Chapter 4.3, Problem 46E

To determine

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

Answer to Problem 46E

Fraction is not equivalent $\frac{30}{36}\ne \frac{57}{72}$

Simplest Form of $\frac{30}{36}=\frac{5}{6}$ .

Simplest Form of $\frac{57}{72}=\frac{19}{24}$ .

Explanation of Solution

Given information: $\frac{30}{36},\frac{57}{72}$

Formula Used: Factorisation

Calculation:

  $\frac{30}{36}$ and $\frac{57}{72}$

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

  $\frac{30}{36}=\frac{2\times 3\times 5}{2\times 2\times 3\times 3}$ and $\frac{57}{72}=\frac{3\times 19}{2\times 2\times 2\times 3\times 3}$

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

  $\frac{2\times 3\times 5}{2\times 2\times 3\times 3}=\frac{5}{2\times 3}$ and $\frac{3\times 19}{2\times 2\times 2\times 3\times 3}=\frac{19}{2\times 2\times 2\times 3}$

Hence, fraction in simplest form

  $\frac{30}{36}=\frac{5}{6}$ and $\frac{57}{72}=\frac{19}{24}$

Fraction is not equivalent $\frac{30}{36}\ne \frac{57}{72}$