Percentages
🎯 We are going to ...
- find percentages of whole numbers and shapes.
🧠 Key Words
- operator
- percentage
- per cent
Show Definitions
- operator: A mathematical symbol or instruction that tells you what calculation to perform on numbers.
- percentage: A way of expressing a number as a fraction of 100, often used to compare proportions.
- per cent: A term meaning “out of every 100,” commonly written using the symbol $\%$.
🛍️ Spotting Sales in Shops
Have you ever seen a shop that is having a sale? Sometimes shops will offer an amount off the price, for example $5 off. More often though they offer a percentage off, for example 10% off or 25% off.
❓ EXERCISES
1. Find $10\%$ of these quantities.
a. $40$
b. $70\text{ cm}$
c. $20$
d. $120\text{ kg}$
👀 Show answer
b. $7\text{ cm}$
c. $2$
d. $12\text{ kg}$
2. A man has a mass of $80\text{ kg}$. $60\%$ of his total mass is water. What is the mass of this water?
👀 Show answer
3. Helga says, ‘To calculate $10\%$ of a quantity, you divide it by $10$, so to find $50\%$, you divide by $5$.’ Helga is not correct. Explain what is wrong with her statement.
👀 Show answer
4. What percentage of the diagram is shaded?
👀 Show answer
5. What percentage of each diagram is shaded?
👀 Show answer
b. $20\%$
c. $20\%$
6. Calculate.
a. $15\%$ of $120$
b. $45\%$ of $240$
c. $65\%$ of $180$
👀 Show answer
b. $108$
c. $117$
7. Amy has $\$400$. She spends $40\%$ of her money on a new bike. How much does she spend on the bike?
👀 Show answer
8. Song has strip of paper $20\text{ cm}$ long. He cuts a $5\text{ cm}$ piece off the strip. What percentage of the strip does he cut off?
👀 Show answer
9. a. A coat originally costs $\$40$. The price goes up by $10\%$. What is the new price?
b. A garden centre sells plants at $25\%$ off at the end of the month. The price of a plant was originally $\$8$. What is its price at the end of the month?
👀 Show answer
b. $25\%$ off $8 = 2$ so price $= \$6$
10. The pie chart shows the favourite animals of Stage $6$ children.
$32$ children chose elephants. How many children are in Stage $6$? Explain your answer.
👀 Show answer
🧠 Think like a Mathematician
Challenge: Here are twelve numbers.
$10,\; 20,\; 25,\; 40,\; 50,\; 60,\; 75,\; 100,\; 150,\; 160,\; 500,\; 600$
Can you write four number sentences using each of the twelve numbers once?
$\square\%$ of $\square$ is $\square$
$\square\%$ of $\square$ is $\square$
$\square\%$ of $\square$ is $\square$
$\square\%$ of $\square$ is $\square$
Show Answers
- 1:$10\%$ of $500$ is $50$
- 2:$20\%$ of $600$ is $120$
- 3:$25\%$ of $160$ is $40$
- 4:$75\%$ of $200$ is $150$
💡 Quick Math Tip
Move-and-check method: Cut out number cards and move them around until your number sentence works correctly.