Comparison of Unlike Fractions
In comparison of unlike fractions, we change the unlike fractions to like fractions and then compare.
Let us compare two fractions \(\frac{4}{7}\) and \(\frac{4}{9}\) which have same numerator.
Since 4 shaded parts of 7 is bigger than the 4 shaded parts of 9 therefore \(\frac{4}{7}\) > \(\frac{4}{9}\).
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 examples on comparing fractions
(i.e. unlike fractions).
1. Which one is greater, \(\frac{4}{7}\) or \(\frac{3}{5}\)?
First we convert these fractions into like fractions. To convert unlike fraction into like fraction first of all find the L.C.M. of their denominators.
L.C.M. of 7 and 5 = 35
Now, divide this L.C.M. by the denominator of both the fractions.
35 ÷ 7 = 5
35 ÷ 5 = 7
Multiply both the numerator and denominator with the number you get after dividing.
i.e., \(\frac{4 × 5}{7 × 5}\) = \(\frac{20}{35}\)
\(\frac{3 × 7}{5 × 7}\) = \(\frac{21}{35}\)
because \(\frac{21}{35}\) > \(\frac{20}{35}\)
So, \(\frac{3}{5}\) > \(\frac{4}{7}\)
We can compare two fractions by cross multiplication also.
Let us solve the above example by cross multiplication. Here, we cross multiply as follows.
4 × 5 = 20
3 × 7 = 21
Since, 21 > 20
Therefore, \(\frac{3}{5}\) > \(\frac{4}{7}\)
2. Compare 3\(\frac{2}{5}\) and 2\(\frac{3}{4}\).
First we convert these mixed numbers into improper
fractions.
2\(\frac{3}{4}\) = \(\frac{4 × 2 + 3}{4}\) = \(\frac{11}{4}\)
3\(\frac{2}{5}\) = \(\frac{5 × 3 + 2}{5}\) = \(\frac{17}{5}\)
Now, we compare \(\frac{11}{4}\) and \(\frac{17}{5}\) by cross multiplication.
11 × 5 = 55 and 17 × 4 = 68
We see that 68 > 55.
Therefore, \(\frac{17}{5}\) > \(\frac{11}{4}\) or, 3\(\frac{2}{5}\) > 2\(\frac{3}{4}\)
3. Let us
compare \(\frac{5}{7}\) and \(\frac{3}{5}\).
\(\frac{5}{7}\)
= \(\frac{5 × 5}{7 × 5}\) = \(\frac{25}{35}\)
Multiply
the numerator and denominator by 5.
\(\frac{3}{5}\)
= \(\frac{3 × 7}{5 × 7}\) = \(\frac{21}{35}\)
Multiply
the numerator and denominator by 7.
Hence, \(\frac{25}{35}\)
> \(\frac{21}{35}\)
Therefore, \(\frac{5}{7}\)
> \(\frac{3}{5}\)
We will
learn an alternative method i.e. cross multiply to compare the given fractions.
4. Let us
compare \(\frac{2}{3}\) and \(\frac{4}{5}\).
2 × 5 = 10
and 3 × 4 = 12
Since, 12
> 10, hence \(\frac{4}{5}\) > \(\frac{2}{3}\)
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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
4th Grade Math Activities
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