Tricky topics in GCSE Maths: Calculating Percentages for Ratios
Through analysing the usage data of Tassomai students and identifying some common mistakes in their quizzes we can see which topics GCSE maths students struggle with the most. In this series of blogs we’ll post a brief explainer on each of these tricky topics to help GCSE maths students get up to speed and prepare for exams.
Calculating Percentages for Ratios is an important topic for GCSE maths students to get to grips with, as it’s an exam specification point for major exam boards including:
✔ AQA
✔ EDEXCEL
✔ OCR 21ST CENTURY
✔ OCR GATEWAY
✔ WJEC
What is Calculating Percentages for Ratios?
Calculating percentages for ratios is a way of expressing parts of a whole in terms of percentages. This helps you understand what portion each part makes up out of 100%.
Example:
If you have a ratio of 3:2, this means you have two parts, with the first part representing "3" and the second part representing "2." Together, these make a total of 5 parts (3 + 2 = 5).
To convert this ratio to percentages:
Find the Total: Add the parts in the ratio to get the total amount.
Here, 3 + 2 = 5.
Calculate Each Part's Percentage:
For the first part: 3/5 = 60%
For the second part: 2/5 = 40%
Conclusion: The ratio 3:2 can be expressed as 60% and 40%.
Key Steps Recap:
Add the parts of the ratio to find the total.
Divide each part by the total.
Multiply each answer by 100 to convert it to a percentage.
Here’s a Tassomai quiz question about Calculating Percentages for Ratios:
This is one of several retrieval practice questions about Calculating Percentages for Ratios that’s shown to Tassomai students. Retrieval practice is a proven learning method to embed knowledge through testing.
To help us dive deeper into this topic we’ve enlisted the help of Mai, Tassomai’s built-in AI-powered tutor.
Tassomai users can ask Mai for help if they’re stuck on a quiz question or need some terminology explained to them.
If a student chooses the wrong answer, they can ask Mai to explain why it’s incorrect.
Let’s ask Mai to explain the answers to the quiz question!
Understanding the Percentage of Children in the Town
To solve this problem, we need to find out what fraction of the total population is made up of children. Here's the correct approach:
Total population: 36,000 people
Number of children: 9,000 children
Calculation: 9000 over 36000 = 0.25 =25%
This tells us that 25% of the population are children. 🎉
Why THE Other Options Were Incorrect:
"9000 over 27,000 = 0.333 = 33.3%” refers to the fraction of children among the adults, not the entire population. It's like saying, "Out of every adult, 33.3% are actually children," which sounds a bit funny, doesn't it? 😄 We need to consider the whole town's population to find the correct percentage.
"27,000 over 36,000 = 0.75 = 75%": This calculation finds the percentage of adults, not children. It tells us that 75% of the town's population are adults.
"27,000 – 9000 over 36,000 = 0.5 = 50%": This one is a bit of a mix-up. It subtracts the number of children from the adults and then divides by the total population, which doesn't represent any meaningful percentage in this context.
Fun Fact:
Did you know that percentages are just fractions in disguise? They're a way of showing parts per hundred, which makes it easier to compare different numbers directly. So, next time you see a percentage, remember it's just a fraction with a bit of a makeover! 🕵️♂️✨
Here’s how Mai’s explanation would look when shown to students using the Tassomai app.
As you can see, Mai sometimes throws in a fun fact to help students remember a topic.
Learn more about Calculating Percentages for Ratios
We hope you found Mai’s explanation helpful. If you’d like to learn more about Calculating Percentages for Ratios this GCSE maths Live Lesson on Percentages in more detail.
To see more tricky GCSE topics explained, click here for the full list of Tricky Topics blogs.
New to Tassomai?
The best way to get to know Tassomai is to try it for yourself. Schools and families can both trial our award-winning online learning program for FREE!