Chapter 4.3, Problem 44E

To determine

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

Answer to Problem 44E

Fraction is equivalent $\frac{63}{84}=\frac{45}{60}$

Simplest Form of $\frac{63}{84}=\frac{3}{4}$ .

Simplest Form of $\frac{45}{60}=\frac{3}{4}$ .

Explanation of Solution

Given information: $\frac{63}{84},\frac{45}{60}$

Formula Used: Factorisation

Calculation:

  $\frac{63}{84}$ and $\frac{45}{60}$

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

  $\frac{63}{84}=\frac{3\times 3\times 7}{2\times 2\times 3\times 7}$ and $\frac{45}{60}=\frac{3\times 3\times 5}{2\times 2\times 3\times 5}$

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

  $\frac{3\times 3\times 7}{2\times 2\times 3\times 7}=\frac{3}{2\times 2}$ and $\frac{3\times 3\times 5}{2\times 2\times 3\times 5}=\frac{3}{2\times 2}$

Hence, fraction in simplest form

  $\frac{63}{84}=\frac{3}{4}$ and $\frac{45}{60}=\frac{3}{4}$

Fraction is equivalent $\frac{63}{84}=\frac{45}{60}$