Out of a hundred

Primary 6 Percentage study guide: the whole chapter, step by step

About this subtopic

The idea in brief. Percent means out of a hundred. That is a claim about the WHOLE before it is a claim about any share of it, so the film counts the whole first - ten rows of ten - and only then names a part. One small square is 1 hundredth, and 1 hundredth is 1 percent. When the whole really is a hundred parts the count IS the percentage, and the same count is a fraction over a hundred, a decimal in the first two decimal places and a percentage: three spellings of one quantity, not three facts. In the lesson. Those are three spellings of one quantity, not three answers.

Lesson video, with the working

Out of a hundred

4 min 02 s

The film teaches 2 questions in turn. Each question shows first; its working is written as the film explains it.

Watch on its own page

Today's question

A hundred square is made up of 100 small squares of the same size. 37 of the squares are shaded. What percentage of the hundred square is shaded?

  1. 37% of the hundred square is shaded.

Ans: 37%

Example 1

A car park has exactly 100 parking spaces. 15 of the spaces are occupied. What percentage of the spaces is empty?

  1. 85% of the spaces are empty.

Ans: 85%

How to solve it
  1. Check the whole: 10 rows of 10 make one hundred small squares. Percent means out of a hundred.
  2. Count the part: 3 shaded rows are 30, and 7 more squares make 37 shaded squares.
  3. Write it three ways: 37 over one hundred as a fraction, zero point three seven as a decimal, and 37 percent.
  4. To find a part you are not given, work from the whole: one hundred spaces minus 15 occupied leaves 85 empty.
  5. Read it off the same way: 85 out of one hundred is 85 hundredths, zero point eight five, or 85 percent.

The 85 empty spaces are 85 over one hundred, zero point eight five, and 85 percent. Those are three spellings of one quantity, not three answers.

Practice questions with worked solutions

Question 1 is free to try. The other 5 open in the free trial, each with its full working.

Basic

1Free23

Intermediate

4

Challenge

56

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Question 1 of 6 · Basic · free to tryA hundred-square is made up of 100 small squares of the same size. 63 of the…A hundred-square is made up of…

A hundred-square is made up of 100 small squares of the same size. 63 of the squares are shaded. What percentage of the hundred-square is not shaded?

63 shaded100 squares,
%

Show the working and the answer

Video solution · 1 min 9 s

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Working

  1. shaded = 63 out of the 100 parts = 63%
  2. not shaded = 100% − 63% = 37%

Answer: 37%

For parents

How do you read a percentage on a hundred square in P6?

Percent means out of a hundred.

What your child learns here

Percent means out of a hundred. This opening page of the Percentage chapter uses a whole of exactly 100 equal parts, so your child can see a percentage as a count before working with other wholes. It revises the first percentage outcomes from the year before.

  • Understand the % sign as 'out of 100'.
  • Express a part of a whole of 100 as a percentage, a fraction and a decimal.
  • Find the part not shaded or not taken by working from the whole of 100.
  • Read a percentage back as a number of parts of 100.
Does the answer make sense?

A hundred-square has only 100 parts, so every answer your child gives here, a percentage or a number of small squares, must lie between 0 and 100. When the question asks about the squares not shaded or the empty spaces, that answer and the given part must add up to exactly 100.

How to practise these questions

The Basic questions train reading a percentage as parts of a hundred, and back again. Intermediate questions add how many more parts are needed to reach a given percentage. Challenge questions spread a part over two hundred-squares, or describe it by a relation instead of a count. When out of a hundred is not yet clear, read the written step-by-step solution together.

Questions parents ask

What does percent mean? Percent means out of 100. 30% is 30 out of every 100, the same as the fraction 30 over 100 and the decimal 0.3. The % sign is first taught the year before Primary 6.

Why start percentage with a hundred square? When a whole has exactly 100 equal parts, the count of parts is the percentage. It shows what the % sign means before your child works with wholes of other sizes.

Is a hundred square percentage question revision in Primary 6? Yes. Expressing a part of a whole as a percentage and the use of % are taught the year before. The Primary 6 percentage outcomes build on them, so a quick revision helps.