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Pioneers Maths

Maths · Fractions, Decimals & Percentages

Convert F ↔ D ↔ %

Swap between fractions, decimals, and percentages.

Not startedCAMBRIDGE · 7CBSE · VIIIB · MYP-1

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Three Ways to Show the Same Amount

Fractions, decimals and percentages are different ways to describe parts of a whole. They're like three languages saying the same thing! For example, one-half equals 0.5 and also equals 50%.

Fraction to Decimal

To turn a fraction into a decimal, divide the top number (numerator) by the bottom number (denominator). So ¾ becomes 3 ÷ 4 = 0.75.

Decimal to Percentage

Multiply the decimal by 100 to get a percentage. Moving the decimal point two places right does this quickly. So 0.75 becomes 75%.

Percentage to Fraction

Write the percentage as a fraction over 100, then simplify if possible. For example, 75% = 75/100 = ¾ when simplified.

Handy Shortcuts

Learn common conversions like ½ = 0.5 = 50%, ¼ = 0.25 = 25%, and ⅕ = 0.2 = 20%. These pop up everywhere!

Worked examples

  1. 1. Convert 3/5 to a percentage.

    1. First convert the fraction to a decimal: 3 ÷ 5 = 0.6
    2. Then multiply by 100 to get the percentage: 0.6 × 100 = 60
    3. So 3/5 = 60%

  2. 2. Convert 0.35 to a fraction in simplest form.

    1. Write 0.35 as 35/100 (35 hundredths)
    2. Find the highest common factor of 35 and 100, which is 5
    3. Divide both numerator and denominator by 5: 35 ÷ 5 = 7, 100 ÷ 5 = 20
    4. So 0.35 = 7/20 in simplest form

  3. 3. Convert 45% to a decimal.

    1. Divide the percentage by 100: 45 ÷ 100 = 0.45
    2. Or move the decimal point two places left: 45.0 becomes 0.45
    3. So 45% = 0.45

Try it yourself

Convert 2/5 to a percentage.

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