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
equivalent fraction
with denominator equal to the
L.C.M.
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 :

Let us convert each of the given fractions into an equivalent fraction with denominator equal to 96.

17⁄32 = (17 x 3)⁄(32 x 3) = 51⁄96 7⁄12 = (7 x 8)⁄(12 x 8) = 56⁄96 19⁄48 = (19 x 2)⁄(48 x 2) = 38⁄96 13⁄24 = (13 x 4)⁄(24 x 4) = 52⁄96 9⁄16 = (9 x 6)⁄(16 x 6) = 54⁄96

Now these fractions are like fractions (denominators same). By Rule 1, the fraction with bigger numerator is bigger.

So, the ascending order of these fractions is 38⁄96, 51⁄96, 52⁄96, 54⁄96, 56⁄96 i.e. 19⁄48, 17⁄32, 13⁄24, 9⁄16, 7⁄12 Ans.

Exercise 1 on Comparing Fractions

Solve the following problems on Comparing Fractions

Compare 8⁄9 with 15⁄17

Arrange the following fractions in descending order : 17⁄27, 11⁄12, 3⁄10, 13⁄15, 7⁄18.

For Answers, see at the bottom of the page.

Fraction Lying between two given Fractions

If a⁄b and c⁄dare two fractions, then the fraction(a + c)⁄(b + d) lies betweena⁄b and c⁄d. Thus, a⁄b <

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(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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