Here, we will see which fractions are bigger(smaller)and arranging them in ascending/descending order, Fraction(s) Lying between two given Fractions, with number of solved examples and problems for practice with answers.
Rules for deciding which fractions are bigger(smaller)
Rule 1 :
Between two fractions with same denominator, the one with greater numerator is greater of the two.
Comparing fractions with different numerators and denominators
Method 1: Cross Products Method
Let a⁄b and c⁄dbe two fractions.
Find cross products ad and bc.
If ad > bc, then a⁄b >c⁄d.
If ad < bc, then a⁄b <c⁄d.
If ad =
bc, then a⁄b =c⁄d.
Solved Example 1 of Comparing Fractions
Compare 5⁄6 with 11⁄13
Solution: Find the cross products 5 x 13 and 6 x 11.
We know 5 x 13 = 65; 6 x 11 = 66. 65 < 66 ⇒ 5 x 13 < 6 x 11 ⇒ 5⁄6 < 11⁄13. Ans.
Cross products method is useful for comparing two fractions.
For comparing a number of fractions (ordering of the fractions), Method 2 is more convenient.
Method 2 : L.C.M. method
Change each one of the given fractions into an
with denominator equal to the
of the denominators of the givenfractions. Now the new fractions are like fractions which can be compared by Rule 1.
Solved Example 2 of Comparing Fractions
Arrange the following fractions in ascending order :
(i) Solution : Applying the above Formula,the fraction lying between 1⁄2 and 3⁄4 is (1 + 3)⁄(2 + 4) = 4⁄6 = 2⁄3. Ans. Thus, 1⁄2 < 2⁄3 < 3⁄4.
(ii) Solution : We have, 1⁄2 < 2⁄3 < 3⁄4. To get one more fraction in between 1⁄2 and 3⁄4, let us get a fraction in between 1⁄2 and 2⁄3.
Applying the above formula, again, the fraction lying between 1⁄2 and 2⁄3 is (1 + 2)⁄(2 + 3) = 3⁄5. Ans. Thus, 1⁄2 < 3⁄5 < 2⁄3 < 3⁄4.
Thus,Two fractions lying between 1⁄2 and 3⁄4 are 3⁄5 and 2⁄3. Ans.
(iii) Solution : We have, 1⁄2 < 3⁄5 < 2⁄3 < 3⁄4 To get one more fraction in between 1⁄2 and 3⁄4, let us get a fraction in between 2⁄3 and 3⁄4.
Applying the above formula, again, the fraction lying between 2⁄3 and 3⁄4 is (2 + 3)⁄(3 + 4) = 5⁄7. Ans. Thus, 1⁄2 < 3⁄5 < 2⁄3 < 5⁄7 < 3⁄4.
Thus,Three fractions lying between 1⁄2 and 3⁄4 are 3⁄5, 2⁄3 and 5⁄7. Ans.
Exercise 2 on Comparing Fractions
Between 1⁄3 and 8⁄9
Insert one fraction
Insert two fractions
Insert three fractions
For Answers, see at the bottom of the page.
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