Year 5: Comparing and ordering fractions
Part of the Year 5 equivalent fractions and mixed numbers chapter. Chapter overview · whole chapter on one page · Download worksheet (PDF) · Answers (PDF)
Comparing and ordering fractions
Which is bigger,
There are three useful rules.
1. Same denominator: the bigger numerator is the bigger fraction.
To order a list, change every fraction to the same denominator, then order the numerators. Remember to write the original fractions in your answer. You can also compare with
Key ideas
- Same denominator: the bigger numerator is the bigger fraction.
- Same numerator: the smaller denominator is the bigger fraction (halves are bigger than quarters).
- Different denominators: change to a common denominator (a multiple of both), then compare the numerators.
- To order, change every fraction, order the numerators, then write the original fractions.
- Mixed numbers: compare the whole numbers first, or write everything as improper fractions.
Key words. To compare fractions is to say which is bigger. < means “is less than” and > means “is greater than”. A common denominator is a bottom number that both denominators go into.
Method. Make the denominators the same. Then the fraction with the bigger numerator is the bigger fraction.
- Find a common denominator. The denominators must be the same before we compare or add. Every smaller denominator goes into 8, so 8 will do.8 ÷ 4 = 2, so 4 goes into 8
- Change both fractions to the common denominator. Multiply the top and the bottom by the same number each time, so the value does not change.
3 4 3 × 2 4 × 2 6 8 5 8 - Compare the top numbers. With the same bottom number, the fraction with the bigger top number is bigger.6 > 5
- Write the answer. Use the original fractions in your answer.
3 4 5 8
Watch out. A bigger denominator does not mean a bigger fraction: 1/8 is smaller than 1/4.
Key words. To compare fractions is to say which is bigger. < means “is less than” and > means “is greater than”. A common denominator is a bottom number that both denominators go into.
Method. Make the denominators the same. Then the fraction with the bigger numerator is the bigger fraction.
- Find a common denominator. The denominators must be the same before we compare or add. Every smaller denominator goes into 10, so 10 will do.10 ÷ 5 = 2, so 5 goes into 10
- Change both fractions to the common denominator. Multiply the top and the bottom by the same number each time, so the value does not change.
7 10 3 5 3 × 2 5 × 2 6 10 - Compare the top numbers. With the same bottom number, the fraction with the bigger top number is bigger.7 > 6
- Write the answer. Use the original fractions in your answer.
7 10 3 5
Watch out. A bigger denominator does not mean a bigger fraction: 1/8 is smaller than 1/4.
Key words. To compare fractions is to say which is bigger. < means “is less than” and > means “is greater than”. A common denominator is a bottom number that both denominators go into.
Method. Make the denominators the same. Then the fraction with the bigger numerator is the bigger fraction.
- Find a common denominator. The denominators must be the same before we compare or add. Every smaller denominator goes into 12, so 12 will do.12 ÷ 3 = 4, so 3 goes into 12
- Change both fractions to the common denominator. Multiply the top and the bottom by the same number each time, so the value does not change.
2 3 2 × 4 3 × 4 8 12 7 12 - Compare the top numbers. With the same bottom number, the fraction with the bigger top number is bigger.8 > 7
- Write the answer. Use the original fractions in your answer.
2 3 7 12
Watch out. A bigger denominator does not mean a bigger fraction: 1/8 is smaller than 1/4.
Key words. To order fractions is to put them in a line from the smallest to the largest (ascending) or from the largest to the smallest (descending). Key words. To compare fractions is to say which is bigger. < means “is less than” and > means “is greater than”. A common denominator is a bottom number that both denominators go into.
Method. Change every fraction to the same denominator. Then order the numerators.
- Find a common denominator. The denominators must be the same before we compare or add. Every smaller denominator goes into 8, so 8 will do.8 ÷ 2 = 4, so 2 goes into 8
8 ÷ 4 = 2, so 4 goes into 8 - Change every fraction to the common denominator. Multiply the top and the bottom by the same number each time.
1 2 1 × 4 2 × 4 4 8 3 8 3 4 3 × 2 4 × 2 6 8 5 8 - Put the top numbers in order. With the same bottom number, the bigger the top number, the bigger the fraction. We want smallest to largest.3, 4, 5, 6 (out of 8)
- Write the original fractions in that order. The answer uses the fractions from the question, not the changed ones.
3 8 1 2 5 8 3 4
Check. Read the numerators again: 3, 4, 5, 6 go up each time. ✓
Watch out. Write down the original fractions in your final answer.
Key words. To order fractions is to put them in a line from the smallest to the largest (ascending) or from the largest to the smallest (descending). Key words. To compare fractions is to say which is bigger. < means “is less than” and > means “is greater than”. A common denominator is a bottom number that both denominators go into.
Method. Change every fraction to the same denominator. Then order the numerators.
- Find a common denominator. The denominators must be the same before we compare or add. Every smaller denominator goes into 12, so 12 will do.12 ÷ 3 = 4, so 3 goes into 12
12 ÷ 6 = 2, so 6 goes into 12 - Change every fraction to the common denominator. Multiply the top and the bottom by the same number each time.
2 3 2 × 4 3 × 4 8 12 5 6 5 × 2 6 × 2 10 12 7 12 - Put the top numbers in order. With the same bottom number, the bigger the top number, the bigger the fraction. We want largest to smallest.10, 8, 7 (out of 12)
- Write the original fractions in that order. The answer uses the fractions from the question, not the changed ones.
5 6 2 3 7 12
Check. Read the numerators again: 10, 8, 7 go down each time. ✓
Watch out. Write down the original fractions in your final answer.
Key words. To order fractions is to put them in a line from the smallest to the largest (ascending) or from the largest to the smallest (descending). Key words. To compare fractions is to say which is bigger. < means “is less than” and > means “is greater than”. A common denominator is a bottom number that both denominators go into.
Method. Change every fraction to the same denominator. Then order the numerators.
- Write the mixed numbers as improper fractions. This makes every number a fraction, so we can compare them.1
3 4 1 × 4 + 3 4 7 4
2 =2 1
15 8 1 × 8 + 5 8 13 8 - Find a common denominator. The denominators must be the same before we compare or add. Every smaller denominator goes into 8, so 8 will do.8 ÷ 4 = 2, so 4 goes into 8
- Change every fraction to the common denominator. Multiply the top and the bottom by the same number each time.
7 4 7 × 2 4 × 2 14 8 2 1 2 × 8 1 × 8 16 8 13 8 11 8 - Put the top numbers in order. With the same bottom number, the bigger the top number, the bigger the fraction. We want smallest to largest.11, 13, 14, 16 (out of 8)
- Write the original fractions in that order. The answer uses the fractions from the question, not the changed ones.
11 8 5 8 3 4
Check. Read the numerators again: 11, 13, 14, 16 go up each time. ✓
Watch out. Write down the original fractions in your final answer.
Key words. To compare fractions is to say which is bigger. < means “is less than” and > means “is greater than”. A common denominator is a bottom number that both denominators go into.
Method. Write both fractions with the same denominator. Then pick a numerator between the two numerators.
- Find a common denominator. The denominators must be the same before we compare or add. Every smaller denominator goes into 4, so 4 will do.4 ÷ 2 = 2, so 2 goes into 4
- Write both fractions with the common denominator. Then we can see the numerators.
1 2 1 × 2 2 × 2 2 4 3 4 - There is no whole number between the numerators. Double the denominator. Cutting every part in half makes room.
2 4 4 8 3 4 6 8 - Choose a numerator between them. Any whole number between 4 and 6 works.4 < 5 < 6, so use 5.
- Write the answer.
1 2 5 8 3 4
Check.
Watch out. If the numerators are next to each other, double the denominator to make room.
Key words. To compare fractions is to say which is bigger. < means “is less than” and > means “is greater than”. A common denominator is a bottom number that both denominators go into.
Method. Change the fractions to the same denominator (10). Then find the numerators that fit between.
- Write the two end fractions with denominator 10. The box fraction has a bottom number of 10, so we change the others to match.
3 5 3 × 2 5 × 2 6 10 4 5 4 × 2 5 × 2 8 10 - Look at the numerators. The box must be bigger than the first numerator and smaller than the second.6 < ? < 8
- List the numbers that fit. Only whole numbers go in the box.7
Check. Try it:
Watch out. The numbers at the ends do not count: the box has to be strictly between them.
Key words. To compare fractions is to say which is bigger. < means “is less than” and > means “is greater than”. A common denominator is a bottom number that both denominators go into.
Method. To compare fractions that have different denominators, change them to the same denominator. Then compare the numerators.
- Find a common denominator. We need a number that all the denominators go into. List the multiples of each one until you see a number in every list.Multiples of 5: 5, 10, 15, 20, 25, 30, 35, 40
Multiples of 8: 8, 16, 24, 32, 40
The first number in every list is 40. - Change both fractions to the common denominator. Multiply the top and the bottom by the same number each time.
3 5 3 × 8 5 × 8 24 40 5 8 5 × 5 8 × 5 25 40 - Compare the top numbers. With the same denominator, the bigger numerator is the bigger fraction.24 < 25, so
24 40 25 40 - Write a sentence to prove it. In a “prove it” question the last line must say what you have shown.No.
3 5 24 40 5 8 25 40 3 5 5 8
Check. The bars: the
Watch out. Do not guess from the numbers. Show the common denominator and the two new fractions.
Watch out
A bigger denominator does not make a bigger fraction.Exercise 6C Comparing and ordering fractions
Non-calculatorKey words. To compare fractions is to say which is bigger. < means “is less than” and > means “is greater than”. A common denominator is a bottom number that both denominators go into.
Method. The denominators are the same, so compare the numerators.
- Look at the denominators. If the bottom numbers are the same, the parts are the same size.Both are 8, so we can compare the top numbers.
- Compare the top numbers. With the same bottom number, the fraction with the bigger top number is bigger.3 < 5
- Write the answer. Use the original fractions in your answer.
3 8 5 8
Check. Look at the changed fractions again:
Watch out. A bigger denominator does not mean a bigger fraction: 1/8 is smaller than 1/4.
Key words. To compare fractions is to say which is bigger. < means “is less than” and > means “is greater than”. A common denominator is a bottom number that both denominators go into.
Method. The denominators are the same, so compare the numerators.
- Look at the denominators. If the bottom numbers are the same, the parts are the same size.Both are 10, so we can compare the top numbers.
- Compare the top numbers. With the same bottom number, the fraction with the bigger top number is bigger.7 > 4
- Write the answer. Use the original fractions in your answer.
7 10 4 10
Check. Look at the changed fractions again:
Watch out. A bigger denominator does not mean a bigger fraction: 1/8 is smaller than 1/4.
Key words. To compare fractions is to say which is bigger. < means “is less than” and > means “is greater than”. A common denominator is a bottom number that both denominators go into.
Method. The denominators are the same, so compare the numerators.
- Look at the denominators. If the bottom numbers are the same, the parts are the same size.Both are 12, so we can compare the top numbers.
- Compare the top numbers. With the same bottom number, the fraction with the bigger top number is bigger.5 < 9
- Write the answer. Use the original fractions in your answer.
5 12 9 12
Check. Look at the changed fractions again:
Watch out. A bigger denominator does not mean a bigger fraction: 1/8 is smaller than 1/4.
Key words. To compare fractions is to say which is bigger. < means “is less than” and > means “is greater than”. A common denominator is a bottom number that both denominators go into.
Method. The denominators are the same, so compare the numerators.
- Look at the denominators. If the bottom numbers are the same, the parts are the same size.Both are 7, so we can compare the top numbers.
- Compare the top numbers. With the same bottom number, the fraction with the bigger top number is bigger.6 > 2
- Write the answer. Use the original fractions in your answer.
6 7 2 7
Check. Look at the changed fractions again:
Watch out. A bigger denominator does not mean a bigger fraction: 1/8 is smaller than 1/4.
Key words. To compare fractions is to say which is bigger. < means “is less than” and > means “is greater than”. A common denominator is a bottom number that both denominators go into.
Method. Make the denominators the same. Then the fraction with the bigger numerator is the bigger fraction.
- Find a common denominator. We need a number that all the denominators go into. List the multiples of each one until you see a number in every list.Multiples of 3: 3, 6, 9, 12, 15
Multiples of 5: 5, 10, 15
The first number in every list is 15. - Change both fractions to the common denominator. Multiply the top and the bottom by the same number each time, so the value does not change.
1 3 1 × 5 3 × 5 5 15 1 5 1 × 3 5 × 3 3 15 - Compare the top numbers. With the same bottom number, the fraction with the bigger top number is bigger.5 > 3
- Write the answer. Use the original fractions in your answer.
1 3 1 5
Check. Look at the changed fractions again:
Watch out. A bigger denominator does not mean a bigger fraction: 1/8 is smaller than 1/4.
Key words. To compare fractions is to say which is bigger. < means “is less than” and > means “is greater than”. A common denominator is a bottom number that both denominators go into.
Method. Make the denominators the same. Then the fraction with the bigger numerator is the bigger fraction.
- Find a common denominator. The denominators must be the same before we compare or add. Every smaller denominator goes into 8, so 8 will do.8 ÷ 4 = 2, so 4 goes into 8
- Change both fractions to the common denominator. Multiply the top and the bottom by the same number each time, so the value does not change.
3 4 3 × 2 4 × 2 6 8 3 8 - Compare the top numbers. With the same bottom number, the fraction with the bigger top number is bigger.6 > 3
- Write the answer. Use the original fractions in your answer.
3 4 3 8
Check. Look at the changed fractions again:
Watch out. A bigger denominator does not mean a bigger fraction: 1/8 is smaller than 1/4.
Key words. To compare fractions is to say which is bigger. < means “is less than” and > means “is greater than”. A common denominator is a bottom number that both denominators go into.
Method. Make the denominators the same. Then the fraction with the bigger numerator is the bigger fraction.
- Find a common denominator. We need a number that all the denominators go into. List the multiples of each one until you see a number in every list.Multiples of 3: 3, 6, 9, 12, 15
Multiples of 5: 5, 10, 15
The first number in every list is 15. - Change both fractions to the common denominator. Multiply the top and the bottom by the same number each time, so the value does not change.
2 5 2 × 3 5 × 3 6 15 2 3 2 × 5 3 × 5 10 15 - Compare the top numbers. With the same bottom number, the fraction with the bigger top number is bigger.6 < 10
- Write the answer. Use the original fractions in your answer.
2 5 2 3
Check. Look at the changed fractions again:
Watch out. A bigger denominator does not mean a bigger fraction: 1/8 is smaller than 1/4.
Key words. To compare fractions is to say which is bigger. < means “is less than” and > means “is greater than”. A common denominator is a bottom number that both denominators go into.
Method. Make the denominators the same. Then the fraction with the bigger numerator is the bigger fraction.
- Find a common denominator. The denominators must be the same before we compare or add. Every smaller denominator goes into 12, so 12 will do.12 ÷ 6 = 2, so 6 goes into 12
- Change both fractions to the common denominator. Multiply the top and the bottom by the same number each time, so the value does not change.
5 6 5 × 2 6 × 2 10 12 5 12 - Compare the top numbers. With the same bottom number, the fraction with the bigger top number is bigger.10 > 5
- Write the answer. Use the original fractions in your answer.
5 6 5 12
Check. Look at the changed fractions again:
Watch out. A bigger denominator does not mean a bigger fraction: 1/8 is smaller than 1/4.
Key words. To compare fractions is to say which is bigger. < means “is less than” and > means “is greater than”. A common denominator is a bottom number that both denominators go into.
Method. Make the denominators the same. Then the fraction with the bigger numerator is the bigger fraction.
- Find a common denominator. The denominators must be the same before we compare or add. Every smaller denominator goes into 8, so 8 will do.8 ÷ 2 = 4, so 2 goes into 8
- Change both fractions to the common denominator. Multiply the top and the bottom by the same number each time, so the value does not change.
1 2 1 × 4 2 × 4 4 8 3 8 - Compare the top numbers. With the same bottom number, the fraction with the bigger top number is bigger.4 > 3
- Write the answer. Use the original fractions in your answer.
1 2 3 8
Check. Look at the changed fractions again:
Watch out. A bigger denominator does not mean a bigger fraction: 1/8 is smaller than 1/4.
Key words. To compare fractions is to say which is bigger. < means “is less than” and > means “is greater than”. A common denominator is a bottom number that both denominators go into.
Method. Make the denominators the same. Then the fraction with the bigger numerator is the bigger fraction.
- Find a common denominator. The denominators must be the same before we compare or add. Every smaller denominator goes into 8, so 8 will do.8 ÷ 4 = 2, so 4 goes into 8
- Change both fractions to the common denominator. Multiply the top and the bottom by the same number each time, so the value does not change.
3 4 3 × 2 4 × 2 6 8 5 8 - Compare the top numbers. With the same bottom number, the fraction with the bigger top number is bigger.6 > 5
- Write the answer. Use the original fractions in your answer.
3 4 5 8
Check. Look at the changed fractions again:
Watch out. A bigger denominator does not mean a bigger fraction: 1/8 is smaller than 1/4.
Key words. To compare fractions is to say which is bigger. < means “is less than” and > means “is greater than”. A common denominator is a bottom number that both denominators go into.
Method. Make the denominators the same. Then the fraction with the bigger numerator is the bigger fraction.
- Find a common denominator. The denominators must be the same before we compare or add. Every smaller denominator goes into 8, so 8 will do.8 ÷ 4 = 2, so 4 goes into 8
- Change both fractions to the common denominator. Multiply the top and the bottom by the same number each time, so the value does not change.
1 4 1 × 2 4 × 2 2 8 3 8 - Compare the top numbers. With the same bottom number, the fraction with the bigger top number is bigger.2 < 3
- Write the answer. Use the original fractions in your answer.
1 4 3 8
Check. Look at the changed fractions again:
Watch out. A bigger denominator does not mean a bigger fraction: 1/8 is smaller than 1/4.
Key words. To compare fractions is to say which is bigger. < means “is less than” and > means “is greater than”. A common denominator is a bottom number that both denominators go into.
Method. Make the denominators the same. Then the fraction with the bigger numerator is the bigger fraction.
- Find a common denominator. The denominators must be the same before we compare or add. Every smaller denominator goes into 8, so 8 will do.8 ÷ 4 = 2, so 4 goes into 8
- Change both fractions to the common denominator. Multiply the top and the bottom by the same number each time, so the value does not change.
7 8 3 4 3 × 2 4 × 2 6 8 - Compare the top numbers. With the same bottom number, the fraction with the bigger top number is bigger.7 > 6
- Write the answer. Use the original fractions in your answer.
7 8 3 4
Check. Look at the changed fractions again:
Watch out. A bigger denominator does not mean a bigger fraction: 1/8 is smaller than 1/4.
Key words. To compare fractions is to say which is bigger. < means “is less than” and > means “is greater than”. A common denominator is a bottom number that both denominators go into.
Method. Make the denominators the same. Then the fraction with the bigger numerator is the bigger fraction.
- Find a common denominator. The denominators must be the same before we compare or add. Every smaller denominator goes into 6, so 6 will do.6 ÷ 3 = 2, so 3 goes into 6
- Change both fractions to the common denominator. Multiply the top and the bottom by the same number each time, so the value does not change.
2 3 2 × 2 3 × 2 4 6 5 6 - Compare the top numbers. With the same bottom number, the fraction with the bigger top number is bigger.4 < 5
- Write the answer. Use the original fractions in your answer.
2 3 5 6
Check. Look at the changed fractions again:
Watch out. A bigger denominator does not mean a bigger fraction: 1/8 is smaller than 1/4.
Key words. To compare fractions is to say which is bigger. < means “is less than” and > means “is greater than”. A common denominator is a bottom number that both denominators go into.
Method. Make the denominators the same. Then the fraction with the bigger numerator is the bigger fraction.
- Find a common denominator. The denominators must be the same before we compare or add. Every smaller denominator goes into 8, so 8 will do.8 ÷ 4 = 2, so 4 goes into 8
- Change both fractions to the common denominator. Multiply the top and the bottom by the same number each time, so the value does not change.
3 4 3 × 2 4 × 2 6 8 5 8 - Compare the top numbers. With the same bottom number, the fraction with the bigger top number is bigger.6 > 5
- Write the answer. Use the original fractions in your answer.
3 4 5 8
Check. Look at the changed fractions again:
Watch out. A bigger denominator does not mean a bigger fraction: 1/8 is smaller than 1/4.
Key words. To compare fractions is to say which is bigger. < means “is less than” and > means “is greater than”. A common denominator is a bottom number that both denominators go into.
Method. Make the denominators the same. Then the fraction with the bigger numerator is the bigger fraction.
- Find a common denominator. The denominators must be the same before we compare or add. Every smaller denominator goes into 10, so 10 will do.10 ÷ 5 = 2, so 5 goes into 10
- Change both fractions to the common denominator. Multiply the top and the bottom by the same number each time, so the value does not change.
7 10 3 5 3 × 2 5 × 2 6 10 - Compare the top numbers. With the same bottom number, the fraction with the bigger top number is bigger.7 > 6
- Write the answer. Use the original fractions in your answer.
7 10 3 5
Check. Look at the changed fractions again:
Watch out. A bigger denominator does not mean a bigger fraction: 1/8 is smaller than 1/4.
Key words. To compare fractions is to say which is bigger. < means “is less than” and > means “is greater than”. A common denominator is a bottom number that both denominators go into.
Method. Make the denominators the same. Then the fraction with the bigger numerator is the bigger fraction.
- Find a common denominator. The denominators must be the same before we compare or add. Every smaller denominator goes into 12, so 12 will do.12 ÷ 3 = 4, so 3 goes into 12
- Change both fractions to the common denominator. Multiply the top and the bottom by the same number each time, so the value does not change.
5 12 1 3 1 × 4 3 × 4 4 12 - Compare the top numbers. With the same bottom number, the fraction with the bigger top number is bigger.5 > 4
- Write the answer. Use the original fractions in your answer.
5 12 1 3
Check. Look at the changed fractions again:
Watch out. A bigger denominator does not mean a bigger fraction: 1/8 is smaller than 1/4.
Key words. To compare fractions is to say which is bigger. < means “is less than” and > means “is greater than”. A common denominator is a bottom number that both denominators go into.
Method. Make the denominators the same. Then the fraction with the bigger numerator is the bigger fraction.
- Find a common denominator. The denominators must be the same before we compare or add. Every smaller denominator goes into 10, so 10 will do.10 ÷ 5 = 2, so 5 goes into 10
- Change both fractions to the common denominator. Multiply the top and the bottom by the same number each time, so the value does not change.
4 5 4 × 2 5 × 2 8 10 7 10 - Compare the top numbers. With the same bottom number, the fraction with the bigger top number is bigger.8 > 7
- Write the answer. Use the original fractions in your answer.
4 5 7 10
Check. Look at the changed fractions again:
Watch out. A bigger denominator does not mean a bigger fraction: 1/8 is smaller than 1/4.
Key words. To compare fractions is to say which is bigger. < means “is less than” and > means “is greater than”. A common denominator is a bottom number that both denominators go into.
Method. Make the denominators the same. Then the fraction with the bigger numerator is the bigger fraction.
- Find a common denominator. The denominators must be the same before we compare or add. Every smaller denominator goes into 12, so 12 will do.12 ÷ 2 = 6, so 2 goes into 12
- Change both fractions to the common denominator. Multiply the top and the bottom by the same number each time, so the value does not change.
1 2 1 × 6 2 × 6 6 12 5 12 - Compare the top numbers. With the same bottom number, the fraction with the bigger top number is bigger.6 > 5
- Write the answer. Use the original fractions in your answer.
1 2 5 12
Check. Look at the changed fractions again:
Watch out. A bigger denominator does not mean a bigger fraction: 1/8 is smaller than 1/4.
Key words. To compare fractions is to say which is bigger. < means “is less than” and > means “is greater than”. A common denominator is a bottom number that both denominators go into.
Method. Make the denominators the same. Then the fraction with the bigger numerator is the bigger fraction.
- Find a common denominator. The denominators must be the same before we compare or add. Every smaller denominator goes into 8, so 8 will do.8 ÷ 4 = 2, so 4 goes into 8
- Change both fractions to the common denominator. Multiply the top and the bottom by the same number each time, so the value does not change.
5 8 3 4 3 × 2 4 × 2 6 8 - Compare the top numbers. With the same bottom number, the fraction with the bigger top number is bigger.5 < 6
- Write the answer. Use the original fractions in your answer.
5 8 3 4 3 4
Check. Look at the changed fractions again:
Watch out. A bigger denominator does not mean a bigger fraction: 1/8 is smaller than 1/4.
Key words. To compare fractions is to say which is bigger. < means “is less than” and > means “is greater than”. A common denominator is a bottom number that both denominators go into.
Method. Make the denominators the same. Then the fraction with the bigger numerator is the bigger fraction.
- Find a common denominator. The denominators must be the same before we compare or add. Every smaller denominator goes into 10, so 10 will do.10 ÷ 5 = 2, so 5 goes into 10
- Change both fractions to the common denominator. Multiply the top and the bottom by the same number each time, so the value does not change.
3 10 1 5 1 × 2 5 × 2 2 10 - Compare the top numbers. With the same bottom number, the fraction with the bigger top number is bigger.3 > 2
- Write the answer. Use the original fractions in your answer.
3 10 1 5 3 10
Check. Look at the changed fractions again:
Watch out. A bigger denominator does not mean a bigger fraction: 1/8 is smaller than 1/4.
Key words. To order fractions is to put them in a line from the smallest to the largest (ascending) or from the largest to the smallest (descending). Key words. To compare fractions is to say which is bigger. < means “is less than” and > means “is greater than”. A common denominator is a bottom number that both denominators go into.
Method. Change every fraction to the same denominator. Then order the numerators.
- Find a common denominator. The denominators must be the same before we compare or add. Every smaller denominator goes into 10, so 10 will do.10 ÷ 2 = 5, so 2 goes into 10
10 ÷ 5 = 2, so 5 goes into 10 - Change every fraction to the common denominator. Multiply the top and the bottom by the same number each time.
3 10 1 2 1 × 5 2 × 5 5 10 2 5 2 × 2 5 × 2 4 10 - Put the top numbers in order. With the same bottom number, the bigger the top number, the bigger the fraction. We want smallest to largest.3, 4, 5 (out of 10)
- Write the original fractions in that order. The answer uses the fractions from the question, not the changed ones.
3 10 2 5 1 2
Check. Read the numerators again: 3, 4, 5 go up each time. ✓
Watch out. Write down the original fractions in your final answer.
Key words. To order fractions is to put them in a line from the smallest to the largest (ascending) or from the largest to the smallest (descending). Key words. To compare fractions is to say which is bigger. < means “is less than” and > means “is greater than”. A common denominator is a bottom number that both denominators go into.
Method. Change every fraction to the same denominator. Then order the numerators.
- Find a common denominator. The denominators must be the same before we compare or add. Every smaller denominator goes into 16, so 16 will do.16 ÷ 2 = 8, so 2 goes into 16
16 ÷ 4 = 4, so 4 goes into 16
16 ÷ 8 = 2, so 8 goes into 16 - Change every fraction to the common denominator. Multiply the top and the bottom by the same number each time.
3 4 3 × 4 4 × 4 12 16 5 8 5 × 2 8 × 2 10 16 1 2 1 × 8 2 × 8 8 16 11 16 - Put the top numbers in order. With the same bottom number, the bigger the top number, the bigger the fraction. We want smallest to largest.8, 10, 11, 12 (out of 16)
- Write the original fractions in that order. The answer uses the fractions from the question, not the changed ones.
1 2 5 8 11 16 3 4
Check. Read the numerators again: 8, 10, 11, 12 go up each time. ✓
Watch out. Write down the original fractions in your final answer.
Key words. To order fractions is to put them in a line from the smallest to the largest (ascending) or from the largest to the smallest (descending). Key words. To compare fractions is to say which is bigger. < means “is less than” and > means “is greater than”. A common denominator is a bottom number that both denominators go into.
Method. Change every fraction to the same denominator. Then order the numerators.
- Find a common denominator. The denominators must be the same before we compare or add. Every smaller denominator goes into 12, so 12 will do.12 ÷ 2 = 6, so 2 goes into 12
12 ÷ 3 = 4, so 3 goes into 12
12 ÷ 6 = 2, so 6 goes into 12 - Change every fraction to the common denominator. Multiply the top and the bottom by the same number each time.
7 12 2 3 2 × 4 3 × 4 8 12 1 2 1 × 6 2 × 6 6 12 5 6 5 × 2 6 × 2 10 12 - Put the top numbers in order. With the same bottom number, the bigger the top number, the bigger the fraction. We want smallest to largest.6, 7, 8, 10 (out of 12)
- Write the original fractions in that order. The answer uses the fractions from the question, not the changed ones.
1 2 7 12 2 3 5 6
Check. Read the numerators again: 6, 7, 8, 10 go up each time. ✓
Watch out. Write down the original fractions in your final answer.
Key words. To order fractions is to put them in a line from the smallest to the largest (ascending) or from the largest to the smallest (descending). Key words. To compare fractions is to say which is bigger. < means “is less than” and > means “is greater than”. A common denominator is a bottom number that both denominators go into.
Method. Change every fraction to the same denominator. Then order the numerators.
- Find a common denominator. The denominators must be the same before we compare or add. Every smaller denominator goes into 10, so 10 will do.10 ÷ 5 = 2, so 5 goes into 10
- Change every fraction to the common denominator. Multiply the top and the bottom by the same number each time.
4 5 4 × 2 5 × 2 8 10 7 10 3 5 3 × 2 5 × 2 6 10 9 10 - Put the top numbers in order. With the same bottom number, the bigger the top number, the bigger the fraction. We want smallest to largest.6, 7, 8, 9 (out of 10)
- Write the original fractions in that order. The answer uses the fractions from the question, not the changed ones.
3 5 7 10 4 5 9 10
Check. Read the numerators again: 6, 7, 8, 9 go up each time. ✓
Watch out. Write down the original fractions in your final answer.
Key words. To order fractions is to put them in a line from the smallest to the largest (ascending) or from the largest to the smallest (descending). Key words. To compare fractions is to say which is bigger. < means “is less than” and > means “is greater than”. A common denominator is a bottom number that both denominators go into.
Method. Change every fraction to the same denominator. Then order the numerators.
- Find a common denominator. The denominators must be the same before we compare or add. Every smaller denominator goes into 12, so 12 will do.12 ÷ 3 = 4, so 3 goes into 12
12 ÷ 4 = 3, so 4 goes into 12
12 ÷ 6 = 2, so 6 goes into 12 - Change every fraction to the common denominator. Multiply the top and the bottom by the same number each time.
5 6 5 × 2 6 × 2 10 12 2 3 2 × 4 3 × 4 8 12 3 4 3 × 3 4 × 3 9 12 7 12 - Put the top numbers in order. With the same bottom number, the bigger the top number, the bigger the fraction. We want largest to smallest.10, 9, 8, 7 (out of 12)
- Write the original fractions in that order. The answer uses the fractions from the question, not the changed ones.
5 6 3 4 2 3 7 12
Check. Read the numerators again: 10, 9, 8, 7 go down each time. ✓
Watch out. Write down the original fractions in your final answer.
Key words. To order fractions is to put them in a line from the smallest to the largest (ascending) or from the largest to the smallest (descending). Key words. To compare fractions is to say which is bigger. < means “is less than” and > means “is greater than”. A common denominator is a bottom number that both denominators go into.
Method. Change every fraction to the same denominator. Then order the numerators.
- Find a common denominator. The denominators must be the same before we compare or add. Every smaller denominator goes into 8, so 8 will do.8 ÷ 2 = 4, so 2 goes into 8
8 ÷ 4 = 2, so 4 goes into 8 - Change every fraction to the common denominator. Multiply the top and the bottom by the same number each time.
3 8 1 2 1 × 4 2 × 4 4 8 1 4 1 × 2 4 × 2 2 8 - Put the top numbers in order. With the same bottom number, the bigger the top number, the bigger the fraction. We want largest to smallest.4, 3, 2 (out of 8)
- Write the original fractions in that order. The answer uses the fractions from the question, not the changed ones.
1 2 3 8 1 4
Check. Read the numerators again: 4, 3, 2 go down each time. ✓
Watch out. Write down the original fractions in your final answer.
Key words. The denominator (bottom number) tells us how many equal parts the whole is cut into. The numerator (top number) tells us how many parts we have.
Method. Count the steps from 0 to each letter. Each step is one twelfth.
- Count to A. A is 3 steps from 0.
3 12 - Count to B. B is 8 steps from 0.
8 12 - Count to C. C is 5 steps from 0.
5 12
Check. The denominator is 12 for all of them. ✓
Watch out. Count the steps (gaps), not the tick marks.
Key words. To compare fractions is to say which is bigger. < means “is less than” and > means “is greater than”. A common denominator is a bottom number that both denominators go into.
Method. Read each letter in twelfths, then compare the numerators.
- Write A, B and C as twelfths. Each step on the line is one twelfth.A =
3 12 8 12 5 12 - Compare the numerators. All three have the same denominator.8 > 5 > 3
- Write the order. B has the biggest numerator.B is the largest, then C, then A.
Check. B is furthest to the right on the line. ✓
Watch out. Count the steps from 0.
Key words. To compare fractions is to say which is bigger. < means “is less than” and > means “is greater than”. A common denominator is a bottom number that both denominators go into.
Method. Change the fractions to the same denominator (10). Then find the numerators that fit between.
- Write the two end fractions with denominator 10. The box fraction has a bottom number of 10, so we change the others to match.
3 5 3 × 2 5 × 2 6 10 4 5 4 × 2 5 × 2 8 10 - Look at the numerators. The box must be bigger than the first numerator and smaller than the second.6 < ? < 8
- List the numbers that fit. Only whole numbers go in the box.7
Check. Try it:
Watch out. The numbers at the ends do not count: the box has to be strictly between them.
Key words. To compare fractions is to say which is bigger. < means “is less than” and > means “is greater than”. A common denominator is a bottom number that both denominators go into.
Method. Change the fractions to the same denominator (8). Then find the numerators that fit between.
- Write the two end fractions with denominator 8. The box fraction has a bottom number of 8, so we change the others to match.
1 2 1 × 4 2 × 4 4 8 3 4 3 × 2 4 × 2 6 8 - Look at the numerators. The box must be bigger than the first numerator and smaller than the second.4 < ? < 6
- List the numbers that fit. Only whole numbers go in the box.5
Check. Try it:
Watch out. The numbers at the ends do not count: the box has to be strictly between them.
Key words. To compare fractions is to say which is bigger. < means “is less than” and > means “is greater than”. A common denominator is a bottom number that both denominators go into.
Method. Change the fractions to the same denominator (12). Then find the numerators that fit between.
- Write the two end fractions with denominator 12. The box fraction has a bottom number of 12, so we change the others to match.
1 3 1 × 4 3 × 4 4 12 1 2 1 × 6 2 × 6 6 12 - Look at the numerators. The box must be bigger than the first numerator and smaller than the second.4 < ? < 6
- List the numbers that fit. Only whole numbers go in the box.5
Check. Try it:
Watch out. The numbers at the ends do not count: the box has to be strictly between them.
Key words. To compare fractions is to say which is bigger. < means “is less than” and > means “is greater than”. A common denominator is a bottom number that both denominators go into.
Method. Change the fractions to the same denominator (20). Then find the numerators that fit between.
- Write the two end fractions with denominator 20. The box fraction has a bottom number of 20, so we change the others to match.
2 5 2 × 4 5 × 4 8 20 1 2 1 × 10 2 × 10 10 20 - Look at the numerators. The box must be bigger than the first numerator and smaller than the second.8 < ? < 10
- List the numbers that fit. Only whole numbers go in the box.9
Check. Try it:
Watch out. The numbers at the ends do not count: the box has to be strictly between them.
Key words. To compare fractions is to say which is bigger. < means “is less than” and > means “is greater than”. A common denominator is a bottom number that both denominators go into.
Method. A fraction is greater than
- Find half of each denominator. Half of a whole is the same as half the number of parts.
3 8 1 2 5 8 1 2 4 10 1 2 7 12 1 2 6 12 1 2 - Pick the fractions that are greater than one half. Ignore any that are equal or smaller.
5 8 7 12
Check.
Watch out. A fraction equal to one half, like 6/12, is not greater than one half.
Key words. To compare fractions is to say which is bigger. < means “is less than” and > means “is greater than”. A common denominator is a bottom number that both denominators go into.
Method. Make the denominators the same. Then the fraction with the bigger numerator is the bigger fraction.
- Write the mixed numbers as improper fractions. This makes every number a fraction, so we can compare them.1
3 4 1 × 4 + 3 4 7 4
15 8 1 × 8 + 5 8 13 8 - Find a common denominator. The denominators must be the same before we compare or add. Every smaller denominator goes into 8, so 8 will do.8 ÷ 4 = 2, so 4 goes into 8
- Change both fractions to the common denominator. Multiply the top and the bottom by the same number each time, so the value does not change.
7 4 7 × 2 4 × 2 14 8 13 8 - Compare the top numbers. With the same bottom number, the fraction with the bigger top number is bigger.14 > 13
- Write the answer. Use the original fractions in your answer.1
3 4 5 8
Check. Look at the changed fractions again:
Watch out. A bigger denominator does not mean a bigger fraction: 1/8 is smaller than 1/4.
Key words. To compare fractions is to say which is bigger. < means “is less than” and > means “is greater than”. A common denominator is a bottom number that both denominators go into.
Method. Make the denominators the same. Then the fraction with the bigger numerator is the bigger fraction.
- Write the mixed numbers as improper fractions. This makes every number a fraction, so we can compare them.2
1 2 2 × 2 + 1 2 5 2
24 10 2 × 10 + 4 10 24 10 - Find a common denominator. The denominators must be the same before we compare or add. Every smaller denominator goes into 10, so 10 will do.10 ÷ 2 = 5, so 2 goes into 10
- Change both fractions to the common denominator. Multiply the top and the bottom by the same number each time, so the value does not change.
5 2 5 × 5 2 × 5 25 10 24 10 - Compare the top numbers. With the same bottom number, the fraction with the bigger top number is bigger.25 > 24
- Write the answer. Use the original fractions in your answer.2
1 2 4 10
Check. Look at the changed fractions again:
Watch out. A bigger denominator does not mean a bigger fraction: 1/8 is smaller than 1/4.
Key words. To compare fractions is to say which is bigger. < means “is less than” and > means “is greater than”. A common denominator is a bottom number that both denominators go into.
Method. Make the denominators the same. Then the fraction with the bigger numerator is the bigger fraction.
- Write the mixed numbers as improper fractions. This makes every number a fraction, so we can compare them.2
1 2 2 × 2 + 1 2 5 2 - Find a common denominator. The denominators must be the same before we compare or add. Every smaller denominator goes into 4, so 4 will do.4 ÷ 2 = 2, so 2 goes into 4
- Change both fractions to the common denominator. Multiply the top and the bottom by the same number each time, so the value does not change.
9 4 5 2 5 × 2 2 × 2 10 4 - Compare the top numbers. With the same bottom number, the fraction with the bigger top number is bigger.9 < 10
- Write the answer. Use the original fractions in your answer.
9 4 1 2
Check. Look at the changed fractions again:
Watch out. A bigger denominator does not mean a bigger fraction: 1/8 is smaller than 1/4.
Key words. To compare fractions is to say which is bigger. < means “is less than” and > means “is greater than”. A common denominator is a bottom number that both denominators go into.
Method. Make the denominators the same. Then the fraction with the bigger numerator is the bigger fraction.
- Write the mixed numbers as improper fractions. This makes every number a fraction, so we can compare them.1
7 8 1 × 8 + 7 8 15 8
2 =2 1 - Change both fractions to the common denominator. Multiply the top and the bottom by the same number each time, so the value does not change.
15 8 2 1 2 × 8 1 × 8 16 8 - Compare the top numbers. With the same bottom number, the fraction with the bigger top number is bigger.15 < 16
- Write the answer. Use the original fractions in your answer.1
7 8
Check. Look at the changed fractions again:
Watch out. A bigger denominator does not mean a bigger fraction: 1/8 is smaller than 1/4.
Key words. To order fractions is to put them in a line from the smallest to the largest (ascending) or from the largest to the smallest (descending). Key words. To compare fractions is to say which is bigger. < means “is less than” and > means “is greater than”. A common denominator is a bottom number that both denominators go into.
Method. Change every fraction to the same denominator. Then order the numerators.
- Write the mixed numbers as improper fractions. This makes every number a fraction, so we can compare them.1
1 2 1 × 2 + 1 2 3 2
17 8 1 × 8 + 7 8 15 8 - Find a common denominator. The denominators must be the same before we compare or add. Every smaller denominator goes into 8, so 8 will do.8 ÷ 2 = 4, so 2 goes into 8
8 ÷ 4 = 2, so 4 goes into 8 - Change every fraction to the common denominator. Multiply the top and the bottom by the same number each time.
3 2 3 × 4 2 × 4 12 8 5 4 5 × 2 4 × 2 10 8 15 8 11 8 - Put the top numbers in order. With the same bottom number, the bigger the top number, the bigger the fraction. We want smallest to largest.10, 11, 12, 15 (out of 8)
- Write the original fractions in that order. The answer uses the fractions from the question, not the changed ones.
5 4 11 8 1 2 7 8
Check. Read the numerators again: 10, 11, 12, 15 go up each time. ✓
Watch out. Write down the original fractions in your final answer.
Key words. To compare fractions is to say which is bigger. < means “is less than” and > means “is greater than”. A common denominator is a bottom number that both denominators go into.
Method. To compare fractions that have different denominators, change them to the same denominator. Then compare the numerators.
- Find a common denominator. We need a number that all the denominators go into. List the multiples of each one until you see a number in every list.Multiples of 3: 3, 6, 9, 12, 15, 18, 21, 24
Multiples of 8: 8, 16, 24
The first number in every list is 24. - Change both fractions to the common denominator. Multiply the top and the bottom by the same number each time.
5 8 5 × 3 8 × 3 15 24 2 3 2 × 8 3 × 8 16 24 - Compare the top numbers. With the same denominator, the bigger numerator is the bigger fraction.15 < 16, so
15 24 16 24 - Write a sentence to prove it. In a “prove it” question the last line must say what you have shown.No.
5 8 15 24 2 3 16 24 5 8 2 3
Check. The bars: the
Watch out. Do not guess from the numbers. Show the common denominator and the two new fractions.
Key words. To compare fractions is to say which is bigger. < means “is less than” and > means “is greater than”. A common denominator is a bottom number that both denominators go into.
Method. Work the question out yourself first. Then compare your working with the working in the question and find where it goes wrong.
- Work it out correctly. We need the right answer to compare with.
1 4 3 12 1 6 2 12 1 4 1 6 - Find the mistake. Leo compared the bottom numbers. A bigger bottom number means the whole is cut into more, smaller pieces. So each piece is smaller.Leo says
1 6 1 4 - Write the correct answer. The correct answer is
1 6 1 4
Check. On a fraction wall the sixth brick is shorter than the quarter brick. ✓
Watch out. Think about sharing a pizza: more people means smaller slices.
Key words. Always means true every time. Never means false every time. Sometimes means true for some numbers and false for others.
Method. Test the statement with some numbers. If it is always true, never true, or true for some numbers only, that gives the answer.
- Try some examples. Testing numbers helps us see if the statement is true every time.
3 8 5 8 2 9 7 9 4 5 1 5 - Decide: always, sometimes or never? When the denominators are the same, the parts are the same size. So more parts means a bigger fraction.Always
Check. Every example agreed. ✓
Watch out. To show a statement is “always” true you need a reason. A few examples are not enough to prove it, but one counter-example shows it is not always true.
Key words. Always means true every time. Never means false every time. Sometimes means true for some numbers and false for others.
Method. Test the statement with some numbers. If it is always true, never true, or true for some numbers only, that gives the answer.
- Try some examples. Testing numbers helps us see if the statement is true every time.
1 3 1 5 1 5 1 3 - Look for an example that does not work. One example that breaks the rule is a counter-example.
1 4 3 8 1 4 2 8 3 8 - Decide: always, sometimes or never? It works when the numerators are the same, but not always when the numerators are different.Sometimes
Check. We found one example that works and one that does not. ✓
Watch out. To show a statement is “always” true you need a reason. A few examples are not enough to prove it, but one counter-example shows it is not always true.
Key words. To compare fractions is to say which is bigger. < means “is less than” and > means “is greater than”. A common denominator is a bottom number that both denominators go into.
Method. Write both fractions with the same denominator. Then pick a numerator between the two numerators.
- Find a common denominator. We need a number that all the denominators go into. List the multiples of each one until you see a number in every list.Multiples of 2: 2, 4, 6, 8, 10
Multiples of 5: 5, 10
The first number in every list is 10. - Write both fractions with the common denominator. Then we can see the numerators.
2 5 2 × 2 5 × 2 4 10 1 2 1 × 5 2 × 5 5 10 - There is no whole number between the numerators. Double the denominator. Cutting every part in half makes room.
4 10 8 20 5 10 10 20 - Choose a numerator between them. Any whole number between 8 and 10 works.8 < 9 < 10, so use 9.
- Write the answer.
2 5 9 20 1 2
Check.
Watch out. If the numerators are next to each other, double the denominator to make room.