COMPARING RATIONAL NUMBERS WORKSHEET

Questions 1-12 : Compare the given two rational numbers.

Question 1 :

³⁄₇ and ⁵⁄₇

Question 2 :

⅗ and ⅖

Question 3 :

⁻³⁄₇ and ⁻⁵⁄₇

Question 4 :

⁻⁵⁄₇ and ⁻⁴⁄₇

Question 5 :

⁻²⁄₅ and ⅕

Question 6 :

²⁄₇ and ⁻⅛

Question 7 :

⅙ and ¼

Question 8 :

¾ and ⅚

Question 9 :

⁻¹¹⁄₅ and ⁻²¹⁄₈

Question 10 :

³⁄₋₄ and ⁻¹⁄₂

Question 11 :

⅘ and ⅔

Question 12 :

⁻³⁄₈ and ⁻²⁄₋₅

Questions 13-14 : Compare the given rational numbers and arrange them in ascending and descending orders.

Question 13 :

⁻⁵⁄₁₂, ⁻¹¹⁄₈, ⁻¹⁵⁄₂₄, ⁻⁷⁄₋₉, ¹²⁄₃₆

Question 14 :

⁻¹⁷⁄₁₀, ⁻⁷⁄₅, 0, ⁻²⁄₄, ⁻¹⁹⁄₂₀

Answers

1. Answer :

Both ³⁄₇ and ⁵⁄₇ are positive and they have the same denominator 7.

Compare the numerators 3 and 5.

3 < 5

Therefore,

³⁄₇ < ⁵⁄₇

2. Answer :

Both ⅗ and ⅖ are positive with same denominator.

Compare the numerators 3 and 2.

3 > 2

Therefore,

⅗ > ⅖

3. Answer :

Both ⁻³⁄₇ and ⁻⁵⁄₇ are negative with same denominator.

Compare the numerators -3 and -5.

-3 > -5

Therefore,

⁻³⁄₇ > ⁻⁵⁄₇

4. Answer :

Both ⁻⁵⁄₇ and ⁻⁴⁄₇ are negative with same denominator.

Compare the numerators -5 and -4.

-5 < -4

Therefore,

⁻⁵⁄₇ < ⁻⁴⁄₇

5. Answer :

Since ⁻²⁄₅ and ⅕ are having different signs, the positive rational number is always greater than the negative rational number.

Therefore,

⁻²⁄₅ < ⅕

6. Answer :

Since ²⁄₇ and ⁻⅛ are having different signs, the positive rational number is always greater than the negative rational number.

Therefore,

²⁄₇ > ⁻⅛

7. Answer :

Since ⅙ and ¼ are having different denominators, find the least common multiple of the denominators.

Least common multiple of (6, 4) = 12.

Make 12 as denominator for both the fractions by multiplying both the fractions by the approproate numbers. 

Multiply both numerator and denominator of the fraction ⅙ by 2 to get the denominator 12.

⁽¹ˣ²⁾⁄₍₆ₓ₂₎ = ²⁄₁₂ ----(1)

Multiply both numerator and denominator of the fraction ¼ by 3 to get the denominator 12.

⁽¹ˣ³⁾⁄₍₄ₓ₃₎ = ³⁄₁₂ ----(2)

In (1) and (2), compare the numerators.

2 < 3

Therefore,

²⁄₁₂ < ³⁄₁₂ ----> ⅙ < ¼

8. Answer :

Since ¾ and ⅚ are having different denominators, find the least common multiple of the denominators.

Least common multiple of (4, 6) = 12.

Make 12 as denominator for both the fractions by multiplying both the fractions by the approproate numbers.

Multiply both numerator and denominator of the fraction ¾ by 3 to get the denominator 12.

⁽³ˣ³⁾⁄₍₄ₓ₃₎ = ⁹⁄₁₂ ----(1)

Multiply both numerator and denominator of the fraction ⅚ by 2 to get the denominator 12.

⁽⁵ˣ²⁾⁄₍₆ₓ₂₎ = ¹⁰⁄₁₂ ----(2)

In (1) and (2), compare the numerators 9 and 10.

9 < 10

Therefore,

⁹⁄₁₂ < ¹⁰⁄₁₂ ----> ¾ < ⅚

9. Answer :

Since ⁻¹¹⁄₅ and ⁻²¹⁄₈ are having different denominators, find the least common multiple of the denominators.

Least common multiple of (5, 8) = 40.

Make 40 as denominator for both the fractions by multiplying both the fractions by the approproate numbers. 

Multiply both numerator and denominator of the fraction ⁻¹¹⁄₅ by 8 to get the denominator 40.

⁽⁻¹¹ˣ⁸⁾⁄₍₅ₓ₈₎ = ⁻⁸⁸⁄₄₀ ----(1)

Multiply both numerator and denominator of the fraction ⁻²¹⁄₈ by 5 to get the denominator 40.

⁽⁻²¹ˣ⁵⁾⁄₍₈ₓ₅₎ = ⁻¹⁰⁵⁄₄₀ ----(2)

In (1) and (2), compare the numerators.

-88 > -105

Therefore,

⁻⁸⁸⁄₄₀ > ⁻¹⁰⁵⁄₄₀ ----> ⁻¹¹⁄₅ > ⁻²¹⁄₈

10. Answer :

³⁄₋₄ can be written as ⁻³⁄₄.

Since ⁻³⁄₄ and ⁻¹⁄₂ are having different denominators, find the least common multiple of the denominators.

Least common multiple of (4, 2) = 4.

The fraction ⁻³⁄₄ is already having the denominator 4.

⁻³⁄₄ ----(1)

Multiply both numerator and denominator of the fraction ⁻¹⁄₂ by 2 to get the denominator 4.

⁽⁻¹ˣ²⁾⁄₍₂ₓ₂₎ = ⁻²⁄₄ ----(2)

In (1) and (2), compare the numerators.

-3 < -2

Therefore,

⁻³⁄₄ < ⁻²⁄₄ ----> ³⁄₋₄ < ⁻¹⁄₂

11. Answer :

Since ⅘ and ⅔ are having different denominators, find the least common multiple of the denominators.

Least common multiple of (5, 3) = 15.

Make 15 as denominator for both the fractions by multiplying both the fractions by the approproate numbers.

Multiply both numerator and denominator of the fraction ⅘ by 3 to get the denominator 15.

⁽⁴ˣ³⁾⁄₍₅ₓ₃₎ = ¹²⁄₁₅ ----(1)

Multiply both numerator and denominator of the fraction ⅔ by 5 to get the denominator 15.

⁽²ˣ⁵⁾⁄₍₃ₓ₅₎ = ¹⁰⁄₁₅ ----(2)

In (1) and (2), compare the numerators.

12 > 10

Therefore,

¹²⁄₁₅ > ¹⁰⁄₁₅ ----> ⅘ > ⅔

12. Answer :

⁻²⁄₋₅ = ²⁄₅

Since ⁻³⁄₈ and ²⁄₅ are having different signs, the positive rational number is always greater than the negative rational number.

Therefore,

⁻³⁄₈ < ²⁄₅ ----> ⁻³⁄₈ < ⁻²⁄₋₅

13. Answer :

⁻⁵⁄₁₂, ⁻¹¹⁄₈, ⁻¹⁵⁄₂₄, ⁻⁷⁄₋₉, ¹²⁄₃₆

Least common multiple of (12, 8, 24, 9, 36) = 144.

⁽⁻⁵ˣ¹²⁾⁄₍₁₂ₓ₁₂₎ = ⁻⁶⁰⁄₁₄₄

⁽⁻¹¹ˣ¹⁸⁾⁄₍₈ₓ₁₈₎ = ⁻¹⁹⁸⁄₁₄₄

⁽⁻¹⁵ˣ⁶⁾⁄₍₂₄ₓ₆₎ = ⁻⁹⁰⁄₁₄₄

⁽⁻⁷ˣ¹⁶⁾⁄₍₋₉ₓ₁₆₎ = ¹¹²⁄₁₄₄

⁽¹²ˣ⁴⁾⁄₍₃₆ₓ₄₎ = ⁴⁸⁄₁₄₄

⁻¹⁹⁸⁄₁₄₄ > ⁻⁹⁰⁄₁₄₄ > ⁻⁶⁰⁄₁₄₄ > ⁴⁸⁄₁₄₄ > ¹¹²⁄₁₄₄

Ascending Order :

⁻¹¹⁄₈, ⁻¹⁵⁄₂₄, ⁻⁵⁄₁₂, ¹²⁄₃₆, ⁻⁷⁄₋₉

Descending Order :

⁻⁷⁄₋₉, ¹²⁄₃₆, ⁻⁵⁄₁₂, ⁻¹⁵⁄₂₄, ⁻¹¹⁄₈

14. Answer :

⁻¹⁷⁄₁₀, ⁻⁷⁄₅, 0, ⁻²⁄₄, ⁻¹⁹⁄₂₀

Least common multiple of (10, 5, 4, 20) = 20.

⁽⁻¹⁷ˣ²⁾⁄₍₁₀ₓ₂₎ = ⁻³⁴⁄₂₀

⁽⁻⁷ˣ⁴⁾⁄₍₅ₓ₄₎ = ⁻²⁸⁄₂₀

⁽⁻²ˣ⁵⁾⁄₍₄ₓ₅₎ = ⁻¹⁰⁄₂₀

⁽⁻¹⁹ˣ¹⁾⁄₍₂₀ₓ₁₎ = ⁻¹⁹⁄₂₀

⁻³⁴⁄₂₀ > ⁻²⁸⁄₂₀ > ⁻¹⁹⁄₂₀ > ⁻¹⁰⁄₂₀ > 0

Ascending Order :

⁻¹⁷⁄₁₀, ⁻⁷⁄₅, ⁻¹⁹⁄₂₀, ⁻²⁄₄, 0

Descending Order :

0, ⁻²⁄₄, ⁻¹⁹⁄₂₀, ⁻⁷⁄₅, ⁻¹⁷⁄₁₀

Kindly mail your feedback to v4formath@gmail.com

We always appreciate your feedback.