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Comparing Like Fractions

In comparing like fractions it is always easy to compare two or more because their denominators are same.

To compare two like fractions it is just enough to compare their numerators. If there are two like fractions, then the fraction with greater numerator is greater.

For example:

⁹/₁₃ > ⁵/₁₃ or ⁵/₁₃ ⁹/₁₃ Also, ¹⁵/₇ > ¹³/₇ or ¹³/₇ < ¹⁵/₇

Three or more like fractions can be arranged in ascending or descending order by arranging their numerators in ascending or descending order.

For example:

The fractions, ¹³/₈, ⁵/₈, ⁷/₈, ¹/₈, ¹¹/₈, ¹⁵/₈ can be arranged in ascending order as ¹/₈ < ⁵/₈ < ⁷/₈ < ¹¹/₈ < ¹³/₈ < ¹⁵/₈.

Similarly, the fractions ³/₁₁, ¹/₁₁, ⁸/₁₁, ⁶/₁₁, ⁷/₁₁, ⁹/₁₁ can be arranged in descending order as ⁹/₁₁ < ⁸/₁₁ < ⁷/₁₁ < ⁶/₁₁ < ³/₁₁ < ¹/₁₁.

For example:

1. Compare the following fractions and put an appropriate signs < or >.

(i) ⁵/₁₆ __ ²/₁₆

Solution:

⁵/₁₆ > ²/₁₆

(ii) 3/6 __ 0/6

Solution:

3/6 > 0/6

(iii) ¹/₉ __ ⁶/₉

Solution:

¹/₉ < ⁶/₉

(iv) ⁸/₁₂ __ ⁵/₁₂

Solution:

⁸/₁₂ > ⁵/₁₂

(v) ³/₁₁ __ ⁵/₁₁

Solution:

³/₁₁ < ⁵/₁₁

(vi) 4/15 __ 0/15

Solution:

4/15 > 0/15

(vii) ²/₂₀ __ ⁴/₂₀

Solution:

²/₂₀ < ⁴/₂₀

(viii) ¹/₁₇ __ ¹³/₁₇

Solution:

¹/₁₇ < ¹³/₁₇

2. Arrange ³/₈, ⁶/₈, ⁴/₈ in ascending order

Solution:

³/₈, ⁴/₈, ⁶/₈.

3. Arrange ⁶/₉, ⁴/₉, ⁸/₉, ³/₉ in ascending order

Solution:

³/₉, ⁴/₉, ⁶/₉, ⁸/₉.

4. Arrange ³/₆, ⁴/₆, ²/₆, ¹/₆, ⁵/₆, ⁶/₆ in descending order.

Solution:

⁶/₆, ⁵/₆, ⁴/₆, ³/₆, ²/₆, ¹/₆

5. Arrange ²/₉, ⁷/₉, ³/₉, ⁴/₉, ¹/₉, ⁶/₉, ⁵/₉ in descending order.

Solution:

⁷/₉, ⁶/₉, ⁵/₉, ⁴/₉, ³/₉, ²/₉, ¹/₉