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Finding one number as a percentage of another

percentage symbols
As children progress through Years 5 and 6 of primary school, they will have to tackle more and more questions that are about percentages. You can guarantee that there will be at least a few questions on the Y6 SATS around percentages. It is important that children understand how to solve these with confidence. Here, we tackle the tricky question of how to find one number as a percentage of another.

To find one number as a percentage of another, primary children can follow a few simple steps.

First, it’s a good idea to go over some of the basics and remind your child how to find a percentage of a number (for instance, find 15% of 100).

Breaking down percentages 

Step 1: Remind children that a percentage represents a number as parts of one hundred. For example, 10% simply means 10 parts out of 100.

Step 2: Recognising the relationship between fractions and percentages can really help. For example, ask your child to write down a percentage as a fraction. This would be with the numerator (top number) corresponding to the given number and a denominator (bottom number) of 100. For example, if they are given 20%, they would write it as 20/100.

Step 3: Using decimals can also help children with percentages. To represent a percentage as a decimal, they simply divide the given number by 100. For instance, if they have 20%, they convert it to 0.2. This is because 20 divided by 100 = 0.2

Step 4: By having this knowledge secure, your child can now use this to solve percentage problems. Suppose they are asked to find 10% of 4 kg. Since 10% is equivalent to 1/10 (or 0.1) and they need to find 1/10 of the quantity, they divide 4 kg by 10. The result is 0.4 kg.

Finding a percentage of a number

To find 25% of 80, your child would need to:

Step 1: Recognise that 25% represents 25 parts out of 100.

Step 2: Express 25% as a fraction e.g. 25/100.

Step 3: Represent 25% as a decimal by dividing 25 by 100, resulting in 0.25.

Step 4: Then multiply 0.25 by 80. The calculation is as follows:

0.25 × 80 = 20. Therefore, 25% of 80 is 20.

Let's work through another example to find 15% of 200:

Step 1: Recognise that 15% represents 15 parts out of 100.

Step 2: Express 15% as a fraction. This means they write it as 15/100.

Step 3: Divide 15 by 100, resulting in 0.15.

Step 4: To find 15% of 200, they multiply 0.15 by 200. The calculation is as follows:

0.15 × 200 = 30

Therefore, 15% of 200 is 30.

Finding one number as a percentage of another

Sometimes it is useful to find one number as a percentage of another. This sort of question is not only a useful life skill but also comes up in many SATS style questions. Children often find this process quite easy, especially if they are able to use a calculator to help. However, since the change to SATS in 2016 and the removal of the calculator paper, any questions relating to this method would be kept simple and would more than likely be a test of multiplication knowledge. Here are two simple examples – one for when using a calculator and one for when using a mental or written method:

Calculator method:

To find 23 as a percentage of 80, you can use the following formula:

  • Percentage = (Part/Whole) x 100
  • In this case, the part is 23 and the whole is 80.
  • Percentage = (23/80) x 100
  • Percentage = 0.2875 x 100
  • Percentage = 28.75%
  • Therefore, 23 is approximately 28.75% of 80.

Pencil and Paper / mental method:

  • Find 2 as a percentage of 10.
  • Write down the given values: Part = 2 and Whole = 10.
  • Set up the equation: Percentage = (Part/Whole) x 100.
  • Divide the Part by the Whole: 2 ÷ 10 = 0.2.
  • Multiply the result by 100 to convert it to a percentage: 0.2 x 100 = 20.
  • The final result is 20%.
  • Therefore, 2 is 20% of 10.