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Fractions, Decimals, and Percentages - Converting between fractions, decimals, and percentages

Grade 5IGCSE

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

🔑Concepts

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Fractions, decimals, and percentages are different ways of expressing the same value (parts of a whole).

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The word 'percent' comes from 'per centum', meaning 'out of 100'.

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To convert a decimal to a percentage, multiply the decimal by 100 and add the % symbol.

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To convert a percentage to a decimal, divide the number by 100 and remove the % symbol.

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To convert a fraction to a percentage, find an equivalent fraction with a denominator of 100, or divide the numerator by the denominator and multiply by 100.

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A fraction is in its simplest form when the numerator and denominator have no common factors other than 1.

📐Formulae

Decimal×100=Percentage%\text{Decimal} \times 100 = \text{Percentage}\%

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

ab→(a÷b)×100=Percentage%\frac{a}{b} \rightarrow (a \div b) \times 100 = \text{Percentage}\%

Percentage%=Percentage100 (then simplify)\text{Percentage}\% = \frac{\text{Percentage}}{100} \text{ (then simplify)}

💡Examples

Problem 1:

Convert 45\frac{4}{5} into a percentage.

Solution:

80%80\%

Explanation:

Step 1: To get a denominator of 100, multiply both the numerator and denominator by 20. 4×205×20=80100\frac{4 \times 20}{5 \times 20} = \frac{80}{100}. Step 2: Since it is now out of 100, it is 80%80\%.

Problem 2:

Convert 0.350.35 into a fraction in its simplest form.

Solution:

720\frac{7}{20}

Explanation:

Step 1: 0.350.35 has two decimal places, so write it as 35100\frac{35}{100}. Step 2: Simplify by dividing both the numerator and denominator by their highest common factor, which is 5. 35÷5=735 \div 5 = 7 and 100÷5=20100 \div 5 = 20. Result is 720\frac{7}{20}.

Problem 3:

Convert 7%7\% into a decimal.

Solution:

0.070.07

Explanation:

To convert a percentage to a decimal, divide by 100. 7÷100=0.077 \div 100 = 0.07. This is done by moving the decimal point two places to the left.

Problem 4:

Express 38\frac{3}{8} as a decimal.

Solution:

0.3750.375

Explanation:

Divide the numerator (3) by the denominator (8). 3÷8=0.3753 \div 8 = 0.375. This can be done using long division.