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.
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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