EQUIVALENT RATIONAL NUMBERS WORKSHEET

Problems 1-6 : Write four rational numbers equivalent to the given rational number.

Problem 1 :

½

Problem 2 :

¾

Problem 3 :

⁻³⁄₅

Problem 4 :

⅞

Problem 5 :

3½

Problem 6 :

2.4 

Problem 7 :

Express ⅚ as a rational number with denominator 30.

Problem 8 :

Express ⁻³⁄₇ as a rational number with denominator 28.

Problem 9 :

Express 0.4 as a rational number with denominator 25.

Problem 10 :

Express 1.03 as a rational number with denominator 1000.

Problem 11 :

Express ¹⁰⁄₁₄ as a rational number with denominator 7.

Problem 12 :

Express ²⁸⁄₃₅ as a rational number with denominator 5.

Problem 13 :

¾ two ˣ⁄₁₂

If the above two rational numbers are equivalent, find the value of x.

Problem 14 :

⁻⁵⁄₆ and ᵏ⁄₄₂

If the above two rational numbers are equivalent, find the value of k.

Problem 15 :

ᶻ⁄₂ and ¹²⁄₈

If the two rational numbers above are equivalent, find the value of z.

Answers

1. Answer :

To find four rational numbers equivalent to ½, multiply both numerator and denominator of the fraction ½ by 2, 3, 4 and 5.

½ x ²⁄₂ = ²⁄₄

½ x ³⁄₃ = ³⁄₆

½ x ⁴⁄₄ = ⁴⁄₈

½ x ⁵⁄₅ = ⁵⁄₁₀

The four rational numbers equivalent to ½ are

²⁄₄, ³⁄₆, ⁴⁄₈, ⁵⁄₁₀

2. Answer :

¾ x ²⁄₂ = ⁶⁄₈

¾ x ³⁄₃ = ⁹⁄₁₂

¾ x ⁴⁄₄ = ¹²⁄₁₆

¾ x ⁵⁄₅ = ¹⁵⁄₂₀

The four rational numbers equivalent to ¾ are

⁶⁄₈, ⁹⁄₁₂, ¹²⁄₁₆, ¹⁵⁄₂₀

3. Answer :

⁻³⁄₅ x ²⁄₂ = ⁻⁶⁄₁₀

⁻³⁄₅ x ³⁄₃ = ⁻⁹⁄₁₅

⁻³⁄₅ x ⁴⁄₄ = ⁻¹²⁄₂₀

⁻³⁄₅ x ⁵⁄₅ = ⁻¹⁵⁄₂₅

The four rational numbers equivalent to ⁻³⁄₅ are

⁻⁶⁄₁₀, ⁻⁹⁄₁₅, ⁻¹²⁄₂₀, ⁻¹⁵⁄₂₅

4. Answer :

⅞ x ²⁄₂ = ¹⁴⁄₁₆

⅞ x ³⁄₃ = ²¹⁄₂₄

⅞ x ⁴⁄₄ = ²⁸⁄₃₂

⅞ x ⁵⁄₅ = ³⁵⁄₄₀

The four rational numbers equivalent to ⅞ are

¹⁴⁄₁₆, ²¹⁄₂₄, ²⁸⁄₃₂, ³⁵⁄₄₀

5. Answer :

3½ is a mixed number. To get four equivalent rational numbers to 3½, convert 3½ to  an improper fraction.

3½ = ⁷⁄₂

To find four equivalent rational numbers, multiply both numerator and denominator of the fraction ⁷⁄₂ by 2, 3, 4 and 5.

⁷⁄₂ x ²⁄₂ = ¹⁴⁄₄

⁷⁄₂ x ³⁄₃ = ²¹⁄₆

⁷⁄₂ x ⁴⁄₄ = ²⁸⁄₈

⁷⁄₂ x ⁵⁄₅ = ³⁵⁄₁₀

The four rational numbers equivalent to 3½ are

¹⁴⁄₄, ²¹⁄₆, ²⁸⁄₈, ³⁵⁄₁₀

6. Answer :

Convert the given decimal number to a fraction.

2.4 = ²⁴⁄₁₀

= ¹²⁄₅

To find four equivalent rational numbers, multiply both numerator and denominator of the fraction ¹²⁄₅ by 2, 3, 4 and 5.

¹²⁄₅ x ²⁄₂ = ²⁴⁄₁₀

¹²⁄₅ x ³⁄₃ = ³⁶⁄₁₅

¹²⁄₅ x ⁴⁄₄ = ⁴⁸⁄₂₀

¹²⁄₅ x ⁵⁄₅ = ⁶⁰⁄₂₅

The four rational numbers equivalent to 2.4 are

²⁴⁄₁₀, ³⁶⁄₁₅, ⁴⁸⁄₂₀, ⁶⁰⁄₂₅

7. Answer :

In the given fraction ⅚, the denominator is 6. To get denominator 30, we need to multiply 6 by 5.

To find a rational number equivalent to ⅚with denominator 30, multiply both numerator and denominator of the fraction ⅚ by 5.

⅚ = ⁽⁵ˣ⁵⁾⁄₍₆ₓ₅₎

= ²⁵⁄₃₀

8. Answer :

In the given fraction ⁻³⁄₇, the denominator is 7. To get denominator 28, we need to multiply 7 by 7.

To find a rational number equivalent to ⁻³⁄₇ with denominator 28, multiply both numerator and denominator of the fraction ⁻³⁄₇ by 4.

⁻³⁄₇ = ⁻⁽³ˣ⁴⁾⁄₍₇ₓ₄₎

= ⁻¹²⁄₂₈

9. Answer :

Convert the given decimal number to a fraction.

0.4 = ⁴⁄₁₀

= ²⁄₅

In the fraction ²⁄₅, the denominator is 5. To get denominator 25, we need to multiply 5 by 5.

To find a rational number equivalent to ²⁄₅ with denominator 25, multiply both numerator and denominator of the fraction ²⁄₅ by 5.

²⁄₅ = ⁽²ˣ⁵⁾⁄₍₅ₓ₅₎

= ¹⁰⁄₂₅

10. Answer :

Convert the given decimal number to a fraction.

1.03 = ¹⁰³⁄₁₀₀

In the fraction ¹⁰³⁄₁₀₀, the denominator is 100. To get denominator 1000, we need to multiply 100 by 10.

To find a rational number equivalent to ¹⁰³⁄₁₀₀ with denominator 1000, multiply both numerator and denominator of the fraction ¹⁰³⁄₁₀₀ by 10.

¹⁰³⁄₁₀₀ = ⁽¹⁰³ˣ¹⁰⁾⁄₍₁₀₀ₓ₁₀₎

= ¹⁰³⁰⁄₁₀₀₀

11. Answer :

In the given fraction ¹⁰⁄₁₄, the denominator is 14. To get denominator 7, we need to divide 14 by 2.

To find a rational number equivalent to ¹⁰⁄₁₄ with denominator 7, divide both numerator and denominator of the fraction ¹⁰⁄₁₄ by 2.

¹⁰⁄₁₄ = ⁽¹⁰^÷²⁾⁄₍₁₄÷₂₎

= ⁵⁄₇

12. Answer :

In the given fraction ²⁸⁄₃₅, the denominator is 35. To get denominator 5, we have to divide 35 by 7.

To get a rational number equivalent to ²⁸⁄₃₅ with denominator 5, divide both numerator and denominator of the fraction ²⁸⁄₃₅ by 7.

²⁸⁄₃₅ = ⁽²⁸^÷⁷⁾⁄₍₃₅÷₇₎

= ⅘

13. Answer :

Since ¾ two ˣ⁄₁₂ are equivalent rational numbers,

¾ = ˣ⁄₁₂

The denominator on the right side is 12. In the fraction ¾, the denominator is 4. To get denominator 12, we need to multiply 4 by 3.

To find a rational number equivalent to ¾ with denominator 12, multiply both numerator and denominator of the fraction ¾ by 3.

⁽³ˣ³⁾⁄₍₄ₓ₃₎ = ˣ⁄₁₂

⁹⁄₁₂ = ˣ⁄₁₂

The above two rational numbers are equivalent with the same denominator. Then, the numerators must be equal.

Therefore,

x = 9

14. Answer :

Since ⁻⁵⁄₆ and ᵏ⁄₄₂ are equivalent rational numbers,

⁻⁵⁄₆ = ᵏ⁄₄₂

The denominator on the right side is 42. In the fraction ⁻⁵⁄₆, the denominator is 42. To get denominator 42, we need to multiply 6 by 7.

To find a rational number equivalent to ⁻⁵⁄₆ with denominator 42, multiply both numerator and denominator of the fraction ⁻⁵⁄₆ by 7.

⁻⁽⁵ˣ⁷⁾⁄₍₆ₓ₇₎ = ᵏ⁄₄₂

⁻³⁵⁄₄₂ = ᵏ⁄₄₂

Therefore,

k = -35

15. Answer :

Since ᶻ⁄₂ and ¹²⁄₈ are equivalent rational numbers,

ᶻ⁄₂ = ¹²⁄₈

The denominator on the right side is 8. In the fraction ¹²⁄₈, the denominator is 8. To get denominator 2, need to divide 4 by 2.

To find a rational number equivalent to ¹²⁄₈ with denominator 2, divide both numerator and denominator of the fraction ¹²⁄₈ by 4.

ᶻ⁄₂ = ⁽¹²^÷⁴⁾⁄₍₈÷₄₎

ᶻ⁄₂ = ³⁄₂

Therefore,

z = 3

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