Comparison of Like Fractions
Any two like
fractions can be compared by comparing their numerators. The fraction with
larger numerator is greater than the fraction with smaller numerator, for
example \(\frac{7}{13}\) > \(\frac{2}{13}\) because 7 > 2.
1. In comparison of like fractions here are some rectangular figures.
(i)
In (i) shaded portion represents \(\frac{2}{7}\)
(ii)
In (ii) shaded portion represents \(\frac{3}{7}\)
(iii)
In (iii) shaded portion represents \(\frac{5}{7}\)
It is clear that \(\frac{2}{7}\) < \(\frac{3}{7}\) < \(\frac{5}{7}\)
or \(\frac{5}{7}\) > \(\frac{3}{7}\) > \(\frac{2}{7}\)
Thus, in like fractions or fractions having same denominator, that fraction is greater which has the greater numerator.
Accordingly, 3/5 > 2/5; 2/5 < 3/5
15/17 > 10/17; 10/17 < 15/17
2. Again, let us
consider \(\frac{2}{5}\) and \(\frac{3}{5}\).


\(\frac{2}{5}\) represents 2 parts out of 5 equal parts on the strip.



\(\frac{3}{5}\) represents 3 parts out of 5 equal parts on the strip.

3 > 2
Hence, for
any two like fractions, the fraction with the larger numerator is greater than
the fraction with smaller numerator.
If
there are three or more like fractions, they may be arranged in
ascending (increasing) and descending (decreasing) order. The order will
be according to the order of the numerators.
(a) Ascending order: 1/9, 2/9, 3/9, 4/9, 5/9, 7/9, 8/9:
as, 1 < 2 < 3 < 4 < 5 < 7 < 8
(b) Descending order: 8/9, 7/9, 5/9, 4/9, 3/9, 2/9, 1/9:
as, 8 > 7 > 5 > 4 > 3 > 2 > 1
Similarly again;
(a) Ascending order: 5/17, 7/17, 8/17, 11/17, 13/17, 14/17, 16/17:
as, 5 < 7 < 8 < 11 < 13 < 14 < 16
(b) Descending order: 16/17, 14/17, 13/17, 11/17, 8/17, 7/17, 5/17:
as, 16 > 14 > 13 > 11 > 8 > 7 > 5
Comparison of Fractions:
Fractions with same Denominator:
If two fractions have the same denominator, the fraction with greater numerator denotes the greater fraction.
For example,
\(\frac{6}{9}\) > \(\frac{4}{9}\)
\(\frac{2}{3}\) < \(\frac{5}{3}\)
Comparison of fractions with the same denominator
Observe the following figures.
In the first figure, 2 parts out of 6 equal parts are shaded.
In the second figure, 3 parts out of 6 equal parts are shaded.
Clearly, shaded parts in the second circle are more than those in the first circle.
Thus, \(\frac{3}{6}\) > \(\frac{2}{6}\) or \(\frac{2}{6}\) < \(\frac{3}{6}\)
Hence, among two fractions having the same denominator, the fraction with the greater numerator is greater than the other.
1. Compare 2/5 and 4/5
Solution:
Consider 2/5, 4/5
Since, 4 > 2, hence 4/5 > 2/5 or 2/5 < 4/5
2. Compare 7/15 and 8/15
Solution:
Consider 7/15, 8/15
Since, 8 > 7, hence 8/5 > 7/5 or 7/5 < 8/5
Worksheet on Comparison of Like Fractions:
1. Compare the given fractions and put the right sign <,> or =.
(i) \(\frac{7}{4}\) …… \(\frac{11}{4}\)
(ii) \(\frac{8}{13}\) …… \(\frac{2}{13}\)
(iii) \(\frac{5}{24}\) …… \(\frac{7}{24}\)
Answers:
1. (i) <
(ii) >
(iii) <
2. Put the appropriate sign >, < or = in the box.
(i) \(\frac{3}{8}\) ______ \(\frac{2}{8}\)
(ii) \(\frac{11}{7}\) ______ \(\frac{13}{7}\)
(iii) \(\frac{2}{9}\) ______ \(\frac{7}{9}\)
(iv) \(\frac{5}{11}\) ______ \(\frac{1}{11}\)
Answers:
2. (i) >
(ii) <
(iii) <
(iv) >
You might like these
The fractions having the same value are called equivalent fractions. Their numerator and denominator can be different but, they represent the same part of a whole. We can see the shade portion with respect to the whole shape in the figures from (i) to (viii) In; (i) Shaded
In mental math on fractions we will solve different type of problems on types of fractions, equivalent fractions, fraction in lowest terms, comparison of fractions, fraction in lowest term, types of fractions, addition of fractions, subtraction of fractions and word problems
In worksheet on fractions, all grade students can practice the questions on fractions on a whole number and also on representation of a fraction. This exercise sheet on fractions can be practiced
In worksheet on fractions, the questions are based on comparing the fractions; arranging the fractions in ascending and descending order; find the sum and the difference of the fractions
In conversion of improper fractions into mixed fractions, we follow the following steps: Step I: Obtain the improper fraction. Step II: Divide the numerator by the denominator
In conversion of mixed fractions into improper fractions, we may follow the following steps: Step I: Obtain the mixed fraction. Let the mixed fraction be 22/5. Step II: Identify the whole number
What is the difference between proper fraction and improper fraction? Proper fraction: The fractions 1/4, 3/8, 5/11, 9/13, 14/25, etc. are the fractions where the numerators are smaller than
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
The three types of fractions are : Proper fraction, Improper fraction, Mixed fraction, Proper fraction: Fractions whose numerators are less than the denominators are called proper fractions. (Numerator < denominator). Two parts are shaded in the above diagram.
To find the difference between like fractions we subtract the smaller numerator from the greater numerator. In subtraction of fractions having the same denominator, we just need to subtract the numerators of the fractions.
To add two or more like fractions we simplify add their numerators. The denominator remains same. Thus, to add the fractions with the same denominator, we simply add their numerators and write the common denominator.
In comparison of unlike fractions, we change the unlike fractions to like fractions and then compare. To compare two fractions with different numerators and different denominators, we multiply by a number to convert them to like fractions. Let us consider some of the
In comparison of fractions having the same numerator the following rectangular figures having the same lengths are divided in different parts to show different denominators. 3/10 < 3/5 < 3/4 or 3/4 > 3/5 > 3/10 In the fractions having the same numerator, that fraction is
There are two methods to reduce a given fraction to its simplest form, viz., H.C.F. Method and Prime Factorization Method. If numerator and denominator of a fraction have no common factor other than 1(one), then the fraction is said to be in its simple form or in lowest
How to find fraction as a part of collection? Let there be 14 rectangles forming a box or rectangle. Thus, it can be said that there is a collection of 14 rectangles, 2 rectangles in each row. If it is folded into two halves, each half will have 7 rectangles. So, we can say
Related Concept
4th Grade Math Activities
From Comparison of Like Fractions to HOME PAGE
Didn't find what you were looking for? Or want to know more information
about Math Only Math.
Use this Google Search to find what you need.
Share this page:
What’s this?


New! Comments
Have your say about what you just read! Leave me a comment in the box below. Ask a Question or Answer a Question.