Primary 5 · Mathematics

P5 percentage

Percentage is where fractions, decimals and percentages finally line up as the same thing. The most common slip is a conversion that moves the decimal point one place instead of two, turning a third of something into almost nothing. Here is where it happens.

Level
P5
Usually taught
Term 3
Covers
4 concepts

What changes at P5

In Primary 5, percentage joins fractions and decimals as a third way to write the same thing: a part out of a hundred. Twenty-five percent, a quarter and 0.25 are one amount in three different notations.

Most of the early work is converting between the three and finding a percentage of an amount. It sounds routine, and it is, right up until one conversion quietly loses a factor of ten.

The sentence that costs the mark

Write 0.3 as a percentage.

What the working usually does

× 100.3=3%

Moves the decimal point one place. It lands on a clean percentage, so the working looks finished.

What the question asked

× 1000.3=30%

Moves the point two places, because a percentage is a count out of a hundred, not out of ten.

Both give a tidy percentage and 3% looks like a real figure, so nothing flags as careless. The only check is what percent means: 0.3 is thirty hundredths, so it has to be 30%. The setup is three words, out of a hundred.

The whole is 100%, split into ten equal parts worth 10% each. 0.3 shades three of them, which is thirty out of a hundred, or 30%.

The same question, worked properly

  1. Remember what percent means

    percent = out of 100

    Per cent is Latin for out of a hundred, so a percentage is always a count of hundredths. That is the fact that decides how far the point moves.

  2. Multiply by 100, not 10

    0.3 × 100 = 30

    This is the step that fails. Because a percentage is out of a hundred, you multiply by 100, which moves the point two places. Multiplying by 10 moves it one place and gives 3%, the wrong amount.

  3. Write it as a percentage

    0.3 = 30% = 30100\frac{30}{100}

    Thirty hundredths. The decimal, the fraction and the percentage are three names for the same amount, which is the whole point of the topic.

  4. Check the size

    30% of 10 = 3, and 0.3 of 10 = 3

    Both take the same 3 out of 10, so 0.3 and 30% are equal. A 3% answer would take about a third of one out of ten, far too little to be right.

How can you tell it has clicked?

You can check this without doing the conversion yourself. Ask your child what percent means, in their own words. If the answer is out of a hundred, they have the one idea the question is testing.

Then ask them to write 0.3 as a percentage and watch which way the point moves. Two places to 30% is right. One place to 3% is the mistake, and it is the same mistake every time.

One thing to try tonight

Money makes it concrete. A dollar is 100 cents, so cents are already counted out of a hundred. Thirty cents out of a dollar is 30%.

Ask what 0.3 of a dollar is in cents. Thirty, not three. The dollar being a hundred is what turns the decimal into the percentage, two places at a time.

What your child will meet in this topic

  • Percentages
  • Percent of a Number
  • Fractions and Percents
  • Decimals and Percents

Most Singapore schools introduce this in Term 3, though schools do differ by a term either way. If your child’s school runs a different order, you can set it in the schedule on your dashboard.

What it leads to

Percentage runs through the whole of P6: discount, GST, increase and decrease all start from percent meaning out of a hundred. The conversion here is the foundation the harder questions stand on.

A child fluent at moving between fraction, decimal and percentage rarely gets stuck later. One who guesses the conversion carries the guess into every percentage question that follows.

The methods your child will use here

Each one is the same method wherever it turns up, so it is worth learning once.

The same topic in other years

It comes back each year and gets harder, so it helps to see what came before and what is coming.

More in Primary 5

Other topics in the same year, so you can see what sits either side of this one.

Struggling with the working rather than the topic itself? How to help your child with problem sums

See how your child is doing on this topic

StudyLah marks each step separately, so you can see whether it was the setup or the arithmetic that cost the mark.

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