7TH NUMBERS TALENT -CONVERSON OF FRACTIONS AND EQUIVALENT FRACTIONS

Fractions & Equivalent Fractions Quiz

1. Which fraction is NOT equivalent to 18/24 when simplified to its lowest terms?

• A) 3/4
• B) 12/16
• C) 27/36
• D) 14/20

Correct Answer: D) 14/20
Explanation: Simplifying 18/24 by dividing numerator and denominator by 6 gives 3/4.
A) 3/4 = 3/4
B) 12/16 ÷ 4/4 = 3/4
C) 27/36 ÷ 9/9 = 3/4
D) 14/20 ÷ 2/2 = 7/10 ≠ 3/4.

2. Convert the improper fraction 79/6 into a mixed fraction.

• A) 13 1/6
• B) 12 5/6
• C) 13 5/6
• D) 14 1/6

Correct Answer: A) 13 1/6
Explanation: Divide 79 by 6. Quotient = 13, Remainder = 1. Therefore, 79/6 = 13 1/6.

3. Express the mixed number 8 7/12 as an improper fraction.

• A) 96/12
• B) 103/12
• C) 105/12
• D) 112/12

Correct Answer: B) 103/12
Explanation: Multiply the whole number by the denominator and add the numerator: (8 × 12) + 7 = 96 + 7 = 103. The denominator remains 12, giving 103/12.

4. An online store gives a discount of 0.375 on an item. What is this value expressed as a simplified fraction?

• A) 3/8
• B) 37/100
• C) 7/16
• D) 5/8

Correct Answer: A) 3/8
Explanation: Convert decimal to fraction: 0.375 = 375/1000. Divide numerator and denominator by 125 to reduce: (375 ÷ 125) / (1000 ÷ 125) = 3/8.

5. If 5/7 of a cake is equivalent to x/42, what is the value of x?

• A) 25
• B) 30
• C) 35
• D) 40

Correct Answer: B) 30
Explanation: Equivalent fractions satisfy 5/7 = x/42. Multiply denominator 7 by 6 to get 42. Multiply numerator 5 by 6: 5 × 6 = 30.

6. Maya ate 4/9 of a pizza, while Sam ate 12/27 of an identical pizza. Who ate more?

• A) Maya
• B) Sam
• C) They ate equal amounts
• D) Cannot be determined

Correct Answer: C) They ate equal amounts
Explanation: Simplify Sam's portion: 12/27 ÷ 3/3 = 4/9. Since both fractions are equivalent (4/9 = 4/9), they ate equal amounts.

7. Convert the repeating decimal 0.444... into its simplest fractional form.

• A) 4/10
• B) 4/9
• C) 2/5
• D) 44/99

Correct Answer: B) 4/9
Explanation: Let x = 0.444... Then 10x = 4.444... Subtracting the equations gives 9x = 4 → x = 4/9. (Note: 44/99 simplifies to 4/9, but 4/9 is the simplest form).

8. Which of the following fractions is larger than 5/8?

• A) 1/2
• B) 9/16
• C) 13/20
• D) 3/5

Correct Answer: C) 13/20
Explanation: Convert to decimals: 5/8 = 0.625.
A) 1/2 = 0.500
B) 9/16 = 0.5625
C) 13/20 = 0.650 (Larger than 0.625)
D) 3/5 = 0.600.

9. A container holds 3.65 liters of water. Express this quantity as a mixed fraction in its lowest terms.

• A) 3 13/20
• B) 3 65/100
• C) 3 7/20
• D) 3 13/25

Correct Answer: A) 3 13/20
Explanation: 3.65 = 3 + 65/100. Simplify 65/100 by dividing numerator and denominator by 5 to get 13/20. Thus, 3 13/20.

10. Find the value of k if (k - 2) / 15 is equivalent to 16/60.

• A) 4
• B) 6
• C) 8
• D) 10

Correct Answer: B) 6
Explanation: First simplify 16/60 by dividing by 4: 16/60 = 4/15.
Set equations equal: (k - 2) / 15 = 4/15 → k - 2 = 4 → k = 6.

11. A carpenter needs a plank of length 45/4 inches. If his measuring tape only marks mixed numbers, what should he measure?

• A) 11 1/4 inches
• B) 10 3/4 inches
• C) 11 3/4 inches
• D) 12 1/4 inches

Correct Answer: A) 11 1/4 inches
Explanation: Divide 45 by 4: Quotient = 11, Remainder = 1. So, 45/4 = 11 1/4 inches.

12. Which fraction pair consists of two fractions that are NOT equivalent?

• A) 4/10 and 10/25
• B) 6/14 and 15/35
• C) 8/18 and 12/28
• D) 9/12 and 15/20

Correct Answer: C) 8/18 and 12/28
Explanation: Simplify each pair:
A) 4/10 = 2/5 and 10/25 = 2/5 (Equivalent)
B) 6/14 = 3/7 and 15/35 = 3/7 (Equivalent)
C) 8/18 = 4/9 while 12/28 = 3/7 (NOT Equivalent)
D) 9/12 = 3/4 and 15/20 = 3/4 (Equivalent).

13. Express 5/16 as a percentage.

• A) 31.25%
• B) 31.5%
• C) 32.25%
• D) 28.75%

Correct Answer: A) 31.25%
Explanation: Multiply the fraction by 100%: (5/16) × 100% = 500 / 16 = 31.25%.

14. Reduce the fraction 126/180 to its simplest form.

• A) 7/10
• B) 9/10
• C) 14/20
• D) 6/9

Correct Answer: A) 7/10
Explanation: Find GCD of 126 and 180, which is 18. Divide numerator and denominator by 18: (126 ÷ 18) / (180 ÷ 18) = 7/10.

15. A recipe requires 2 3/8 cups of flour. If you want to triple the recipe, how many cups of flour will you need as a mixed number?

• A) 6 9/8 cups
• B) 7 1/8 cups
• C) 7 3/8 cups
• D) 6 3/8 cups

Correct Answer: B) 7 1/8 cups
Explanation: Convert to improper fraction: 2 3/8 = 19/8. Triple it: 19/8 × 3 = 57/8. Convert 57/8 back to a mixed number: 57 ÷ 8 = 7 with a remainder of 1 → 7 1/8 cups.