Fractions & percentages
Equivalence, comparing and ordering fractions
Equivalent fractions look different but are worth the same amount. Once you can find them, you can compare and order fractions too.
Proper fractions
A proper fraction is less than a whole. Its top number (numerator) is smaller than its bottom number (denominator). For example, 3/8 is a proper fraction, but 8/8 equals a whole and 9/8 is more than a whole.
Finding equivalent fractions
Equivalent fractions have the same value. You can make one by multiplying (or dividing) the top and bottom by the same number. ā¢ 1/2 = 2/4 = 4/8 = 5/10 ā¢ 3/4 = 6/8 A diagram helps too: 4 out of 16 squares is the same as 1 out of 4 columns, so 4/16 = 1/4.
Comparing fractions
There are two easy cases: ā¢ Same denominator: the fraction with the bigger numerator is greater, so 5/8 > 3/8. ā¢ Same numerator: the fraction with the bigger denominator is smaller, because the pieces are smaller, so 3/8 < 3/4. If they are different, change them to equivalent fractions with the same denominator first.
Ordering fractions
To order fractions, change them so they all share the same denominator, then order by the numerators. Example: 1/2, 5/8, 3/8, 3/4 become 4/8, 5/8, 3/8, 6/8. In order that is 3/8, 4/8, 5/8, 6/8, which is 3/8, 1/2, 5/8, 3/4.
Worked examples
Is 3/8 a proper fraction?
- Compare the top number (3) with the bottom number (8).
- 3 is smaller than 8, so it is less than a whole.
Answer: Yes, 3/8 is a proper fraction.
Find a fraction equal to 3/4 in eighths
- The bottom goes from 4 to 8, which is doubling.
- Double the top too: 3 Ć 2 = 6.
- So 3/4 = 6/8.
Answer: 3/4 = 6/8.
Compare 3/8 and 3/4
- The numerators are the same (3).
- 3/4 = 6/8, which is more than 3/8.
- A bigger denominator means smaller pieces, so 3/8 is less.
Answer: 3/8 < 3/4.
Order 1/2, 5/8, 3/8, 3/4
- Change each fraction to eighths: 4/8, 5/8, 3/8, 6/8.
- Order the numerators: 3, 4, 5, 6.
- Write the fractions in that order.
Answer: 3/8, 1/2, 5/8, 3/4.
Where you see this in real life
- Seeing that half a pizza is the same as four eighths of it.
- Sharing a chocolate bar and checking two pieces are equal.
- Comparing how much two jugs are filled.
- Ordering slices of cake from smallest to largest.
Key words
- Numerator
- The top number of a fraction, which tells how many parts you have.
- Denominator
- The bottom number of a fraction, which tells how many equal parts the whole is split into.
- Proper fraction
- A fraction that is less than a whole.
- Equivalent fraction
- Fractions that look different but are worth the same amount.
- Order
- To arrange fractions from smallest to largest or largest to smallest.