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

Grade 6IGCSE

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

🔑Concepts

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

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To convert a fraction to a decimal, divide the numerator by the denominator.

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

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To convert a percentage to a fraction, place the percentage value over 100 and simplify the resulting fraction.

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Decimals use place value (tenths, hundredths, thousandths) which directly relates to fractions with denominators of 10, 100, or 1000.

📐Formulae

Fraction to Decimal=Numerator÷Denominator\text{Fraction to Decimal} = \text{Numerator} \div \text{Denominator}

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

Percentage to Decimal=Percentage100\text{Percentage to Decimal} = \frac{\text{Percentage}}{100}

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

Fraction to Percentage=(Numerator÷Denominator)×100%\text{Fraction to Percentage} = (\text{Numerator} \div \text{Denominator}) \times 100\%

💡Examples

Problem 1:

Convert 38\frac{3}{8} into a decimal and a percentage.

Solution:

Decimal: 0.375; Percentage: 37.5%

Explanation:

To find the decimal, divide 3 by 8 (3 ÷ 8 = 0.375). To find the percentage, multiply the decimal by 100 (0.375 × 100 = 37.5%).

Problem 2:

Convert 0.45 into a fraction in its simplest form.

Solution:

920\frac{9}{20}

Explanation:

0.45 is 45 hundredths, written as 45100\frac{45}{100}. To simplify, divide both the numerator and denominator by their greatest common factor, which is 5. 45÷5=945 \div 5 = 9 and 100÷5=20100 \div 5 = 20.

Problem 3:

Convert 12.5% into a decimal.

Solution:

0.125

Explanation:

To convert a percentage to a decimal, divide by 100. Moving the decimal point two places to the left gives 12.5÷100=0.12512.5 \div 100 = 0.125.

Problem 4:

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

Solution:

80%

Explanation:

Method 1: Multiply the numerator and denominator to make the denominator 100: 4×205×20=80100=80%\frac{4 \times 20}{5 \times 20} = \frac{80}{100} = 80\%. Method 2: 4÷5=0.84 \div 5 = 0.8, and 0.8×100=80%0.8 \times 100 = 80\%.