Question

Write an equivalent fraction of \[\dfrac{8}{9}\] with numerator 32.

Answer 1

Hint:
We are required to write the equivalent fraction. To do this, we will multiply the numerator with a suitable number. We will then multiply the denominator with the same number so that the fraction does not get altered. By doing this we will obtain the required equivalent form.

Complete step by step answer:
The concept of equivalent fractions is very important to solve this question.
Equivalent fractions are those fractions that have different numerators and denominators but the proportion represented by them is the same. Usually, these are obtained by multiplying the numerator and the denominator of a given fraction with the same number.
For example, the equivalent fraction of \[\dfrac{1}{3}\] can be obtained as follows–
Multiply both the numerator and the denominator by 2.
\[\dfrac{{1 \times 2}}{{3 \times 2}} = \dfrac{2}{6}\]
Multiply both the numerator and the denominator by 3.
\[\dfrac{{1 \times 3}}{{3 \times 3}} = \dfrac{3}{9}\]
Thus, the equivalent fractions of \[\dfrac{1}{3}\] are \[\dfrac{2}{6}\] and \[\dfrac{3}{9}\].
More fractions can be further obtained by multiplying as many numbers as needed. Thus, the equivalent fractions of a given fraction are infinite.
We will multiply both the numerator and the denominator with the same number so that the fraction does not get altered.
Now, let us find the equivalent fraction of \[\dfrac{8}{9}\] with numerator 32.
We have to find a number which when multiplied by 8 gives 32. We know that such a number is 4.
\[8 \times 4 = 32\]
Now, we will multiply the numerator and the denominator of the fraction \[\dfrac{8}{9}\] with 4 to get the equivalent fraction with the numerator 32.
\[\dfrac{{8 \times 4}}{{9 \times 4}} = \dfrac{{32}}{{36}}\]
$\therefore $ The required equivalent fraction is \[\dfrac{{32}}{{36}}\].

Note:
Here in this question, the numerator of the equivalent fraction of \[\dfrac{8}{9}\] is given as 32. We can also find the fraction by taking the denominator of the required fraction as \[x\].We will then equate the required fraction with \[\dfrac{8}{9}\].
Let \[x\] be the denominator of the fraction.
Now, equating both the fraction, we get:
\[\dfrac{8}{9} = \dfrac{{32}}{x}\]
Now, by cross multiplication, we get
\[8x = 32 \times 9\]
Dividing both side of the equation by 8, we get
\[x = \dfrac{{32 \times 9}}{8}\]
We will simplify the above equation to obtain \[x\].
\[x = 4 \times 9\]
Multiplying the terms, we get
\[x = 36\]
$\therefore $ The required fraction is \[\dfrac{{32}}{{36}}\].