Chapter 4.3, Problem 45E

To determine

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

Answer to Problem 45E

Fraction is equivalent $\frac{49}{63}=\frac{21}{27}$

Simplest Form of $\frac{49}{63}=\frac{7}{9}$ .

Simplest Form of $\frac{21}{27}=\frac{7}{9}$ .

Explanation of Solution

Given information: $\frac{49}{63},\frac{21}{27}$

Formula Used: Factorisation

Calculation:

  $\frac{49}{63}$ and $\frac{21}{27}$

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

  $\frac{49}{63}=\frac{7\times 7}{3\times 3\times 7}$ and $\frac{21}{27}=\frac{3\times 7}{3\times 3\times 3}$

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

  $\frac{7\times 7}{3\times 3\times 7}=\frac{7}{3\times 3}$ and $\frac{3\times 7}{3\times 3\times 3}=\frac{7}{3\times 3}$

Hence, fraction in simplest form

  $\frac{49}{63}=\frac{7}{9}$ and $\frac{21}{27}=\frac{7}{9}$

Fraction is equivalent $\frac{49}{63}=\frac{21}{27}$