Practice Maths

Fractions, Decimals & Percentages

The Big Idea

Fractions, decimals, and percentages all represent parts of a whole. We can convert between them using division and powers of 10.

Key Terms

fraction
a way of expressing a part of a whole as a numerator divided by a denominator (e.g. 34)
decimal
a number written using place value with digits after the decimal point representing tenths, hundredths, etc. (e.g. 0.75)
percentage
a value expressed as parts per hundred, written with the % symbol (e.g. 75%)
equivalent
having the same value even though expressed differently (e.g. 12 = 0.5 = 50%)
convert
to change a value from one form to another without changing its size
Hot Tip A percentage is simply a fraction with a denominator of 100. “Per cent” literally means “out of one hundred.”

Conversion Methods:

  • Fraction → Decimal: Divide the numerator by the denominator.
    Example: 3 ÷ 8 = 0.375
  • Decimal → Percentage: Multiply by 100.
    Example: 0.375 × 100 = 37.5%
  • Percentage → Decimal: Divide by 100.
    Example: 45% ÷ 100 = 0.45
  • Percentage → Fraction: Write over 100, then simplify.
    Example: 60% = 60100 = 35

Worked Example

Convert 38 to a decimal and a percentage.

Step 1: Divide the numerator by the denominator.
3 ÷ 8 = 0.375

Step 2: To convert the decimal to a percentage, multiply by 100.
0.375 × 100 = 37.5%

Step 3: State all three equivalent forms.
38 = 0.375 = 37.5%

Three Ways to Write the Same Thing

Fractions, decimals, and percentages are three different ways of writing the same value. They all describe a part of a whole. For example, half a pizza can be written as 1/2, 0.5, or 50% — they all mean exactly the same amount. Being able to switch between these three forms is a skill you will use constantly in maths and in everyday life.

Converting a Fraction to a Decimal

To convert a fraction to a decimal, divide the numerator (top) by the denominator (bottom). Think of the fraction bar as a division sign.

  • 1/2 = 1 ÷ 2 = 0.5
  • 3/4 = 3 ÷ 4 = 0.75
  • 1/5 = 1 ÷ 5 = 0.2
  • 3/10 = 3 ÷ 10 = 0.3

Shortcut: if you can make the denominator 10 or 100, just read the numerator as decimal digits. For example, 3/5 = 6/10 = 0.6.

Converting a Decimal to a Percentage

To convert a decimal to a percentage, multiply by 100 (and add the % sign). This works because "per cent" means "out of 100".

  • 0.5 × 100 = 50%
  • 0.75 × 100 = 75%
  • 0.08 × 100 = 8%
  • 1.2 × 100 = 120%

To go the other way — from percentage to decimal — divide by 100. So 35% = 0.35.

Converting a Percentage to a Fraction

Write the percentage as a fraction with denominator 100, then simplify. For example:

  • 25% = 25/100 = 1/4 (divide top and bottom by 25)
  • 60% = 60/100 = 3/5 (divide by 20)
  • 75% = 75/100 = 3/4 (divide by 25)

Common Equivalents to Memorise

Knowing these off by heart will save you a lot of time in tests and everyday situations:

  • 1/2 = 0.5 = 50%
  • 1/4 = 0.25 = 25%
  • 3/4 = 0.75 = 75%
  • 1/5 = 0.2 = 20%
  • 1/10 = 0.1 = 10%
  • 1/3 ≈ 0.333 ≈ 33.3%
The Conversion Chain: Fraction → divide → Decimal → ×100 → Percentage. Going backwards: Percentage → ÷100 → Decimal → write over a power of 10 → Fraction. Learn this chain and you can always find your way between the three forms.

Practice Questions

  1. Grid Visualisation Fluency

    On a 100-square grid, 40 squares are coloured orange.

    1. Write the coloured part as a fraction.
    2. Write the coloured part as a decimal.
    3. What percentage of the grid is coloured?

  2. “Not Coloured” Logic Fluency

    Using the same grid from Question 1 (40100 coloured):

    1. How many squares are not coloured?
    2. Write the “not coloured” part as a percentage.

  3. Denominator Power of 10 Fluency

    Convert these fractions to decimals without a calculator:

    1. 85100
    2. 210
    3. 3810

  4. Calculator Conversions Fluency

    Use the division method (numerator ÷ denominator) to find the decimal. Round to 2 decimal places where needed:

    1. 27
    2. 38
    3. 16
    4. 56
    5. 79

  5. Percentage Basics Understanding

    Convert these percentages into fractions with a denominator of 100:

    1. 27%
    2. 5%
    3. 100%
    4. 48%
    5. 3%

  6. Simplifying Percentages Understanding

    Convert 60% into a fraction and simplify it to its lowest terms.

  7. Percentage to Decimal Understanding

    Convert these percentages to decimals by dividing by 100:

    1. 56%
    2. 78%
    3. 45%
    4. 3%
    5. 125%

  8. Word Problem: The Test Score Understanding

    A student scores 27 out of 36 on a test. Express their score as a decimal and as a percentage.

  9. Who Scored Highest? Problem Solving

    Three students compare their test scores:

    • Mia scored 1725
    • Jacob scored 0.71
    • Priya scored 69%
    1. Convert each student’s score to a percentage.
    2. Which student scored highest? Which scored lowest?

  10. The Conversion Table Problem Solving

    Fill in all missing values in the table:

    FractionDecimalPercentage
    12??
    ?0.4?
    ??25%
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