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Percentages

Percent means "per hundred", and once that lands most percentage questions become fractions a child already knows: 50% is a half, 25% a quarter, 10% a tenth. The arithmetic is rarely the difficulty. Recognising which of the three numbers in the question is missing usually is.

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Finding a percentage of a number

What is 20% of 60?

  1. 10% of 60 is 6 — move the digits one place, or divide by ten.
  2. 20% is two lots of 10%.
  3. Two sixes is 12.
  4. 20% of 60 is 12.

Worth knowing. Building from 10% works for most percentages a child meets and needs no formula. 35% is three tens and a five, so three 6s and half a 6.

Finding what percentage one number is of another

What percent of 40 is 10?

  1. Write it as a fraction: 10 out of 40, which is 10/40.
  2. Simplify: 10/40 is 1/4.
  3. A quarter is 25 out of every 100.
  4. 10 is 25% of 40.

Worth knowing. This is the direction children find harder, and it is the same fact asked backwards. Turning it into a fraction first is what makes it ordinary.

Where it usually goes wrong

  • Dividing by the percentage instead of multiplying, so 20% of 60 comes out as 3.
  • Answering the wrong question — giving the part when the percentage was asked for.
  • Treating 20% off and 20% of as the same thing.

The Professor finds 10% first and builds from there. Twenty percent is two of them, five percent is half of one, and thirty-five percent is three and a half.

Practise it

All level paths

Questions teachers and parents ask

What is the quickest way to find a percentage mentally?

Find 10% by moving the digits one place right, then build. 20% is two of them, 5% is half of one, 15% is one and a half. It handles most of what turns up and needs nothing memorised.

When are percentages taught?

Finding a percent of a quantity as a rate per hundred is grade 6 (6.RP.A.3.C), and multistep percent problems — increases, decreases, interest — arrive in grade 7 (7.RP.A.3).

How are percentages, fractions and decimals related?

They are three ways of writing the same thing. 25% is 25/100 is 0.25 is 1/4. Being able to move between them freely is most of what makes percentage questions easy, and it is worth practising as its own skill.

Can a percentage be more than 100?

Yes. 150% of 40 is 60 — one and a half times it. Percentages above 100 turn up constantly in increases and in statistics, and the arithmetic is no different.

Where this shows up

Standards

  • 6.RP · Ratios and proportional relationships
  • 7.RP · Ratios and proportional relationships
  • CCSS.MATH.CONTENT.6.RP.A.3 — Use ratio and rate reasoning to solve real-world and mathematical problems, including with tables and equations.
  • CCSS.MATH.CONTENT.6.RP.A.3.C — Find a percent of a quantity as a rate per hundred, and solve problems involving finding the whole given a part and the percent.
  • CCSS.MATH.CONTENT.7.RP.A.3 — Use proportional relationships to solve multistep ratio and percent problems.

Formats