Question

While comparing like fractions, fraction with greater numerator is:
(a) greater
(b) smaller
(c) equal
(d) can’t compare

Answer 1

Hint: In order to find the solution to this question, we should know that like fractions are nothing but the fractions with the same denominator that is, if any 2 or more fractions have the same denominators then they are like fractions.

Complete step-by-step answer:
In this question, we are asked to find what the fraction with the greater numerator is when we compare like fractions. We know that like fractions are those fractions which have the same denominators, that means we would be working with whole’s that are split into the same number of pieces. It doesn’t matter what the numerator is, so long as the denominators are the same.
In this question, we are given that one of the fractions will have a greater numerator than the other. Let us consider a + c and a as the numerator of both the fractions with the denominator b. So, the fractions are \[\dfrac{a+c}{b}\] and \[\dfrac{a}{b}\].
Now, let us consider \[\dfrac{a}{b}={{x}_{1}}\], then we can see that \[\dfrac{a+c}{b}\] can be written as \[\dfrac{a}{b}+\dfrac{c}{b}\] and we assumed that \[\dfrac{a}{b}={{x}_{1}}\]. Therefore, we can write,
\[\dfrac{a}{b}+\dfrac{c}{b}={{x}_{1}}+\dfrac{c}{b}\]
And we know that \[{{x}_{1}}+\dfrac{c}{b}>{{x}_{1}}\], which means that \[\dfrac{a+c}{b}>\dfrac{a}{b}\].
So, we can say the number with the greater numerator is greater.
Hence, option (a) is the right answer.

Note: We can also solve this question by taking any shape or something like that. For example, let us consider 2 rectangular blocks and we have divided them into 7 equal pieces and both blocks are also equal likewise.

In the first block, we will highlight 3 pieces out of 7 pieces, and in the second block, we will highlight 5 pieces out of 7 pieces. So, in fraction, we can write it as \[\dfrac{3}{7}\] for block 1 and \[\dfrac{5}{7}\] for block 2. Now, based on the area highlighted, we will decide the greater one. In block 1, the area highlighted is less than the area highlighted in block 2. So, we can say that the fraction with the greater numerator is greater. Hence options (a) is the correct answer.