Fractions, Decimals & Percentages
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Introduction to Fractions
Fractions • Equivalent Fractions

A fraction represents part of a whole. It has a numerator (top number) and a denominator (bottom number):

\( \frac{3}{4} \)

Here, the numerator 3 tells how many parts are taken, and the denominator 4 tells how many equal parts make the whole.

  • 1 Proper fraction: numerator < denominator
  • 2 Improper fraction: numerator ≥ denominator
  • 3 Mixed number: whole + fraction (e.g. 1 ¾)

Examples of Fractions

\( \frac{1}{2} \) Half
\( \frac{3}{4} \) Three quarters
\( \frac{1}{2} = \frac{2}{4} = \frac{3}{6} \) Equivalent fractions
\( \frac{2}{3} = \frac{4}{6} = \frac{6}{9} \) Same value, different forms

Fractions to Decimals

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Fractions Quiz

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Simplifying fractions, finding equivalents & comparing sizes. © onlinemaths.org
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Mixed and Improper Fractions
Conversion • Understanding • Simplification

A mixed fraction shows a whole number and a part of a whole, for example \( 2 \frac{1}{3} \).

An improper fraction has a numerator greater than or equal to its denominator, for example \( \frac{7}{4} \).

These two forms show the same value — you can convert between them.

  • 1 To change from mixed → improper: multiply, add, keep denominator
  • 2 To change from improper → mixed: divide numerator by denominator
  • 3 Simplify where possible

Examples

\( 2 \frac{1}{3} = \frac{7}{3} \) Convert mixed → improper
\( 1 \frac{2}{5} = \frac{7}{5} \) Multiply 1 × 5 + 2 = 7
\( \frac{9}{4} = 2 \frac{1}{4} \) Divide 9 ÷ 4 = 2 remainder 1
\( \frac{11}{3} = 3 \frac{2}{3} \) Convert improper → mixed

Mixed & Improper Fractions Quiz

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Convert between mixed numbers and improper fractions. © onlinemaths.org
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Multiplying and Dividing Fractions
Multiply • Divide • Simplify

When we multiply fractions, we multiply the numerators together and the denominators together. Then simplify the result if possible.

To divide by a fraction, we multiply by its reciprocal — that is, we turn the second fraction upside down.

  • 1 Multiply: top × top, bottom × bottom
  • 2 Divide: invert the second fraction and multiply
  • 3 Simplify your final answer

Examples

\( \frac{2}{3} \times \frac{4}{5} = \frac{8}{15} \) Multiply numerators and denominators
\( \frac{3}{4} \times \frac{2}{3} = \frac{6}{12} = \frac{1}{2} \) Simplify after multiplying
\( \frac{3}{5} \div \frac{2}{3} = \frac{3}{5} \times \frac{3}{2} = \frac{9}{10} \) Invert and multiply
\( \frac{5}{6} \div \frac{5}{12} = \frac{5}{6} \times \frac{12}{5} = 2 \) Cancel and simplify

Multiplying & Dividing Fractions Quiz

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Adding and Subtracting Fractions
Like & Unlike Denominators

To add or subtract fractions, the parts must be the same size. This means the fractions must have a common denominator.

If the denominators are already the same, add or subtract the numerators only. If they are different, first make the denominators the same using equivalent fractions.

  • 1 Same denominators → add/subtract numerators
  • 2 Different denominators → find common denominator
  • 3 Simplify your answer if possible

Examples

\( \frac{2}{7} + \frac{3}{7} = \frac{5}{7} \) Like denominators → add numerators
\( \frac{5}{8} - \frac{3}{8} = \frac{2}{8} = \frac{1}{4} \) Subtract and simplify
\( \frac{1}{2} + \frac{1}{3} = \frac{3}{6} + \frac{2}{6} = \frac{5}{6} \) Find a common denominator
\( \frac{3}{4} - \frac{2}{5} = \frac{15}{20} - \frac{8}{20} = \frac{7}{20} \) Convert to equivalent fractions before subtracting

Adding & Subtracting Fractions Quiz

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Add and subtract fractions and give your answer in its simplest form. © onlinemaths.org
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Introduction to Percentages
Fraction • Decimal • Percentage

A percentage is a special kind of fraction with a denominator of 100. The word “percent” means “per 100”.

100% means 1 . 50% means half, \( \frac{1}{2} = 0.5 \). 25% means a quarter, \( \frac{1}{4} = 0.25 \).

To find a percentage of a number - multiply!

  • 1 “Per cent” means “out of 100”

  • 2 100% = 1, 50% = ½, 25% = ¼, 10% = ¹⁄₁₀

  • 3 To find a percentage of a number: multiply

Examples

50% = \( \frac{50}{100} = \frac{1}{2} \) Half
25% = \( \frac{25}{100} = \frac{1}{4} \) Quarter
75% = 0.75 = \( \frac{3}{4} \) Expressed as a decimal and a fraction
20% of 60 = \( \frac{20}{100} \times 60 = 12 \) Convert to a fraction and multiply

100% and 1 on the Number Line

Move the slider to see how a decimal and a percentage name the same point on the number line. Notice what happens when you reach \(1\).

0
0%
0.5
50%
1
100%
1.5
150%
2
200%
Decimal: 0.00 Percentage: 0%
For example, \(0.4 = 40\%\), \(0.75 = 75\%\), and \(1 = 100\%\).
Important: the number 100 would be far to the right on this line. 100 is 100 times larger than 100%. 100 is the same as \(10000\%\).

Percentages to Decimals

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Fractions and Percentages

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Finding a Percentage of a Number

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Increasing or Decreasing by a Percentage

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Finding 100% of a Value

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Sale Price Quiz

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Percentage Profit or Loss

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