Question

Find an equivalent fraction of $ \dfrac{7}{{11}} $ having denominator $ 33 $ .

Answer 1

Hint: To find equivalent fraction of given fraction. We first see either a numerator or denominator of a new fraction will be given. As, in this problem the denominator of fraction is given. Then we find a number with which to multiply a given denominator to obtain a new denominator of fraction. Using the number we can also obtain a new numerator of fraction and hence new equivalent fraction.

Complete step by step solution:
Given fraction is $ \dfrac{7}{{11}} $ .
Now, to write an equivalent fraction whose denominator is $ 33 $ .
We will find a number such that it’s product with denominator of given fraction gives $ 33. $
Therefore, we see that the required number is $ 3. $
Now, on multiplying $ 3 $ with both numerator and denominator we obtain equivalent fraction.
i.e.
 $
  11 \times a = 33 \\
   \Rightarrow a = \dfrac{{33}}{{11}} \\
   \Rightarrow a = 3 \;
  $
Using, this we have
 $ \dfrac{{7 \times a}}{{11 \times a}} = \dfrac{b}{{33}} $
Substituting $ a = 3 $ above we have
 $ \dfrac{{7 \times 3}}{{11 \times 3}} = \dfrac{b}{{33}} $
 $
   \Rightarrow \dfrac{{21}}{{33}} = \dfrac{b}{{33}} \\
   \Rightarrow b = 21 \;
  $
So, the required equivalent fraction of a given fraction is $ \dfrac{{21}}{{33}} $ .

Note: Equivalent fraction are fractions which don’t look the same as the given fraction but they are equal in ratio. Therefore, we can write any number of equivalent fractions of given fraction by using suitable multiples. After simplification to the lowest form every equivalent fraction reduced to its fraction.