Equivalence & comparison
🎯 In this topic you will
- Reduce fractions to their simplest form.
- Recognise equivalent values between fractions, decimals and percentages.
- Compare fractions, decimals and percentages using the symbols =, > and <.
- Order fractions, decimals and percentages.
🧠 Key Words
- equivalent fraction
- simplest form
- simplify
Show Definitions
- equivalent fraction: Fractions that represent the same value even though their numerators and denominators are different.
- simplest form: The form of a fraction where the numerator and denominator have no common factors other than 1.
- simplify: To rewrite a fraction in its simplest form by dividing the numerator and denominator by their greatest common factor.
🔢 Simplifying Fractions
You can simplify a fraction if you can divide both the numerator and the denominator by the same number.
🏁 Reaching the Simplest Form
The fraction $\dfrac{1}{5}$ is the simplest form of the fraction. You will learn how to simplify fractions in this section.
❓ EXERCISES
1. What fraction of the shape is shaded? Write your answer in its simplest form.
👀 Show answer
2. Write these fractions in their simplest form.
a. $\dfrac{4}{16}$
b. $\dfrac{12}{20}$
c. $\dfrac{18}{24}$
👀 Show answer
b. $\dfrac{3}{5}$
c. $\dfrac{3}{4}$
3. Here are six number cards. Use four of these cards to complete the number sentence. Which of the three fractions is in the simplest form?
👀 Show answer
4. Write these numbers in their simplest form.
a. $\dfrac{12}{8}$
b. $\dfrac{20}{16}$
c. $1\dfrac{4}{10}$
👀 Show answer
b. $\dfrac{5}{4}$
c. $1\dfrac{2}{5}$
5. Here are three statements about fractions and percentages. Which statements are true? Which statements are not true? Correct these statements.
A. $\dfrac{3}{100}$ is equal to $3\%$
B. $\dfrac{4}{5}$ is equal to $45\%$
C. $\dfrac{7}{10}$ is equal to $7\%$
👀 Show answer
B. False, $\dfrac{4}{5} = 80\%$
C. False, $\dfrac{7}{10} = 70\%$
6. Which two fractions are equal to $0.6$?
$\dfrac{1}{6}$ $\dfrac{60}{100}$ $\dfrac{1}{60}$ $\dfrac{6}{10}$
👀 Show answer
7. Copy and complete this table to show equivalent values.
| Fraction | Decimal | Percentage |
|---|---|---|
| $\dfrac{57}{100}$ | $0.57$ | $57\%$ |
| $\dfrac{8}{100}$ | $0.08$ | $8\%$ |
| $\dfrac{5}{4}$ | $1.25$ | $125\%$ |
👀 Show answer
8. Write these fractions in order starting with the smallest fraction.
$\dfrac{7}{12}$, $\dfrac{3}{4}$, $\dfrac{1}{2}$, $\dfrac{5}{6}$, $\dfrac{2}{3}$
👀 Show answer
9. Write these numbers in order starting with the largest.
$7.7$, $7.07$, $7.77$, $7.17$, $7.71$
👀 Show answer
10. Use one of the symbols $<$, $>$ or $=$ to make each statement correct.
$\dfrac{7}{10}$ □ $0.07$
$23\%$ □ $0.23$
$75\%$ □ $\dfrac{4}{5}$
👀 Show answer
$23\% = 0.23$
$75\% < \dfrac{4}{5}$
11. Anil says, ‘$0.25$ is smaller than $\dfrac{2}{5}$.’ Is Anil correct? Explain your answer.
👀 Show answer
12. Write these numbers in order, starting with the smallest.
$\dfrac{7}{10}$, $50\%$, $0.65$, $\dfrac{3}{5}$
👀 Show answer
🧠 Think like a Mathematician
Imagine you spin both these spinners to make a fraction.
Investigate how many different fractions you can make.
Write all the proper fractions as percentages.
Write all the improper fractions as decimal numbers.
Order the decimals and percentages starting with the largest number.
Show Answers
- Number of different fractions:$16$ possible fractions.
- Proper fractions as percentages:$\frac{1}{2}=50\%$, $\frac{1}{4}=25\%$, $\frac{1}{5}=20\%$, $\frac{2}{4}=50\%$, $\frac{2}{5}=40\%$, $\frac{4}{5}=80\%$.
- Improper fractions as decimals:$\frac{2}{1}=2$, $\frac{4}{1}=4$, $\frac{5}{1}=5$, $\frac{5}{2}=2.5$, $\frac{5}{4}=1.25$.
- Ordered (largest first):$5$, $4$, $2.5$, $2$, $125\%$, $80\%$, $50\%$, $40\%$, $25\%$, $20\%$.