EQUIVALENT FRACTIONS WORKSHEET

Problem 1 :

Write four fractions which are equivalent to ⅘.

Problem 2 :

Write four fractions which are equivalent to ⁵⁄₇.

Problem 3 :

Write four fractions which are equivalent to 1¾.

Problem 4 :

Write four fractions which are equivalent to 0.5.

Problem 5 :

Write 4 fractions which are equivalent to 0.05.

Problem 6 :

Write 4 fractions which are equivalent to 2.25.

Problem 7 :

Pick out the fractions which are equivalent :

½, ¹⁵⁄₂₅, ¼, ⁵⁄₂₀, ⁴⁰⁄₈₀, ⅗, ¹²⁄₁₆

Problem 8 :

Find the missing numbers :

⁴⁄₇ = ¹²⁄_? = ^?⁄₂₈

Problem 9 :

Find the missing numbers :

⅖ = ⁶⁄_? = ^?⁄₈₀

Problem 10 :

⁵⁄₁₂ and ˣ⁄₃₆

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

Answers

1. Answer :

To find four fractions equivalent to ⅘, multiply both numerator and denominator of the fraction ⅘ by 2, 3, 4 and 5.

⁽⁴ˣ²⁾⁄₍₅ₓ₂₎ = ⁸⁄₁₀

⁽⁴ˣ³⁾⁄₍₅ₓ₃₎ = ¹²⁄₁₅

⁽⁴ˣ⁴⁾⁄₍₅ₓ₄₎ = ¹⁶⁄₂₀

⁽⁴ˣ⁵⁾⁄₍₅ₓ₅₎ = ²⁰⁄₂₅

Four fractions equivalent to ⅘ are

⁸⁄₁₀, ¹²⁄₁₅, ¹⁶⁄₂₀, ²⁰⁄₂₅

2. Answer :

⁽⁵ˣ²⁾⁄₍₇ₓ₂₎ = ¹⁰⁄₁₄

⁽⁵ˣ³⁾⁄₍₇ₓ₃₎ = ¹⁵⁄₂₁

⁽⁵ˣ⁴⁾⁄₍₇ₓ₄₎ = ²⁰⁄₂₈

⁽⁵ˣ⁵⁾⁄₍₇ₓ₅₎ = ²⁵⁄₃₅

Four fractions equivalent to ⁵⁄₇ are

¹⁰⁄₁₄, ¹⁵⁄₂₁, ²⁰⁄₂₈, ²⁵⁄₃₅

3. Answer :

1¾ is a mixed number. Convert 1¾ to an improper fraction.

1¾ = ⁷⁄₄

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

⁽⁷ˣ²⁾⁄₍₄ₓ₂₎ = ¹⁴⁄₈

⁽⁷ˣ³⁾⁄₍₄ₓ₃₎ = ²¹⁄₁₂

⁽⁷ˣ⁴⁾⁄₍₄ₓ₄₎ = ²⁸⁄₁₆

⁽⁷ˣ⁵⁾⁄₍₄ₓ₅₎ = ³⁵⁄₂₀

Four fractions equivalent to 1¾ are

¹⁴⁄₈, ²¹⁄₁₂, ²⁸⁄₁₆, ³⁵⁄₂₀

4. Answer :

0.5 is a decimal. Convert 0.5 to a fraction.

0.5 = ⁵⁄₁₀

= ½

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

⁽¹ˣ²⁾⁄₍₂ₓ₂₎ = ²⁄₄

⁽¹ˣ³⁾⁄₍₂ₓ₃₎ = ³⁄₆

⁽¹ˣ⁴⁾⁄₍₂ₓ₄₎ = ⁴⁄₈

⁽¹ˣ⁵⁾⁄₍₂ₓ₅₎ = ⁵⁄₁₀

Four fractions equivalent to 0.5 are

²⁄₄, ³⁄₆, ⁴⁄₈, ⁵⁄₁₀

5. Answer :

0.05 is a decimal. Convert 0.05 to a fraction.

0.05 = ⁵⁄₁₀₀

= ¹⁄₂₀

To find four fractions equivalent to ¹⁄₂₀, multiply both numerator and denominator of the fraction ¹⁄₂₀ by 2, 3, 4 and 5.

⁽¹ˣ²⁾⁄₍₂₀ₓ₂₎ = ²⁄₄₀

⁽¹ˣ³⁾⁄₍₂₀ₓ₃₎ = ³⁄₆₀

⁽¹ˣ⁴⁾⁄₍₂₀ₓ₄₎ = ⁴⁄₈₀

⁽¹ˣ⁵⁾⁄₍₂₀ₓ₅₎ = ⁵⁄₁₀₀

Four fractions equivalent to 0.05 are

²⁄₄₀, ³⁄₆₀, ⁴⁄₈₀, ⁵⁄₁₀₀

6. Answer :

2.25 is a decimal. Convert 2.25 to a fraction.

2.25 = ²²⁵⁄₁₀₀

= ⁹⁄₄

To find four fractions equivalent to ⁹⁄₄, multiply both numerator and denominator of the fraction ⁹⁄₄ by 2, 3, 4 and 5.

⁽⁹ˣ²⁾⁄₍₄ₓ₂₎ = ¹⁸⁄₈

⁽⁹ˣ³⁾⁄₍₄ₓ₃₎ = ²⁷⁄₁₂

⁽⁹ˣ⁴⁾⁄₍₄ₓ₄₎ = ³⁶⁄₁₆

⁽⁹ˣ⁵⁾⁄₍₄ₓ₅₎ = ⁴⁵⁄₂₀

Four fractions equivalent to 2.25 are

¹⁸⁄₈, ²⁷⁄₁₂, ³⁶⁄₁₆, ⁴⁵⁄₂₀

7. Answer :

½, ¹⁵⁄₂₅, ¼, ⁵⁄₂₀, ⁴⁰⁄₈₀, ⅗, ¹²⁄₂₀

The fractions ½ and ⁴⁰⁄₈₀ are equivalent.

Because,

½ = ⁽¹ˣ⁴⁰⁾⁄₍₂ₓ₄₀₎ = ⁴⁰⁄₈₀

The fractions ¹⁵⁄₂₅, ⅗ and ¹²⁄₂₀ are equivalent.

Because,

¹⁵⁄₂₅ = ⁽¹⁵^÷⁵⁾⁄₍₂₅÷₅₎ = ⅗

and

⅗ = ⁽³ˣ⁴⁾⁄₍₅ₓ₄₎ = ¹²⁄₂₀

The fractions ¼ and ⁵⁄₂₀ are equivalent.

Because,

¼ = ⁽¹ˣ⁵⁾⁄₍₄ₓ₅₎ = ⁵⁄₂₀

8. Answer :

⁴⁄₇ = ¹²⁄_? = ^?⁄₂₈

The numerator of the first two fractions are 4 and 125. And 4 will become 12, when it is multiplied by 3.

So, we need to multiply the denominator of the first fraction 7 by 3 to get the denominator of the second fraction.

7x3 = 21

Hence, the denominator of the second fraction is 21.

The denominator of the first and third fraction are 7 and 28. And 7 will become 28, when it is multiplied by 4. 

So, we need to multiply the numerator of the first fraction 4 by 4 to get the numerator of the third fraction.

4x4 = 16

Hence, the numerator of the third fraction is 16.

⁴⁄₇ = ¹²⁄21 = ¹⁶⁄₂₈

9. Answer :

⅖ = ⁶⁄_? = ^?⁄₈₀

The numerator of the first two fractions are 2 and 6. And 2 will become 6, when it is multiplied by 3.

So, we need to multiply the denominator of the first fraction 5 by 3 to get the denominator of the second fraction.

5x3 = 15

Hence, the denominator of the second fraction is 15.

The denominator of the first and third fraction are 5 and 80. And 5 will become 80, when it is multiplied by 16. 

So, we need to multiply the numerator of the first fraction 4 by 16 to get the numerator of the third fraction.

4x16 = 64

Hence, the numerator of the third fraction is 64.

⅖ = ⁶⁄₁₅ = ⁶⁴⁄₈₀

10. Answer :

Since ⁵⁄₁₂ and ˣ⁄₃₆ are equivalent fractions,

⁵⁄₁₂ = ˣ⁄₃₆

The denominator on the right side is 36. In the fraction ⁵⁄₁₂, the denominator is 12. To get denominator 36, we need to multiply 12 by 3.

To find a fraction equivalent to ⁵⁄₁₂ with denominator 36, multiply both numerator and denominator of the fraction ⁵⁄₁₂ by 3.

⁽⁵ˣ³⁾⁄₍₁₂ₓ₃₎ = ˣ⁄₃₆

¹⁵⁄₃₆ = ˣ⁄₃₆

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

Therefore,

x = 15

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