Percentages

What does "per cent" mean?

Per cent means out of every hundred. The sign for it is %.

When Ama says, "I got 80% in my maths test," she means: for every 100 marks that were possible, she got 80 of them.

Think of a bag of 100 groundnuts. If 25 of them are roasted, then 25% of the groundnuts are roasted. If all 100 are roasted, that is 100%. If none are roasted, that is 0%.

The word comes from Latin: per centum, "by the hundred". Shopkeepers, teachers, banks and footballers all use percentages because comparing things "out of 100" is easy. You do not need to know how many groundnuts, cedis or pupils there are. You only need to know how many out of every hundred.

Try this: Say three places where you have seen the % sign this week.

Why 100?

Why do we compare things out of 100 and not out of 10 or 50?

A hundred is a friendly number. It is big enough to show small differences (71% and 72% are different), but small enough to picture. Our money works in hundreds: 100 pesewas make GH₵1. A square grid of 10 by 10 has 100 little squares.

Imagine Kofi's class has 40 pupils and Abena's class has 25. In Kofi's class, 30 pupils passed. In Abena's class, 20 passed. Which class did better? It is hard to see straight away.

As percentages: Kofi's class, 30 out of 40 = 75%. Abena's class, 20 out of 25 = 80%. Now it is clear. Abena's class did a little better.

Percentages let us compare groups of different sizes fairly. That is their superpower.

Try this: Which is bigger, 3 out of 4 or 7 out of 10? Guess, and we will check later.

The hundred square

Picture a square cut into 10 rows and 10 columns. That gives 100 small squares. Each small square is 1% of the big square.

• Colour one whole row: 10 squares = 10%.
• Colour half the grid: 50 squares = 50%.
• Colour a quarter: 25 squares = 25%.
• Colour everything: 100 squares = 100%.

A hundred square helps you see a percentage. 37% is three full rows and seven squares of the next row. 90% is everything except one row.

Try this: Draw a 10 by 10 grid in your exercise book. Shade 60% of it. Then shade 5% in a different colour. How many squares are left white? What percentage is that?

The answer to the last question is 35%, because 100 − 60 − 5 = 35. The whole grid is always 100%.

Percentages as fractions

A percentage is really a fraction with 100 on the bottom.

• 50% = 50⁄100
• 25% = 25⁄100
• 7% = 7⁄100

We usually simplify these fractions. 50⁄100 simplifies to 1⁄2 (divide top and bottom by 50). 25⁄100 simplifies to 1⁄4 (divide by 25). 10⁄100 simplifies to 1⁄10.

Worked example: Write 40% as a fraction in its simplest form.

40% = 40⁄100. Both 40 and 100 can be divided by 20. 40 ÷ 20 = 2 and 100 ÷ 20 = 5. So 40% = 2⁄5.

Try this: Write these as fractions in their simplest form: 20%, 75%, 60%, 5%.

(Answers: 1⁄5, 3⁄4, 3⁄5, 1⁄20.)

Fractions to percentages

Going the other way: a fraction becomes a percentage when you make the bottom number 100.

Worked example: Change 3⁄4 to a percentage.

Ask: what do I multiply 4 by to get 100? The answer is 25. So multiply the top by 25 too: 3 × 25 = 75. So 3⁄4 = 75⁄100 = 75%.

Worked example: Change 7⁄10 to a percentage.

10 × 10 = 100, so 7 × 10 = 70. 7⁄10 = 70%.

Now we can answer the question from earlier. 3 out of 4 is 75%. 7 out of 10 is 70%. So 3 out of 4 is bigger.

Try this: Change 1⁄2, 2⁄5, 9⁄20 and 13⁄50 to percentages.

(Answers: 50%, 40%, 45%, 26%.)

When the bottom is awkward

What about a fraction like 3⁄8? Eight does not go into 100 evenly.

There is a second method that always works: divide the top by the bottom, then multiply by 100.

3 ÷ 8 = 0.375. Then 0.375 × 100 = 37.5%.

Here is another: 1⁄3. 1 ÷ 3 = 0.333... Multiply by 100 and you get 33.3%. We usually say "about 33%" or write 33⅓%.

This method works for every fraction, so it is worth remembering: top ÷ bottom × 100.

Try this: Change 5⁄8 and 2⁄3 to percentages. Use a calculator if your teacher allows, or long division.

(Answers: 62.5% and about 66.7%.)

Percentages as decimals

A decimal is just another way of writing a fraction out of 10, 100 or 1000. So percentages and decimals are close cousins.

To change a percentage to a decimal, divide by 100. That moves the digits two places to the right of the decimal point.

• 50% = 0.50 = 0.5
• 25% = 0.25
• 8% = 0.08
• 100% = 1.00 = 1
• 150% = 1.5

Watch 8%. It becomes 0.08, not 0.8. Count the two places carefully: 8 → 0.8 → 0.08.

Try this: Write 30%, 3%, 75% and 120% as decimals.

(Answers: 0.3, 0.03, 0.75, 1.2.)

Decimals to percentages

To change a decimal to a percentage, multiply by 100. Move the digits two places to the left.

• 0.5 → 50%
• 0.35 → 35%
• 0.07 → 7%
• 0.9 → 90%
• 1.25 → 125%

Worked example: Kwame's goalkeeper saves 0.8 of the shots at him. As a percentage, 0.8 × 100 = 80%. He saves 80% of shots.

Try this: Write 0.6, 0.45, 0.02 and 0.125 as percentages.

(Answers: 60%, 45%, 2%, 12.5%.)

Remember the rule: % to decimal, divide by 100. Decimal to %, multiply by 100.

The three friends together

Every amount can be written in three ways. Here is a table to learn by heart.

Fraction	Decimal	Percentage
1⁄2	0.5	50%
1⁄4	0.25	25%
3⁄4	0.75	75%
1⁄10	0.1	10%
1⁄5	0.2	20%
1⁄3	0.333…	33⅓%
1	1.0	100%

These are the ones that come up again and again: in tests, at the market, on the radio.

Try this: Cover the table. Write the three forms of a quarter, a fifth and three quarters from memory.

Comparing with percentages

Percentages make it easy to compare fractions that look very different.

Worked example: Which is more: 2⁄5 of a cake or 0.45 of the same cake?

Change both to percentages. 2⁄5 = 40%. 0.45 = 45%. So 0.45 is more.

Worked example: Put in order from smallest to largest: 3⁄4, 0.7, 72%.

3⁄4 = 75%. 0.7 = 70%. 72% stays as it is. Order: 0.7, 72%, 3⁄4.

When you compare, change everything into the same form first. Percentages are usually the quickest.

Try this: Order these from smallest to largest: 1⁄2, 0.55, 48%, 3⁄5.

(Answer: 48%, 1⁄2, 0.55, 3⁄5.)

Finding 50% and 25%

Now for the most useful skill of all: finding a percentage of an amount.

50% is a half. To find 50% of something, divide by 2. 50% of GH₵80 = GH₵40. 50% of 36 oranges = 18 oranges.

25% is a quarter. To find 25%, divide by 4 (or halve, then halve again). 25% of GH₵80 = GH₵20. 25% of 36 = 9.

75% is three quarters. Find 25%, then multiply by 3. 75% of GH₵80 = 3 × GH₵20 = GH₵60.

Try this: Find 50%, 25% and 75% of GH₵120, and of 200 pupils.

(Answers: GH₵60, GH₵30, GH₵90; 100, 50, 150 pupils.)

Finding 10% and 1%

10% is one tenth. To find 10% of an amount, divide by 10. 10% of GH₵250 = GH₵25. 10% of 90 = 9.

1% is one hundredth. To find 1%, divide by 100. 1% of GH₵250 = GH₵2.50. 1% of 900 = 9.

Once you can find 10% and 1%, you can build almost any percentage.

• 20% = 2 lots of 10%
• 30% = 3 lots of 10%
• 5% = half of 10%
• 3% = 3 lots of 1%

Worked example: 30% of GH₵250. 10% is GH₵25, so 30% is 3 × GH₵25 = GH₵75.

Try this: Find 10%, 20%, 5% and 1% of GH₵400.

(Answers: GH₵40, GH₵80, GH₵20, GH₵4.)

Building other percentages

Combine the easy percentages like building blocks.

Worked example: Find 35% of 60 mangoes.

• 10% of 60 = 6
• 30% = 3 × 6 = 18
• 5% = half of 10% = 3
• 35% = 18 + 3 = 21 mangoes

Worked example: Find 15% of GH₵80.

• 10% of 80 = 8
• 5% = 4
• 15% = 8 + 4 = GH₵12

Worked example: Find 99% of 500.

• 100% = 500
• 1% = 5
• 99% = 500 − 5 = 495

Try this: Find 45% of 200, 12% of GH₵50 and 90% of 70.

(Answers: 90, GH₵6, 63.)

The multiply method

There is a method that works for any percentage: change the percentage to a decimal and multiply.

Worked example: Find 37% of 200.

37% = 0.37. Then 0.37 × 200 = 74.

Worked example: Find 18% of GH₵150.

18% = 0.18. Then 0.18 × 150 = GH₵27.

If you prefer fractions: 18% of 150 = 18⁄100 × 150 = (18 × 150) ÷ 100 = 2700 ÷ 100 = 27. Same answer.

Use the building-block method when the numbers are friendly (10%, 25%, 5%). Use the multiply method when they are not (37%, 18%, 63%).

Try this: Find 23% of 300 and 64% of GH₵25 using the multiply method.

(Answers: 69 and GH₵16.)

Percentages at the market

Ama goes to Makola Market with GH₵60. Her mother told her to spend 40% on tomatoes and the rest on onions.

How much goes on tomatoes? 10% of GH₵60 = GH₵6. So 40% = 4 × GH₵6 = GH₵24.

How much on onions? 100% − 40% = 60%. 60% of GH₵60 = 6 × GH₵6 = GH₵36.

Check: GH₵24 + GH₵36 = GH₵60. Correct.

Market traders use percentages every day. A trader might add 20% to her buying price to make a profit, or take 10% off at the end of the day to sell the last of her fish.

Try this: Kofi has GH₵90. He spends 30% on exercise books and 50% on a school bag. How much is left?

(Answer: GH₵18.)

Money and pesewas

Money questions often give answers with pesewas. Remember that GH₵1 = 100 pesewas, so GH₵2.50 means two cedis and fifty pesewas.

Worked example: Find 15% of GH₵9.

• 10% of GH₵9 = GH₵0.90 (90 pesewas)
• 5% = half of that = GH₵0.45
• 15% = GH₵0.90 + GH₵0.45 = GH₵1.35

Worked example: Find 5% of GH₵7.

10% of GH₵7 = GH₵0.70. Half of that = GH₵0.35, which is 35 pesewas.

Always write money with two decimal places: GH₵1.35, not GH₵1.350 or GH₵1.4.

Try this: Find 10% of GH₵3.50, 20% of GH₵12.50 and 1% of GH₵5.

(Answers: GH₵0.35, GH₵2.50, GH₵0.05.)

What is a discount?

A discount is money taken off a price. Shops give discounts to sell goods quickly or to reward customers. The discount is often written as a percentage: "20% off".

To work out the new price:

1. Find the discount amount (the percentage of the old price).
2. Subtract it from the old price.

Worked example: A school bag costs GH₵50. The shop gives 20% off.

Discount = 20% of GH₵50 = GH₵10. New price = GH₵50 − GH₵10 = GH₵40.

The word "off" is your clue that you must subtract.

Try this: A pair of sandals costs GH₵80 with 25% off. What is the new price?

(Answer: GH₵60.)

Discounts: the shortcut

Here is a quicker way. If a shop takes 20% off, you still pay 80% of the price (because 100% − 20% = 80%). So you can find 80% of the price straight away.

Worked example: Trousers cost GH₵120 with 30% off.

You pay 100% − 30% = 70%. 70% of GH₵120: 10% is GH₵12, so 70% is 7 × GH₵12 = GH₵84.

Check the long way: 30% of 120 = 36. 120 − 36 = 84. Same answer.

Worked example: A radio costs GH₵200 with 15% off. You pay 85%. 85% of 200 = 0.85 × 200 = GH₵170.

Try this: Find the sale price of a GH₵60 football with 10% off, and a GH₵45 book with 20% off.

(Answers: GH₵54 and GH₵36.)

Which deal is better?

Two shops at Kejetia Market sell the same rice cooker.

• Shop A: GH₵300, with 25% off.
• Shop B: GH₵280, with 15% off.

Which is cheaper?

Shop A: 25% of 300 = 75. New price = 300 − 75 = GH₵225. Shop B: 15% of 280. 10% = 28, 5% = 14, so 15% = 42. New price = 280 − 42 = GH₵238.

Shop A is cheaper by GH₵13, even though its price looked higher at first.

A bigger discount does not always mean a cheaper price, and a smaller starting price does not always win. Always work it out.

Try this: A dress is GH₵90 with 20% off at one stall, and GH₵75 with 5% off at another. Where is it cheaper?

(Answer: the second stall, GH₵71.25 versus GH₵72.)

Percentage increase

Prices do not only go down. Sometimes they go up by a percentage. Then you add instead of subtract.

Worked example: A loaf of bread cost GH₵8 last year. The price went up by 25%.

Increase = 25% of GH₵8 = GH₵2. New price = GH₵8 + GH₵2 = GH₵10.

The shortcut works here too. After a 25% increase, you pay 125% of the old price. 125% of 8 = 1.25 × 8 = 10.

Worked example: A trader buys yams for GH₵40 and sells them for 30% more. 30% of 40 = 12. She sells at GH₵40 + GH₵12 = GH₵52. Her profit is GH₵12.

Try this: Transport fares rise by 10%. A fare was GH₵5. What is it now?

(Answer: GH₵5.50.)

Exam marks as percentages

Teachers turn marks into percentages so that every test can be compared, whether it was out of 20, 40 or 50.

Rule: percentage = (marks scored ÷ total marks) × 100.

Worked example: Abena scored 36 out of 40.

36 ÷ 40 = 0.9. Then 0.9 × 100 = 90%.

Or with fractions: 36⁄40 = 9⁄10 = 90⁄100 = 90%.

Worked example: Kofi scored 13 out of 20. 13⁄20: multiply top and bottom by 5 to get 65⁄100 = 65%.

Try this: Change these to percentages: 18 out of 20, 30 out of 50, 24 out of 40.

(Answers: 90%, 60%, 60%.)

Marks that do not divide nicely

What if the total is 30 or 60? These do not go into 100.

Use the divide method: marks ÷ total × 100.

Worked example: Kwame scored 21 out of 30.

21 ÷ 30 = 0.7. Then 0.7 × 100 = 70%.

Worked example: Ama scored 45 out of 60.

45 ÷ 60 = 0.75. So 75%.

Worked example: Esi scored 25 out of 30. 25 ÷ 30 = 0.8333… So about 83%. We round to the nearest whole number.

Try this: Change 24 out of 30 and 51 out of 60 to percentages.

(Answers: 80% and 85%.)

Finding the marks from the percentage

Sometimes you know the percentage and want the marks.

Worked example: A test is out of 50. Abena got 84%. How many marks is that?

Find 84% of 50. 10% = 5, so 80% = 40. 1% = 0.5, so 4% = 2. Total: 40 + 2 = 42 marks.

Worked example: The pass mark is 60%. The exam is out of 80. What score do you need to pass?

60% of 80: 10% = 8, so 60% = 48 marks.

Try this: A test is out of 40. What score is 95%? What score is 45%?

(Answers: 38 and 18.)

Comparing test results

Kofi got 42 out of 60 in English and 28 out of 40 in science. Which subject did he do better in?

English: 42 ÷ 60 = 0.7 = 70%. Science: 28 ÷ 40 = 0.7 = 70%.

He did equally well in both. The raw marks looked different, but the percentages are the same.

Now Ama: 38 out of 50 in maths, and 33 out of 40 in social studies.

Maths: 38⁄50 = 76⁄100 = 76%. Social: 33 ÷ 40 = 0.825 = 82.5%.

Her better subject is social studies.

Try this: Abena got 27⁄30 in one test and 44⁄50 in another. Which was better?

(Answer: 27⁄30 = 90%, 44⁄50 = 88%. The first.)

Percentages of a class

Percentages describe groups of people too.

Worked example: There are 40 pupils in Basic 6. 24 are girls. What percentage are girls?

24 ÷ 40 = 0.6 = 60%. So 40% are boys.

Worked example: In a class of 25, 20 pupils came to school on Monday. Attendance = 20⁄25 = 80⁄100 = 80%.

Worked example: 30% of 50 pupils walk to school. How many is that? 10% of 50 = 5, so 30% = 15 pupils.

Try this: In a class of 30, 18 pupils like football best and the rest like ampe. What percentage like ampe?

(Answer: 12 out of 30 = 40%.)

Percentages add up to 100

When you split one whole thing into parts, the percentages of the parts always add up to 100%.

Kwame's day: 35% sleeping, 25% at school, 10% eating, 5% chores. What percentage is left for play and homework?

35 + 25 + 10 + 5 = 75. So 100 − 75 = 25%.

A survey of 200 pupils asked about their favourite food. 45% said jollof, 30% said banku, 15% said fufu. The rest said waakye.

Waakye = 100 − 45 − 30 − 15 = 10%. That is 10% of 200 = 20 pupils.

Try this: A shop's sales were 40% food, 35% drinks and the rest soap. What percentage was soap? If total sales were GH₵500, how much was soap?

(Answers: 25% and GH₵125.)

More than 100%

Can you have more than 100%? Yes, when something grows to more than it was.

If a trader doubles her stock, she now has 200% of what she started with. If a price goes up by 50%, the new price is 150% of the old one.

Worked example: A church had 80 members. After a year it had 120. The new number as a percentage of the old: 120 ÷ 80 = 1.5 = 150%.

But you cannot score more than 100% in a test, and you cannot eat more than 100% of one cake. More than 100% only makes sense when you compare a new amount to an old one.

Try this: A football team scored 20 goals last season and 30 this season. This season's goals as a percentage of last season's?

(Answer: 150%.)

Estimating percentages

Sometimes you only need a rough answer. Round the numbers to make them easy.

Worked example: Roughly, what is 19% of GH₵203?

19% is nearly 20%, and GH₵203 is nearly GH₵200. 20% of 200 = about GH₵40. (The exact answer is GH₵38.57.)

Worked example: About what percentage is 31 out of 59?

That is close to 30 out of 60, which is a half. About 50%. (Exact: 52.5%.)

Estimating is a good habit. It helps you spot mistakes. If you work out 19% of GH₵203 and get GH₵385, you know something went wrong, because the estimate was about GH₵40.

Try this: Estimate 48% of 410, and 9% of GH₵99.

(Rough answers: about 200, about GH₵10.)

Percentages on a calculator

A calculator is allowed for some work. Here is how to use it well.

To find 23% of 350: Type 350 × 23 ÷ 100 = and you get 80.5. Or type 350 × 0.23 = and you get the same.

Some calculators have a % key. Typing 350 × 23 % gives 80.5 directly. But the % key behaves differently on different calculators, so the safest way is to divide by 100 yourself.

To change 27 out of 45 to a percentage: Type 27 ÷ 45 × 100 = and you get 60.

Always estimate first, then check your calculator answer against your estimate.

Try this: Use a calculator to find 17% of GH₵340 and 38 out of 80 as a percentage.

(Answers: GH₵57.80 and 47.5%.)

Common mistakes

Here are the slips that lose marks. Watch out for them.

1. 8% as 0.8. No: 8% = 0.08. Count two places.
2. Forgetting to subtract. "20% off GH₵50" is GH₵40, not GH₵10. The GH₵10 is the discount, not the price.
3. Dividing the wrong way. 15 out of 20 is 15 ÷ 20, not 20 ÷ 15.
4. Adding percentages of different totals. 50% of 40 and 50% of 10 do not make "100%" of anything.
5. Mixing pesewas and cedis. GH₵0.35 is 35 pesewas, not 35 cedis.

Try this: Each of these is wrong. Find the mistake.

• 5% of 200 = 100
• 25% off GH₵80 = GH₵20
• 12⁄50 = 12%

(Answers: 5% of 200 is 10; the sale price is GH₵60; 12⁄50 = 24%.)

Word problem: the fundraiser

Basic 6 is raising money for new reading books. Their target is GH₵800.

By Friday they had raised 65% of the target. How much is that?

10% of 800 = 80. 60% = 480. 5% = 40. 65% = GH₵520.

How much more do they need? GH₵800 − GH₵520 = GH₵280.

What percentage is still needed? 100% − 65% = 35%. Check: 35% of 800 = 280. Correct.

On Saturday a parent gave GH₵200. Now they have GH₵720. What percentage of the target is that? 720 ÷ 800 = 0.9 = 90%.

Try this: The target for a trip is GH₵1,200. The class has raised 45%. How much more is needed?

(Answer: GH₵660.)

Word problem: the harvest

Abena's uncle harvested 250 bags of maize. He kept 20% for his family, sold 70% at the market and gave the rest to neighbours.

Family: 20% of 250 = 2 × 25 = 50 bags. Market: 70% of 250 = 7 × 25 = 175 bags. Neighbours: 100 − 20 − 70 = 10%. 10% of 250 = 25 bags.

Check: 50 + 175 + 25 = 250. All bags are accounted for.

He sold each bag for GH₵120. Then the price rose by 25%. The new price: 25% of 120 = 30, so GH₵150 per bag.

Try this: A fisherman caught 80 fish. 15% were too small and he put them back. How many did he keep?

(Answer: 68.)

Word problem: the mobile phone

Kofi's mother buys a phone for GH₵600. The shop offers two choices:

• Choice A: Pay GH₵600 now, with a 10% discount.
• Choice B: Pay 50% now and 50% next month, with no discount.

Choice A costs 90% of 600 = GH₵540. Choice B costs 300 + 300 = GH₵600.

Choice A saves GH₵60. But Choice B lets her keep GH₵300 for a month. Which is better depends on whether she has the money now.

Maths tells you the numbers. Deciding is still up to the person.

Try this: A fridge costs GH₵1,500. Shop X gives 12% off. Shop Y gives GH₵150 off. Which is cheaper?

(Answer: X gives GH₵180 off, so Shop X is cheaper.)

Percentages in the news

Listen to the radio for a day and you will hear percentages everywhere.

• "Cocoa prices went up by 8%."
• "Fuel prices fell by 3%."
• "Voter turnout was 72%."
• "The team has won 60% of its matches."

Each one is a fraction out of 100 in disguise. 72% voter turnout means 72 out of every 100 registered voters came to vote.

Worked example: 60% of 15 matches won. 10% of 15 = 1.5, so 60% = 9 matches won.

Try this: Find a percentage in a newspaper or on the radio this week. Write it down and explain in one sentence what it means.

Simple interest: money that grows

When you save money at a bank, the bank pays you a little extra called interest, usually a percentage per year.

Worked example: Ama saves GH₵200 at 5% interest per year. After one year she earns 5% of 200 = GH₵10. She now has GH₵210.

After two years (simple interest), she earns another GH₵10, giving GH₵220.

Interest also works the other way. If you borrow GH₵200 at 5%, you must pay back GH₵210 after a year.

Try this: Kwame saves GH₵500 at 4% per year. How much interest does he earn in one year? How much after three years?

(Answers: GH₵20 and GH₵60.)

Percentages and pie charts

A pie chart is a circle cut into slices. The whole circle is 100%. Half the circle is 50%, a quarter is 25%.

A survey of how pupils travel to school:

• Walk: 50% (half the circle)
• Trotro: 25% (a quarter)
• Bicycle: 15%
• Car: 10%

If 80 pupils were surveyed, then 50% of 80 = 40 walk, 25% of 80 = 20 take a trotro, 15% of 80 = 12 cycle and 10% of 80 = 8 come by car.

Check: 40 + 20 + 12 + 8 = 80.

Try this: Draw a circle. Divide it into the four slices above as well as you can. Label each slice with its percentage.

Percentage of a percentage

Sometimes you need a percentage of something that is already a percentage of a total.

Worked example: 60% of the 200 pupils in a school are in the lower primary. 25% of those lower-primary pupils are in Basic 1. How many pupils are in Basic 1?

60% of 200 = 120 lower-primary pupils. 25% of 120 = 30. So 30 pupils are in Basic 1.

Work one step at a time. Do not add 60% and 25%; that would be wrong.

Try this: Ama has GH₵80. She gives 50% to her brother. Her brother spends 25% of what he got. How much did he spend?

(Answer: GH₵10.)

Quick check

Try these without looking back. Then check your answers below.

1. Write 45% as a fraction in its simplest form.
2. Write 3⁄5 as a percentage.
3. Write 0.08 as a percentage.
4. Find 30% of GH₵90.
5. A shirt costs GH₵70 with 20% off. What do you pay?
6. Kofi scored 32 out of 40. What percentage is that?
7. A price of GH₵40 rises by 15%. New price?
8. 35% of a class of 40 are boys. How many girls?

Answers: 1. 9⁄20. 2. 60%. 3. 8%. 4. GH₵27. 5. GH₵56. 6. 80%. 7. GH₵46. 8. 26 girls.

If you got six or more right, well done. If not, go back to the pages on finding 10% and on discounts.

Summary

Here is everything in this book on one page.

• Per cent means out of 100. 37% = 37⁄100 = 0.37.
• Fraction → %: make the bottom 100, or top ÷ bottom × 100.
• % → decimal: divide by 100. Decimal → %: multiply by 100.
• Easy percentages: 50% halve; 25% quarter; 10% divide by 10; 1% divide by 100.
• Build others from those, or use decimal × amount.
• Discount: find the percentage, subtract. Or find what you still pay (100% − discount).
• Increase: find the percentage, add.
• Marks: score ÷ total × 100.
• Parts of a whole add to 100%.
• Estimate first to catch mistakes.

Keep this page. Read it before your next test.

Learn more

• Maths is Fun: Percentages — clear explanations with sliders and practice questions
• Khan Academy: Ratios, rates and percentages — free video lessons and exercises at Basic 6 level
• Khan Academy: The meaning of percent — a short video explaining what per cent means

Watch more

Think about it

1. Why do you think people chose 100 as the number to compare against, instead of 10 or 1,000?
2. A shop says "up to 50% off". What does "up to" mean, and why might a shop use those words?
3. If a price goes up by 10% and then down by 10%, is it back where it started? Try it with GH₵100.
4. Can you think of something in your home or school that could be described with a percentage? Measure it and work it out.
5. Why is it fairer to compare test results as percentages than as raw marks?