Question

Write five fractions equivalent to the following fraction: $ \dfrac{7}{9} $ ?

Answer 1

Hint: In this question, the numerator of the given fraction is $ 7 $ and the denominator is equal to $ 9 $ and we have to find five equivalent fractions. When the numerator and the denominator are in the form of prime factors and don’t have any common factor, the fraction is said to be simplified. We can find an equivalent fraction by multiplying or dividing the numerator and denominator of the fraction by the same number.

Complete step-by-step answer:
So, we have to find five equivalent fractions of the fraction $ \dfrac{7}{9} $ .
So, we have to multiply the given fraction $ \dfrac{7}{9} $ with a number or an expression such that the value of the fraction remains unchanged. As we have to find five fractions equivalent to the given fraction $ \dfrac{7}{9} $ , we would have to multiply the numerator and denominator of the fraction with five numbers.
So, we have, $ \dfrac{7}{9} $ .
We multiply the numerator and denominator of $ \dfrac{7}{9} $ by $ 2 $ . So, we get,
 $ \Rightarrow \dfrac{7}{9} \times \dfrac{2}{2} = \dfrac{{14}}{{18}} $
We multiply the numerator and denominator of $ \dfrac{7}{9} $ by $ 3 $ . So, we get,
 $ \Rightarrow \dfrac{7}{9} \times \dfrac{3}{3} = \dfrac{{21}}{{27}} $
We multiply the numerator and denominator of $ \dfrac{7}{9} $ by $ 4 $ . So, we get,
 $ \Rightarrow \dfrac{7}{9} \times \dfrac{4}{4} = \dfrac{{28}}{{36}} $
Now, we multiply the numerator and denominator of $ \dfrac{7}{9} $ by $ 5 $ . So, we get,
 $ \Rightarrow \dfrac{7}{9} \times \dfrac{5}{5} = \dfrac{{35}}{{45}} $
We multiply the numerator and denominator of $ \dfrac{7}{9} $ by $ 10 $ . So, we get,
 $ \Rightarrow \dfrac{7}{9} \times \dfrac{{10}}{{10}} = \dfrac{{70}}{{90}} $
Hence, the required five equivalent fractions of the given fraction $ \dfrac{7}{9} $ are:
 $ \dfrac{{14}}{{18}} $ , $ \dfrac{{21}}{{27}} $ , $ \dfrac{{28}}{{36}} $ , $ \dfrac{{35}}{{45}} $ and \[\dfrac{{70}}{{90}}\].
So, the correct answer is “ $ \dfrac{{14}}{{18}} $ , $ \dfrac{{21}}{{27}} $ , $ \dfrac{{28}}{{36}} $ , $ \dfrac{{35}}{{45}} $ and \[\dfrac{{70}}{{90}}\]”.

Note: Equivalent fractions are the fractions that have different numerator and denominator but are equal to the same value. Following the information and the steps mentioned in the above solution, we can solve similar questions. Care should be taken while doing calculations in order to be sure of the answer.