Percentage increase for beginners

Quick answer

Percentage increase means finding how much something has grown in size, using a fraction out of 100. You work it out by comparing the new amount to the original amount, then turning that into a percentage.

Learning outcome

By the end of this page, you will be able to find percentage increase by comparing a new amount to an original amount and calculating how much more it is as a percentage.

• You can find the difference between two amounts
• You can turn that difference into a fraction of the original amount
• You can change that fraction into a percentage
• You can use percentage increase in real-life situations like shopping or sports

Why this matters

Knowing how to find percentage increase helps you understand how much things grow or change. This is useful when you are shopping and want to know how much a price has gone up, or when you are tracking your progress in a sport or game. It helps you make smart choices and understand changes in the world around you.

How it works

Let's break it down into simple steps:

1. Find the difference: Subtract the original amount from the new amount.
2. Make a fraction: Put the difference over the original amount.
3. Turn it into a percentage: Multiply the fraction by 100.

This shows how much bigger the new amount is compared to the old one, expressed as a part of 100.

Examples you can see

Let’s look at some examples you can imagine or draw.

Example 1: A toy car

Imagine you had a toy car that cost £20. Now it costs £25. How much more is it now?

1. Difference = New amount – Original amount = £25 – £20 = £5
2. Fraction = Difference ÷ Original amount = £5 ÷ £20 = 1/4
3. Percentage = Fraction × 100 = 1/4 × 100 = 25%

So the price has increased by 25%.

Example 2: Your football score

You scored 10 goals last season. This season you scored 15 goals. What is the percentage increase?

1. Difference = 15 – 10 = 5 goals
2. Fraction = 5 ÷ 10 = 1/2
3. Percentage = 1/2 × 100 = 50%

Your score increased by 50%.

Example 3: A garden

Your garden had 20 flowers. Now it has 30 flowers. What is the percentage increase?

1. Difference = 30 – 20 = 10 flowers
2. Fraction = 10 ÷ 20 = 1/2
3. Percentage = 1/2 × 100 = 50%

Your garden increased by 50%.

Try it as a mini adventure

Adventure: The Growing Garden

You are a gardener who started with 10 plants. Each week, you count how many plants you have. Here’s how your garden grew:

• Week 1: 10 plants
• Week 2: 12 plants
• Week 3: 15 plants
• Week 4: 20 plants

Can you calculate the percentage increase each week? Try this:

1. Week 2: How much more than 10? What percentage?
2. Week 3: How much more than 12? What percentage?
3. Week 4: How much more than 15? What percentage?

Common mistakes

• Mistake: Thinking the percentage increase is just the difference between the numbers.
  Why it happens: Children often forget to compare the difference to the original number.
  Fix: Always divide the difference by the original number, then multiply by 100.
• Mistake: Using the new number instead of the original number in the fraction.
  Why it happens: It's easy to get confused about which number is the base.
  Fix: Remember: the fraction is difference divided by original.
• Mistake: Forgetting to multiply by 100 to get the percentage.
  Why it happens: It's easy to stop at the fraction.
  Fix: Always multiply your fraction by 100 to turn it into a percentage.

Parent and carer guide

Help your child understand percentage increase by using everyday examples. You can use:

• Shopping: Compare prices of the same item at different stores.
• Games: Track scores or levels in a game.
• Food: Measure ingredients and see how much more is needed for a bigger batch.
• Time: See how much longer a journey takes now compared to before.

Ask your child to explain how they found the answer. This helps them understand and remember the process.

Don’t worry if they make mistakes – they are part of learning. Keep it fun and practical!

Practice questions

1. Original: 10, New: 14. What is the percentage increase?
2. Original: 20, New: 25. What is the percentage increase?
3. Original: 50, New: 75. What is the percentage increase?
4. Original: 12, New: 18. What is the percentage increase?
5. Original: 8, New: 12. What is the percentage increase?

Answers:

1. 40%
2. 25%
3. 50%
4. 50%
5. 50%

FAQ

What is percentage increase?

Percentage increase is a way to show how much something has grown, compared to its original size. It is expressed as a part of 100.

How do I calculate percentage increase?

You find the difference between the new and original amounts, divide that by the original, and then multiply by 100.

Can percentage increase be more than 100%?

Yes! If something doubles, it has increased by 100%. If it triples, it has increased by 200%.

Why do we use percentage increase?

It helps us understand how much things change. It's useful for comparing prices, growth in sports, or changes in nature.

Is percentage increase the same as percentage change?

Yes, they are the same thing. Percentage change is another name for percentage increase when the value goes up.