Question

Convert $ \dfrac{3}{5},\dfrac{7}{10},\dfrac{8}{15} $ and $ \dfrac{11}{30} $ into like fractions

Answer 1

Hint: We recall the fractions and definitions of like an, unlike fractions. We find the least common multiple of given factions $ \dfrac{3}{5},\dfrac{7}{10},\dfrac{8}{15} $ and $ \dfrac{11}{30} $ . We multiply the suitable number in numerator and denominator each fraction such that the denominator is equal to the least common multiple of the denominators.

Complete step by step answer:
We know that a fraction represents part of a whole. A fraction is always represented in the form of $ \dfrac{p}{q} $ where the positive number $ p $ above the line is called the numerator and the positive number $ q $ below the line is called the denominator. We call two fractions like fractions when their denominators are equal and we call two fractions unlike fractions when their denominators are not equal.

We are given the fractions $ \dfrac{3}{5},\dfrac{7}{10},\dfrac{8}{15} $ and $ \dfrac{11}{30} $ in the question. We see that the denominators $ 5,10,15,30 $ are not equal . We have to find their least common multiple using tabular method.
\[\begin{align}
  & 2\left| \!{\underline {\,
  5,10,15,30 \,}} \right. \\
 & 3\left| \!{\underline {\,
  5,5,15,15 \,}} \right. \\
 & 5\left| \!{\underline {\,
  5,5,5,5 \,}} \right. \\
 & \hspace{0.3 cm} 1,1,1,1 \\
\end{align}\]
So the least common multiple of the denominators is 30. So we have to convert denominators of all the give fractions. So we multiply 6 in the denominator of $ \dfrac{3}{5} $ to reach to 30, then we have to multiply 6 also in the numerator and get;
\[\dfrac{3}{5}=\dfrac{3\times 6}{5\times 6}=\dfrac{18}{30}\]
We need to multiply 3 in the denominator of $ \dfrac{7}{10} $ to reach to 30, then we have to also multiply 3 also in the numerator and get ;
 \[\dfrac{7}{10}=\dfrac{7\times 3}{10\times 3}=\dfrac{21}{30}\]
We need to multiply 2 in the denominator of $ \dfrac{8}{15} $ to reach to 30, then we have to also multiply 2 also in the numerator and get ;
 \[\dfrac{8}{15}=\dfrac{8\times 2}{15\times 2}=\dfrac{16}{30}\]
The last given fraction $ \dfrac{11}{30} $ has already denominator 30, so we do not need to change. So the like fractions are
\[\dfrac{18}{30},\dfrac{21}{30},\dfrac{16}{30},\dfrac{11}{30}\]

Note:
We note that if we multiply a non-zero number $ k $ in the numerator and denominator of the fraction $ \dfrac{p}{q} $ , we get equivalent fractions of $ \dfrac{p}{q} $ . We also note that we can add and subtract two fractions only when they are like fractions. We can camper two fractions either they are like or their numerators are equal.