Form of $\frac{12}{15}=\frac{4}{5}$ .

Simplest Form of $\frac{26}{30}=\frac{13}{15}$

Explanation of Solution

Given information: $\frac{12}{15},\frac{26}{30}$

Formula Used: Factorisation

Calculation:

  $\frac{12}{15}$ and $\frac{26}{30}$

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

  $\frac{12}{15}=\frac{2\times 2\times 3}{3\times 5}$ and $\frac{26}{30}=\frac{2\times 13}{2\times 3\times 5}$

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

  $\frac{2\times 2\times 3}{3\times 5}=\frac{2\times 2}{5}$ and $\frac{2\times 13}{2\times 3\times 5}=\frac{13}{3\times 5}$

Hence, fraction in simplest form

  $\frac{12}{15}=\frac{4}{5}$ and $\frac{26}{30}=\frac{13}{15}$

Fraction is not equivalent $\frac{12}{15}\ne \frac{26}{30}$