Question

Convert \[\dfrac{1}{4},\dfrac{5}{8},\dfrac{7}{{12}}{\text{ }}and{\text{ }}\dfrac{{13}}{{24}}\] into like fractions

Answer 1

Hint: Like fractions are fractions whose denominators (bottom numbers) are the same.
To convert unlike fractions to like fractions follow the steps below:
First find the LCM(lowest common multiple) of the denominators of the given fractions.
Then convert each fraction to its equivalent fraction with denominator equal to the LCM obtained in Step 1.

Complete step-by-step answer:
Given fractions are \[\dfrac{1}{4},\dfrac{5}{8},\dfrac{7}{{12}}{\text{ }}and{\text{ }}\dfrac{{13}}{{24}}\]
First we find the LCM of the denominators of the given fractions.
We will find the LCM of all the denominators of the fractions mentioned above to find the like fractions by prime factoring.
$24 = 2 \times 2 \times 2 \times 3$
$12 = 2 \times 2 \times 3$
$8 = 2 \times 2 \times 2$
$4 = 2 \times 2$
LCM of 4,8,12,24 \[ = \left( {2 \times 2 \times 2 \times 3} \right) = 24\]
Divide the LCM by the denominators of the given Fractions
For \[\dfrac{1}{4}\], \[\dfrac{24}{4}\] = $6$
For \[\dfrac{5}{8}\], \[\dfrac{24}{8}\] = $3$
For \[\dfrac{7}{{12}}\], \[\dfrac{24}{12}\] = $2$
For \[\dfrac{{13}}{{24}}\], \[\dfrac{24}{24}\] = $1$
Now using the LCM, make all the fractions like fractions.
Converting each of the given fractions into an equivalent fraction with denominator as 24.
Multiply the quotient by the numerator and keep the denominator equal to the LCM. i.e.
We get
\[\begin{array}{*{20}{l}}
\dfrac{{\left( {1 \times 6} \right)}}{{\left( {4 \times 6} \right)}} = \dfrac{6}{{24}} \\
\dfrac{{\left( {5 \times 3} \right)}}{{\left( {8 \times 3} \right)}} = \dfrac{{15}}{{24}} \\
\dfrac{{\left( {7 \times 2} \right)}}{{\left( {12 \times 2} \right)}} = \dfrac{{14}}{{24}} \\
\dfrac{{\left( {13 \times 1} \right)}}{{\left( {24 \times 1} \right)}} = \dfrac{{13}}{{24}} \\
 \end{array}\]

Therefore, \[\dfrac{6}{{24}},\dfrac{{15}}{{24}},\dfrac{{14}}{{24}}and\;\dfrac{{13}}{{24}}\;\] are the required like fractions.

Note: If two fractions have different numerators and denominators it is difficult to determine which fraction is larger. It is easier to determine which is larger if both fractions have the same denominator. And similarly like fractions are used for subtraction and addition unlike fractions also. For unlike fractions addition and subtraction we have to find their like fractions and then we solve the operation mentioned in the problem.