Question

How to make a group of $5$ unlike fractions into like fractions?

Answer 1

Hint: A fraction is just a numerical value which denotes the equal parts of a whole (or collection). We may apply the fraction in our daily life. For example, when we slice a guava, it will split into two or four and so on.
Example:$\dfrac{1}{2},\dfrac{1}{4},\dfrac{2}{3}$
Here, the number above the line is usually called the numerator and the number below the line is called the denominator.
Fractions having same denominators are called like fractions and fractions having different denominators are called unlike fractions.

Complete step by step answer:
Let us consider a group of $5$unlike fractions which are listed below.
$1,\dfrac{4}{5},\dfrac{7}{{10}},\dfrac{1}{2}$
$\dfrac{3}{4},\dfrac{5}{6},\dfrac{1}{3}$
$\dfrac{2}{9},\dfrac{5}{6}$
$\dfrac{3}{4},\dfrac{1}{2},\dfrac{2}{6},\dfrac{3}{9}$
$\dfrac{1}{2},\dfrac{3}{6},\dfrac{5}{9}$

When we are asked to convert unlike fractions into like fractions, we need to find the LCM for the denominators of unlike fractions and then we have to adjust the fractions to the LCM.
i) LCM of $1,5,10,2$ is $10$
Now, we need to adjust the numerator of the fractions to the LCM$10$.
Consider the fraction$\dfrac{1}{1}$ .
When we multiply the numerator by$10$, we get the required fraction (i.e.)$\dfrac{{10}}{{10}}$
Similarly, when we do the same, we will get the like fractions as given below.
$\dfrac{{10}}{{10}},\dfrac{8}{{10}},\dfrac{7}{{10}},\dfrac{5}{{10}}$
ii) LCM of $4,6,3$ is $12$
Now, we need to adjust the numerator of the fractions to the LCM$12$.
Consider the fraction$\dfrac{3}{4}$ .
When we multiply the numerator by$3$, we get the required fraction (i.e.)$\dfrac{9}{{12}}$
Similarly, when we do the same, we will get the like fractions as given below.
$\dfrac{9}{{12}},\dfrac{{10}}{{12}},\dfrac{4}{{12}}$

iii) LCM of $9,6$ is $18$
Now, we need to adjust the numerator of the fractions to the LCM$18$.
Consider the fraction$\dfrac{2}{9}$ .
When we multiply the numerator by$2$, we get the required fraction (i.e.)$\dfrac{4}{{18}}$
Similarly, when we do the same, we will get the like fractions as given below.
$\dfrac{4}{{18}},\dfrac{{15}}{{18}}$

iv) LCM of $4,2,9,6$ is $36$
Now, we need to adjust the numerator of the fractions to the LCM$36$.
Consider the fraction$\dfrac{3}{4}$ .
When we multiply the numerator by$9$, we get the required fraction (i.e.)$\dfrac{{27}}{{36}}$
Similarly, when we do the same, we will get the like fractions as given below.
$\dfrac{{27}}{{36}},\dfrac{{13}}{{36}},\dfrac{{12}}{{36}},\dfrac{{12}}{{36}}$

v) LCM of $2,6,9$ is $18$
Now, we need to adjust the numerator of the fractions to the LCM$18$.
Consider the fraction$\dfrac{1}{2}$ .
When we multiply the numerator by$9$, we get the required fraction (i.e.)$\dfrac{9}{{18}}$
Similarly, when we do the same, we will get the like fractions as given below.
$\dfrac{9}{{18}},\dfrac{6}{{18}},\dfrac{{10}}{{18}}$

Note: Fractions are classified into many types. Among them, the important types of fraction are as follows.
Proper fraction: It is a fraction in which the numerator is less than the denominator.
 Example:$\dfrac{4}{5}$
Improper fraction: It is a fraction in which the numerator is more than or equal to the denominator.
Example:$\dfrac{7}{4},\dfrac{3}{3}$
Mixed fraction: It is a fraction containing both the integral part and a proper fraction.
Example:$5\dfrac{1}{4}$
Like fractions: Fractions contain the same denominators.
Example:$\dfrac{7}{4},\dfrac{3}{4}$
Unlike fractions: Fractions contain different denominators.
Example:$\dfrac{7}{4},\dfrac{3}{3}$