How to calculate percentages: three common problems step by step

You need to calculate a discount, but you get stuck at the first step. Should you multiply or divide? That depends on what you know and what you need to find. We will work through three common types of percentage problems so you can choose the right calculation and understand why it works.

Percent means out of a hundred

One percent is one hundredth. That makes 20% the same as 20/100 = 0.20. Similarly, 50% = 0.50 = one half, and 25% = 0.25 = one quarter. Percentage problems involve three quantities: the whole is the total you start from, the part is an amount of that total, and the proportion tells you how large the part is compared with the whole. Start by asking: What represents 100 percent in this problem?

1. Find the part: What is 20% of 350?

You know the whole, 350, and the percentage, 20%. First write the percentage as a decimal, then multiply: Part = percentage as a decimal × whole 0.20 × 350 = 70 So 20% of 350 is 70. You can check this mentally: 10% of 350 is 35, so 20% is twice as much, or 70.

2. Find the percentage: What percentage is 12 out of 30?

In a group of 30 students, 12 cycle to school. The part is 12 and the whole is 30. Divide the part by the whole: Proportion = part / whole 12 / 30 = 0.40 = 40% Answer: 40% of the students cycle. Check the size of your answer: 12 is less than half of 30, so the percentage should be below 50%.

3. Find the whole: 60 is 15% of what number?

This time you know the part, 60, and the percentage, 15%, but the whole is missing. Write 15% as 0.15 and divide: Whole = part / percentage as a decimal 60 / 0.15 = 400 Check by working backwards: 0.15 × 400 = 60. The answer is correct. Another way to think about it is that 1% represents 60 / 15 = 4. That means 100% represents 400.

Discounts: distinguish the saving from the new price

A jumper costs SEK 350 and has a 20% discount. The saving is 0.20 × 350 = SEK 70. The new price is therefore 350 − 70 = SEK 280. You can also calculate the price directly using the proportion you pay. After a 20% discount, 80% of the original price remains: 0.80 × 350 = SEK 280. The number 0.80 is the percentage multiplier. For a 20% increase, the multiplier is 1.20 instead. Pay attention to which value the percentage is calculated from. If the price first falls by 20% and then rises by 20%, it becomes 350 × 0.80 × 1.20 = SEK 336. The increase is calculated from the reduced price, so it does not bring you back to SEK 350.

Try it yourself: three questions with answers

Try these before looking at the solutions. Identify the part, the percentage and the whole in each problem. 1. What is 25% of 240? 2. What percentage is 18 out of 60? 3. An item has been reduced by 20% and now costs SEK 480. What was its original price? Answers: 1. 0.25 × 240 = 60. 2. 18 / 60 = 0.30 = 30%. 3. After the discount, 80% of the original price remains. The original price is therefore 480 / 0.80 = SEK 600. Check: 600 × 0.80 = SEK 480.

Stuck? Start by identifying 100 percent

Before choosing a calculation, write down what you know and what the question asks you to find. Then check whether your answer makes sense and whether you have used the right unit: money, a count or a percentage. Would you like support with your practice? Mattefix offers online maths help with a student tutor. Bring a problem you are stuck on so you can work through your reasoning together, step by step. Learn more about our maths tutoring or contact us through the website.