Percentages, decimals and fractions
🎯 In this topic you will
- Write tenths, hundredths, quarters and halves as percentages
- Find percentages of shapes
- Find equivalent proper fractions, decimals and percentages
🧠 Key Words
- percentage
- per cent
Show Definitions
- percentage: A way of expressing a number as a fraction of 100.
- per cent: Means “out of every 100” and is another way of writing % when talking about parts of a whole.
Introduction to Percentages
Percentages are commonly used in daily life. You may notice percentage signs when shopping, such as in discounts and sales. This lesson will introduce you to how to work with percentages, fractions, and decimals.
Working with Equivalent Fractions, Decimals, and Percentages
In this section, you will learn how to work with equivalent fractions, decimals, and percentages. For example, $ \dfrac{70}{100} $, $ \dfrac{7}{10} $, and $0.7$ are all equivalent and represent the same amount: 70%. You will also learn how to convert between these forms.
❓ EXERCISES
1. Write these fractions as percentages.
a. $\frac{40}{100}$
b. $\frac{1}{100}$
c. $\frac{1}{10}$
d. $\frac{7}{10}$
e. $\frac{1}{4}$
f. $\frac{3}{5}$
👀 Show answer
b. $1\%$
c. $10\%$
d. $70\%$
e. $25\%$
f. $60\%$
2. What percentage of each diagram is shaded?
👀 Show answer
b. $60\%$
c. $30\%$
3. Which is the odd one out in this set of five percentages? Explain your answer.
$10\%, 11\%, 13\%, 17\%, 19\%$
👀 Show answer
4. Write the percentage of each shape that is shaded.
👀 Show answer
b. $25\%$
c. $50\%$
5. Rajiv draws a pattern of triangles. He colours six triangles.
a. What fraction of the triangles does he colour?
b. Write this fraction as a percentage.
👀 Show answer
a. $\frac{6}{12} = \frac{1}{2}$
b. $50\%$
6. Find the missing number.
$\displaystyle \frac{5}{\square} = 50\%$
👀 Show answer
7. Pablo has six cards: $20\%$, $\frac{2}{5}$, $0.4$, $0.2$, $\frac{4}{10}$, $40\%$.
He finds two sets of cards with equivalent values. List the two sets.
👀 Show answer
$40\% = 0.4 = \frac{2}{5}$
8. Copy and complete the table to show equivalent fractions, decimals and percentages.
| Fraction | Decimal | Percentage |
|---|---|---|
| $\frac{1}{2}$ | $0.5$ | $50\%$ |
| $\frac{1}{10}$ | $0.1$ | $10\%$ |
| $\frac{9}{10}$ | $0.9$ | $90\%$ |
👀 Show answer
9. Sofia makes a fraction using two number cards.
She says, “My fraction is equivalent to $50\%$. One of the number cards is $6$.”
What fractions could Sofia make?
👀 Show answer
$\frac{6}{12}$, $\frac{3}{6}$, $\frac{12}{24}$, etc.
🧠 Think like a Mathematician
Question: Arun has 60 counters. They are red or yellow or blue or green. 50% of the counters are yellow. One third of those that are not yellow are red. 0.25 of those that are neither red nor yellow are blue. The remainder are green. How many counters are there of each colour?
Equipment: None specified.
Method:
- Determine the number of yellow counters by finding 50% of 60.
- Determine how many counters are not yellow (subtract yellow counters from the total).
- Find one third of the remaining counters that are red.
- Find 0.25 of the remaining counters that are blue.
- Calculate the remaining counters to determine how many are green.
Follow-up Questions:
Show Answers
- 1: There are 30 yellow counters.
- 2: There are 10 red counters.
- 3: There are 5 blue counters.
- 4: There are 15 green counters.