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

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Last updated date: 23rd Feb 2024
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IVSAT 2024
Answer
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Hint: To convert given fractions into like fractions we will use LCM method. Firstly we will find out the LCM of all the denominators of the given fractions. Then we will multiply and divide each fraction with a number such that the denominator becomes equal to the LCM. Finally we will simplify each fraction and get the desired answer.

Complete step by step answer:
We have to convert the fractions given below into like fractions.
$\dfrac{3}{5},\dfrac{7}{10},\dfrac{8}{15},\dfrac{11}{30}$……..$\left( 1 \right)$
Firstly we know that denominator of all the fractions are:
$5,10,15,30$
So we will find the factors of each number and take out the each factor with highest power among them as follows:
$5=1\times 5$
$10=2\times 5$
$15=3\times 5$
$30=2\times 3\times 5$
We got the LCM of the denominator as follows:
$\begin{align}
  & LCM\left( 5,10,15,30 \right)=2\times 3\times 5 \\
 & LCM\left( 5,10,15,30 \right)=30 \\
\end{align}$
Next we will make denominator of the fractions from equation (1) 30 by multiplying dividing them by 6, 3, 2 and 1 respectively as below:
 $\begin{align}
  & \dfrac{3}{5}\times \dfrac{6}{6}=\dfrac{18}{30} \\
 & \dfrac{7}{10}\times \dfrac{3}{3}=\dfrac{21}{30} \\
\end{align}$
$\begin{align}
  & \dfrac{8}{15}\times \dfrac{2}{2}=\dfrac{16}{30} \\
 & \dfrac{11}{30}\times \dfrac{1}{1}=\dfrac{11}{30} \\
\end{align}$
So we got the fractions as $\dfrac{18}{30},\dfrac{21}{30},\dfrac{16}{30},\dfrac{11}{30}$
Hence the like fractions are $\dfrac{18}{30},\dfrac{21}{30},\dfrac{16}{30},\dfrac{11}{30}$

Note: Like fractions are the group of two or more fractions which have exactly the same denominator. We simply have to find the LCM of the denominator of the fractions and then according to the LCM obtain multiply and divide a number with each fractions to make the denominator same. LCM is the least common multiple of numbers which is the smallest positive integer divided by all the numbers completely. LCM is used before a fraction can be added or subtracted so that we can make the denominator the same. Also, we can use LCM for comparing simple fractions.