Increase and decrease

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

About this subtopic

In the lesson. And always write it the same way. The change over the original, times one hundred percent.

Lesson video, with the working

Percentage increase and decrease

3 min 31 s

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

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Today's question

Last year, 400 people came to a neighbourhood fair. This year, 500 people came. Find the percentage increase in the number of people who came.

  1. The number of people went up by 25%.

Ans: 25%

Example 1

A jacket costs $200. In a sale, the price is 30% less. What's the sale price?

  1. The sale price is $140.

Ans: $140

How to solve it
  1. Draw the original amount, last year's 400 people, as the 100 percent.
  2. Find the change: 500 minus 400 is 100 more people.
  3. Write the change over the original, times 100 percent: 100 over 400 times 100 percent is 25 percent.
  4. For a decrease, take the percentage off 100 percent. A jacket 30 percent less is 100 minus 30, which is 70 percent of 200 dollars.
  5. Find 70 percent: 1 percent is 2 dollars, so 70 times 2 is 140 dollars.

Always write it the same way. The change over the original, times 100 percent.

Practice questions with worked solutions

Questions 1 and 5 are free to try. The other 8 open in the free trial, each with its full working.

Basic

1Free2345Free

Intermediate

678

Challenge

910

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8 more questions, each with its full working.Answers checked, progress kept, wrong ones come back in revision. No card needed.

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Question 1 of 10 · Basic · free to tryA stall had 50 packets of nuts in the morning. By closing time all 50…A stall had 50 packets of nuts…

A stall had 50 packets of nuts in the morning. By closing time all 50 packets had been sold. Find the percentage decrease in the number of packets at the stall.

%

Show the working and the answer

Video solution · 1 min 18 s

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Working

  1. decrease = 50 − 0 = 50
  2. percentage decrease = 50/50 × 100% = 100%

Answer: 100%

Question 5 of 10 · Basic · free to tryA jacket costs $200. During a sale, the price of the jacket is 30% less…A jacket costs $200. During a…

A jacket costs $200. During a sale, the price of the jacket is 30% less. What is the sale price of the jacket?

$

Show the working and the answer

Working

  1. 100% − 30% = 70%
  2. 1% → $200 ÷ 100 = $2
  3. 70% → 70 × $2 = $140
  4. 70% of $200 = 70/100 × $200 = $140
  5. The sale price is $140.

Answer: $140

For parents

How do you solve percentage increase and decrease questions in P6?

Finding a percentage increase or decrease is a new outcome in Primary 6.

What your child learns here

Finding a percentage increase or decrease is a new outcome in Primary 6. The idea is short: the change over the original amount, times 100%. Everything rests on knowing which amount is the original.

  • Find the increase or decrease, then write it over the original amount and multiply by 100%.
  • Find a new amount after a given percentage increase or decrease.
  • Understand that losing all of a quantity is a 100% decrease.
  • Read a phrase such as '30% less than' as a percentage of the other quantity.
Does the answer make sense?

A percentage decrease can never be more than 100%, because losing everything, like all 50 packets of nuts, is exactly a 100% decrease. When your child finds a new amount after a decrease it must be smaller than the original, and after an increase it must be larger.

How to practise these questions

The Basic questions train finding a percentage change measured on the original amount, and applying an increase or decrease. Intermediate questions add a change whose base is not stated directly. Challenge questions compare which quantity grew by the greater percentage, or split a total rise across two bases. When a percentage change is measured from an unexpected base, read the written step-by-step solution together.

Questions parents ask

Is percentage increase and decrease in the Primary 6 syllabus? Yes. 'Finding percentage increase/decrease' is outcome 1.2 of the Primary 6 Percentage sub-strand, and one of the two new percentage outcomes at this level.

Do you divide by the old number or the new number? The old number. The change is measured against the amount you started with, which is the 100%.

Can a percentage decrease be more than 100%? Not for an amount that cannot go below zero: if all of it is gone, the decrease is 100%. An increase can be more than 100%, such as a price that more than doubles.