Welcome to the Objective Section of the Chapter Achievement Test for "Fractions in Disguise"! This comprehensive module consolidates the most critical Multiple Choice Questions from the test bank.
Challenge yourself to convert fractions to percentages, identify decimal equivalents, and calculate exact values seamlessly. Every single question includes four-pillar concept breakdowns, handwritten notebook solutions, and the official marking scheme to ensure you fully grasp the mechanics.
Challenge yourself to convert fractions to percentages, identify decimal equivalents, and calculate exact values seamlessly. Every single question includes four-pillar concept breakdowns, handwritten notebook solutions, and the official marking scheme to ensure you fully grasp the mechanics.
1 Select the correct option:
What is \(\frac{17}{25}\) expressed as a percentage?
Concept:
1
A percentage literally means "out of 100". To convert any fraction to a percentage, multiply it by 100 and add the % sign.
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Hint:
1
Calculate \(\frac{17}{25} \times 100\).
2
Simplify by dividing 100 by 25 first.
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Mistakes to Avoid:
!
Dividing 17 by 25: Converting to a decimal (0.68) is correct, but leaving it as a decimal without multiplying by 100 fails to express it as a formal percentage.
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Solution:
\(\text{Percentage} = \frac{17}{25} \times 100\%\)
\(= 17 \times 4\%\)
\(= 68\%\)
🎯 Marking Scheme: 1 Mark for selecting the correct option.
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2 Select the correct option:
What is \(\frac{13}{20}\) expressed as a percentage?
Concept:
1
A percentage is a fraction out of 100. Multiply any fraction by 100 to convert it.
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Hint:
1
Calculate \(\frac{13}{20} \times 100\). Simplify \(100 \div 20\) first.
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Mistakes to Avoid:
!
Assuming the numerator is the percentage: \(\frac{13}{20}\) is NOT 13%. The denominator must be 100.
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Solution:
\(\text{Percentage} = \frac{13}{20} \times 100\%\)
\(= 13 \times 5\%\)
\(= 65\%\)
🎯 Marking Scheme: 1 Mark for selecting the correct option.
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3 Select the correct option:
What is \(\frac{19}{25}\) expressed as a percentage?
Concept:
1
A percentage is a fraction out of 100. Multiply any fraction by 100 to convert it.
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Hint:
1
Calculate \(\frac{19}{25} \times 100\). Simplify \(100 \div 25\) first.
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Mistakes to Avoid:
!
Basic multiplication errors: \(19 \times 4\). A quick way is \( (20 \times 4) - 4 = 80 - 4 = 76 \).
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Solution:
\(\text{Percentage} = \frac{19}{25} \times 100\%\)
\(= 19 \times 4\%\)
\(= 76\%\)
🎯 Marking Scheme: 1 Mark for selecting the correct option.
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4 Select the correct option:
What is \(\frac{11}{20}\) expressed as a percentage?
Concept:
1
A percentage is a fraction out of 100. Multiply any fraction by 100 to convert it.
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Hint:
1
Calculate \(\frac{11}{20} \times 100\). Simplify \(100 \div 20\) first.
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Mistakes to Avoid:
!
Assuming the numerator is the percentage: \(\frac{11}{20}\) is NOT 11%. The denominator must be 100.
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Solution:
\(\text{Percentage} = \frac{11}{20} \times 100\%\)
\(= 11 \times 5\%\)
\(= 55\%\)
🎯 Marking Scheme: 1 Mark for selecting the correct option.
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5 Select the correct option:
What is 85% expressed as a fraction in its lowest terms?
Concept:
1
A percentage is a fraction with a denominator of 100. To find the lowest terms, divide both numbers by their Greatest Common Divisor (GCD).
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Hint:
1
Write as \(\frac{85}{100}\).
2
Both numbers end in 5 or 0, so they are divisible by 5.
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Mistakes to Avoid:
!
Stopping at \(\frac{85}{100}\): Option D is a trap. The question specifically requests the fraction in its "lowest terms".
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Solution:
\(85\% = \frac{85}{100}\)
Divide top and bottom by 5:
\(\frac{85 \div 5}{100 \div 5} = \frac{17}{20}\)
🎯 Marking Scheme: 1 Mark for selecting the correct option.
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6 Select the correct option:
What is 45% expressed as a fraction in its lowest terms?
Concept:
1
Place the percentage value over 100, then divide top and bottom by their greatest common factor.
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Hint:
1
\(\frac{45}{100}\). Both end in 5 or 0, so divide by 5.
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Mistakes to Avoid:
!
Choosing unsimplified fractions: Option B represents the exact value, but fails the "lowest terms" requirement.
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Solution:
\(45\% = \frac{45}{100}\)
Divide top and bottom by 5:
\(\frac{45 \div 5}{100 \div 5} = \frac{9}{20}\)
🎯 Marking Scheme: 1 Mark for selecting the correct option.
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7 Select the correct option:
What is 35% expressed as a fraction in its lowest terms?
Concept:
1
Place the percentage value over 100, then divide top and bottom by their greatest common factor.
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Hint:
1
\(\frac{35}{100}\). Both end in 5 or 0, so divide by 5.
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Mistakes to Avoid:
!
Choosing unsimplified fractions: Option B represents the exact value, but fails the "lowest terms" requirement.
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Solution:
\(35\% = \frac{35}{100}\)
Divide top and bottom by 5:
\(\frac{35 \div 5}{100 \div 5} = \frac{7}{20}\)
🎯 Marking Scheme: 1 Mark for selecting the correct option.
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8 Select the correct option:
What is 65% expressed as a fraction in its lowest terms?
Concept:
1
Place the percentage value over 100, then divide top and bottom by their greatest common factor.
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Hint:
1
\(\frac{65}{100}\). Both end in 5 or 0, so divide by 5.
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Mistakes to Avoid:
!
Choosing unsimplified fractions: Option D represents the exact value, but fails the "lowest terms" requirement.
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Solution:
\(65\% = \frac{65}{100}\)
Divide top and bottom by 5:
\(\frac{65 \div 5}{100 \div 5} = \frac{13}{20}\)
🎯 Marking Scheme: 1 Mark for selecting the correct option.
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9 Select the correct option:
Calculate the exact value of 15% of 240.
Concept:
1
"Percent of" translates to multiplication. Convert the percentage to a fraction (\(\frac{15}{100}\)) and multiply by the total.
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Hint:
1
Mentally find 10% by moving the decimal one place to the left.
2
5% is exactly half of 10%. Add them together!
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Mistakes to Avoid:
!
Dividing instead of multiplying: Do not compute \(240 \div 15\). The word "of" in mathematics signifies multiplication.
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Solution:
Method 1 (Standard):
\(\frac{15}{100} \times 240 = \frac{3}{20} \times 240 = 3 \times 12 = 36\).
Method 2 (Mental Math):
\(10\%\) of \(240 = 24\).
\(5\%\) of \(240 = 12\) (half of 24).
\(15\% = 24 + 12 = 36\).
🎯 Marking Scheme: 1 Mark for selecting the correct option.
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10 Select the correct option:
Calculate the exact value of 25% of 180.
Concept:
1
Common percentages can be memorized as fractions. 25% is always exactly \(\frac{1}{4}\) of the total.
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Hint:
1
Calculate \(\frac{180}{4}\). Or, simply find half of 180, and then half it again!
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Mistakes to Avoid:
!
Overcomplicating the math: Writing out \(180 \times \frac{25}{100}\) and doing long multiplication wastes time when you can just divide by 4.
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Solution:
Method 1 (Fraction logic):
\(25\% = \frac{1}{4}\).
\(\frac{1}{4} \times 180 = 45\).
Method 2 (Halving):
\(50\%\) of \(180 = 90\).
Half of \(90 = 45\).
🎯 Marking Scheme: 1 Mark for selecting the correct option.
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