Which pair of fractions are like fractions?

Answer

Hint: In this question, we have to give an example of two pairs of like fractions. For this, we will first understand the meaning of fraction and then like a fraction. Using the definition, we will provide two pairs of the like fractions.

Complete step by step answer:
Here we have given two pairs of like fractions.
But before that, let us first understand what are fractions and like fractions.
A fraction is a number representing a part of a single whole object or a group of objects. It is defined by two numbers, numerator and denominator. The numerator is the number on the top and the denominator is the number at the bottom.
There are two types of fractions when comparing two or more fractions which are like fraction and unlike fraction.
The group of two or more fractions that has exactly the same denominator is called fractions. We can also say that the fraction which has the same numbers in the denominator are called like fractions.
For example: $ \dfrac{1}{7},\dfrac{2}{7},\dfrac{5}{7} $ are all like fraction having denominator equal to 7.
Now let us give two pairs of like fractions.
From the definition, we can say that $ \dfrac{1}{3},\dfrac{2}{3} $ are two like fractions having the same denominator i.e. 3.
Similarly, we can say that $ \dfrac{4}{9},\dfrac{7}{9} $ are two like fraction having the same denominator i.e. 9.
Hence two pairs of like fraction are $ \dfrac{1}{3},\dfrac{2}{3} $ and $ \dfrac{4}{9},\dfrac{7}{9} $ respectively.

Note:
 Students can take any other examples if they want. Try to take numerator smaller than denominator so they can be considered as proper fractions. Students can get confused with the same numerator as a like fraction but it is wrong.

Like and unlike fractions are the two groups of fractions:

(i) 1/5, 3/5, 2/5, 4/5, 6/5

(ii) 3/4, 5/6, 1/3, 4/7, 9/9

In group (i) the denominator of each fraction is 5, i.e., the denominators of the fractions are equal. 

The fractions with the same denominators are called like fractions.

In group (ii) the denominator of each fraction is different, i.e., the denominators of all the fractions are different. 

The fractions with different denominators are called unlike fractions.

Examples of like fractions are: 

(a) (2/9, 3/9, 5/9, 9/9);

(b) (3/10, 7/10, 1/10, 9/10);

(c) (1/7, 2/7, 4/7, 5/7, 7/7)

Examples unlike fractions are:

(a) (1/2, 1/4, 2/3, 5/6)

(b) (3/8, 2/3, 3/5, 2/7)

(c) (1/9, 2/7, 3/4, 2/5).

Like Fractions:

Observe the following figures.

The fraction \(\frac{1}{8}\), \(\frac{2}{8}\), \(\frac{3}{8}\) have the same denominator. Such fractions are called like fractions.

Unlike Fractions:

In figure (i) one part is shaded out of 3 parts, the fraction represented is \(\frac{1}{3}\).

In figure (ii) has two parts shaded out of 3 parts, the fraction represented is \(\frac{2}{5}\).

In figure (iii) we have three parts shaded out of 7 parts, the fraction represented is \(\frac{3}{7}\).

The fraction \(\frac{1}{3}\), \(\frac{2}{5}\), \(\frac{3}{7}\) have different denominators. Such fractions are called unlike fractions.

Related Concept

● Fraction of a Whole Numbers

● Representation of a Fraction

● Equivalent Fractions

● Properties of Equivalent Fractions

● Like and Unlike Fractions

● Comparison of Like Fractions

● Comparison of Fractions having the same Numerator

● Types of Fractions

● Changing Fractions

● Conversion of Fractions into Fractions having Same Denominator

● Conversion of a Fraction into its Smallest and Simplest Form

● Addition of Fractions having the Same Denominator

● Subtraction of Fractions having the Same Denominator

● Addition and Subtraction of Fractions on the Fraction Number Line

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