Ordering Fractions and Saying Why
Apply knowledge of equivalence to compare, order and represent common fractions including halves, thirds and quarters on the same number line and justify their order.
Read this first
Put every fraction over the same bottom number. Then the order is easy to see.
All three sit between 0 and 1. Three quarters is furthest right.
Words you need
- Equivalent
- The same amount written a different way.
- Common denominator
- A bottom number that all the fractions can use.
- Justify
- Give a reason for your answer.
Worked example
e.g. Order 1/2, 2/3 and 3/4 from smallest to largest.
- Look at the bottom numbers. They are 2, 3 and 4.
- Find a number all three divide into. It is 12.
- Rewrite each fraction over 12.
- 1/2 is 6/12. 2/3 is 8/12. 3/4 is 9/12.
- Now compare the tops. The order is 1/2, 2/3, 3/4.
Give the reason too. Say the pieces are now the same size.
Practice
The pictures fade as you go. By the last few you are on your own.
1Which is bigger: 2/3 or 3/4?with a picture
Answer3/4, because 9/12 is more than 8/12.
2Which is bigger: 1/3 or 1/4?with a picture
Answer1/3. Fewer pieces means bigger pieces.
3Order 1/2, 5/8 and 3/8.with a hint
Need a hint?
Change the half into eighths.
Answer3/8, 1/2, 5/8.
4Is 5/9 more or less than a half?with a hint
Need a hint?
Half of 9 is 4.5.
AnswerMore.
5Order 2/5, 1/2 and 7/10.on your own
Answer2/5, 1/2, 7/10.
6Which is bigger: 4/6 or 2/3?on your own
AnswerThey are equal.
7Why can you not compare tops when the bottoms differ?on your own
AnswerThe pieces are different sizes.
Think about it
1
Why does a bigger bottom number make smaller pieces?
One good answerThe whole is cut into more parts, so each part is smaller.
2
How do you find a common denominator quickly?
One good answerLook for a multiple that all the bottoms divide into.
Common mistakes
Comparing the tops when the bottoms differ.
Make the bottoms match first.
Thinking 1/8 is bigger than 1/3.
More pieces means each one is smaller.