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Fractions, Decimals, and Percentages - Calculating percentages of amounts

Grade 6Cambridge (IGCSE)

Review the key concepts, formulae, and examples before starting your quiz.

🔑Concepts

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Definition of Percentage: The word 'percent' means 'per 100'. A percentage is a fraction with a denominator of 100.

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Mental Math Method (Chunking): Percentages like 15% can be found by adding 10% and 5% together.

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The 10% Rule: To find 10% of any amount, divide the amount by 10.

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The 1% Rule: To find 1% of any amount, divide the amount by 100.

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Decimal Multiplier Method: To find a percentage using a calculator, convert the percentage to a decimal (divide by 100) and multiply by the amount.

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Fraction Method: Convert the percentage into a fraction (e.g., 25% = 1/4) and then multiply or divide accordingly.

📐Formulae

Percentage of an Amount=Percentage100×Total Amount\text{Percentage of an Amount} = \frac{\text{Percentage}}{100} \times \text{Total Amount}

Multiplier=Percentage÷100\text{Multiplier} = \text{Percentage} \div 100

Amount=Multiplier×Total Quantity\text{Amount} = \text{Multiplier} \times \text{Total Quantity}

💡Examples

Problem 1:

Calculate 15% of $60 using mental math methods.

Solution:

$9

Explanation:

Step 1: Find 10% of $60 by dividing by 10 ($60÷10=\$60 \div 10 = $6). Step 2: Find 5% by halving the 10% value ($6÷2=\$6 \div 2 = $3). Step 3: Add the two parts together ($6+\$6 + $3 = $9\$9).

Problem 2:

Calculate 24% of 150kg using the decimal multiplier method.

Solution:

36kg

Explanation:

Step 1: Convert 24% to a decimal multiplier by dividing by 100 (24÷100=0.2424 \div 100 = 0.24). Step 2: Multiply the multiplier by the total amount (0.24×150=360.24 \times 150 = 36).

Problem 3:

A school has 400 students. If 45% of the students are girls, how many girls are there in the school?

Solution:

180 girls

Explanation:

Step 1: Set up the fraction 45100×400\frac{45}{100} \times 400. Step 2: Simplify the calculation by dividing 400 by 100 first (400÷100=4400 \div 100 = 4). Step 3: Multiply the result by the numerator (45×4=18045 \times 4 = 180).