More fractions
Ordering and comparing fractions
Knowing which fraction is bigger helps you choose the best deal. You can compare fractions using a number line or fraction strips.
Comparing unit fractions
A unit fraction has 1 on top. The more equal parts a whole is split into, the smaller each part is. So 1/2 is bigger than 1/5, and 1/10 is smaller than 1/5. The bigger the denominator, the smaller the fraction.
Same denominator
When two fractions have the same bottom number, just compare the top numbers. 3/5 is bigger than 2/5 because 3 is more than 2. And 4/10 is smaller than 6/10.
Using < > and =
We write 'is less than' as <, 'is greater than' as >, and 'is equal to' as =. For example 1/4 < 1/3, 1/2 > 1/5, and 2/4 = 1/2.
Equivalent fractions
Equivalent fractions have the same value even though they look different. On equal strips, 2/4 covers the same amount as 1/2, and 5/10 also equals 1/2.
Using a number line
On a number line from 0 to 1, smaller fractions sit closer to 0 and larger fractions sit closer to 1. So 1/10 is near 0 and 3/4 is near 1.
Worked examples
Comparing unit fractions
- Look at 1/2 and 1/5.
- Halves are bigger pieces than fifths.
- So 1/2 is greater than 1/5.
Answer: 1/2 > 1/5
Same denominator
- Look at 2/5 and 3/5.
- The bottom numbers are the same.
- Compare the tops: 3 is more than 2.
- So 3/5 is greater than 2/5.
Answer: 3/5 > 2/5
Finding an equivalent fraction
- Look at 2/4 on a strip.
- It covers the same amount as one half.
- So 2/4 and 1/2 are equivalent.
Answer: 2/4 = 1/2
Choosing the better deal
- Compare 1/2 of $30 and 1/3 of $30.
- 1/2 of $30 is 30 ÷ 2 = $15.
- 1/3 of $30 is 30 ÷ 3 = $10.
- $15 is more than $10, so 1/2 of $30 is better.
Answer: 1/2 of $30 is greater
Where you see this in real life
- Choosing whether you would rather have 1/2 or 1/3 of some money.
- Comparing slices of pizza to see who has more.
- Ordering fraction strips from smallest to largest on a number line.
Key words
- Compare
- To decide which of two fractions is bigger or smaller.
- Order
- To arrange fractions from smallest to largest.
- Equivalent
- Having the same value, even if written differently.
- Inequality
- A statement using < or > to show which is bigger.
- Denominator
- The bottom number — how many equal parts in the whole.