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What are percentages?

Part of MathsPercentages

Key points

  • Percentages represent an amount out of 100. This provides a consistent base to compare against when looking at fractional parts. For example, 50%, means 50 out of 100 or \( \frac{50}{100} \). 50% is the same as one half.
  • Percentages are often used instead of fractions and decimals. This is because parts of 100 can be easier to understand.
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What is a percentage?

  • A percentage is a fraction that is parts out of 100
  • A whole is 100%. The percentages that are part of a whole, to 100%
  • A percentage is written as a number with the % symbol. The number can be an , , fraction or a decimal.
  • A percentage can be represented by shading in a 100 square grid.

Examples

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  1. A one-hundred block grid with the bottom left block highlighted orange.

    What percentage of this grid is orange?

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How to find a missing percentage

  1. Add the given percentages.

  2. Subtract the result from 100%

  3. The difference between 100% and the total given percentage will be the missing percentage.

Remember that the whole is always 100%

Examples

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  1. Example 1: A bar split into three highlighted blocks that are labelled. First is green and labelled twenty-eight percent. Second is orange and labelled with a question mark. Third is blue and labelled forty percent.

    Add the given percentages. 28% + 40% = 68%. Subtract the result (68%) from 100%. The difference between 100% and the total given percentage (68%) is the missing percentage. 100% 鈥 68% = 32%

Question

12% of the bar is blue. 36% of the bar is green. What % of the bar is orange?

A bar split into three highlighted blocks that are labelled. First is blue and labelled twelve percent. Second is green and labelled thirty-six percent. Third is orange and labelled with a question mark.

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A percentage as an operator

A percentage becomes an when it represents a mathematical action.

Finding a percentage of something is a mathematical action. The percentage is an operator. For example, 15% of 100 means work out 15 hundredths of 100

Examples

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  1. Example 1: Fifteen percent of one-hundred.

    15% of 100 is an instruction to work out 15 hundredths of 100

Question

What percentages are represented in these 100-square grids?

Three one-hundred block grids labelled A,B and C and sections highlighted orange. Gird A has the top forty blocks highlighted. Gird B has seventy-five blocks highlighted 鈥 the top right twenty-five blank. Grid C has sixteen middle blocks highlighted with the rest blank.

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Practise percentages

Try this quiz to practise percentages. You may need a pen and paper to help you answer the questions in this quiz.

Quiz

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Real-world maths

A white person holding a tablet with a pie chart on it. Behind is an open laptop.
Statisticians working with data often use percentages in reports.

A statistician is someone who works with data. They often use percentages in reports. To ensure accuracy, the total percentage is always 100%

Newspapers and magazines frequently present information in pie charts using percentages, as well as using them in headlines and reports to make a news story stand out. As a reader it is important to know what a percentage is in order to understand the information.

A white person holding a tablet with a pie chart on it. Behind is an open laptop.
Statisticians working with data often use percentages in reports.
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Game - Divided Islands

Using your maths skills, help to build bridges and bring light back to the islands in this free game from 成人快手 Bitesize.

Play the Divided Islands game!
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More on Percentages

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