Step-by-step Maths Level 5: Comparing and ordering fractions, and equal fractions
Part of the Step-by-step Maths Level 5 adding and subtracting fractions with the same denominator chapter. Chapter overview · whole chapter on one page
Comparing and ordering fractions, and equal fractions
When fractions have the same bottom number, the parts are the same size. Compare the top numbers: 6/8 is more than 3/8.
Equal fractions have the same value but different names. Half of a bar is the same as 2 parts of 4: 1/2 = 2/4.
Key ideas
- Same bottom number: compare the top numbers.
- Multiply the top and bottom by the same number to find an equal fraction.
- A fraction with the top and bottom equal is one whole.
Method. With the same denominator, compare the numerators.
- Look at the bottom numbers. Both fractions have the same bottom number, so the parts are the same size.Both are 8ths
- Compare the top numbers. With the same size of part, the bigger top number is the bigger fraction.3 and 6
- Choose the greater fraction. The fraction with more parts is greater.6/8
Check. Check: 6 parts is more than 3 parts of the same size.
Watch out. Do not compare the bottom numbers. The bigger the bottom number, the smaller each part.
Method. With the same denominator, the order is the order of the numerators.
- Look at the bottom numbers. They are all the same, so compare the top numbers only.All are 6ths
- Order the top numbers. Smallest top number first.1, 2, 4, 5
- Write the fractions in order. Put the fractions back in the same order.1/6, 2/6, 4/6, 5/6
Check. Check: the first fraction has the fewest parts, and the last has the most.
Watch out. The fractions are the same size if the top numbers are equal. Use the top numbers to order them.
Method. Multiply the top and bottom by the same number. The fraction stays the same size.
- Find how many times the bottom number goes into 8. The denominator is multiplied by this number.2 × 4 = 8
- Multiply the top number by the same number. Do the same to the top and bottom, so the fraction stays equal.1 × 4 = 4
- Write the equal fraction. The new fraction has the same value.4/8
Check. Check: 4/8 simplifies to 1/2.
Watch out. Multiply the top and the bottom. Do not add the same number to each.
Watch out
Watch out. 3/8 is not greater than 3/4. The bigger bottom number means smaller parts.
Exam tip
Grown-up tip. Fold a strip of paper into 8 and shade 3 parts, then shade 6 parts on another strip. Compare them.
Exercise 6A Practice: comparing, ordering and equal fractions
Non-calculatorMethod. Multiply the top and bottom by the same number. The fraction stays the same size.
- Find how many times the bottom number goes into 4. The denominator is multiplied by this number.2 × 2 = 4
- Multiply the top number by the same number. Do the same to the top and bottom, so the fraction stays equal.1 × 2 = 2
- Write the equal fraction. The new fraction has the same value.2/4
Check. Check: 2/4 simplifies to 1/2.
Watch out. Multiply the top and the bottom. Do not add the same number to each.
Method. Multiply the top and bottom by the same number. The fraction stays the same size.
- Find how many times the bottom number goes into 6. The denominator is multiplied by this number.2 × 3 = 6
- Multiply the top number by the same number. Do the same to the top and bottom, so the fraction stays equal.1 × 3 = 3
- Write the equal fraction. The new fraction has the same value.3/6
Check. Check: 3/6 simplifies to 1/2.
Watch out. Multiply the top and the bottom. Do not add the same number to each.
Method. Multiply the top and bottom by the same number. The fraction stays the same size.
- Find how many times the bottom number goes into 12. The denominator is multiplied by this number.4 × 3 = 12
- Multiply the top number by the same number. Do the same to the top and bottom, so the fraction stays equal.3 × 3 = 9
- Write the equal fraction. The new fraction has the same value.9/12
Check. Check: 9/12 simplifies to 3/4.
Watch out. Multiply the top and the bottom. Do not add the same number to each.
Method. Multiply the top and bottom by the same number. The fraction stays the same size.
- Find how many times the bottom number goes into 6. The denominator is multiplied by this number.3 × 2 = 6
- Multiply the top number by the same number. Do the same to the top and bottom, so the fraction stays equal.1 × 2 = 2
- Write the equal fraction. The new fraction has the same value.2/6
Check. Check: 2/6 simplifies to 1/3.
Watch out. Multiply the top and the bottom. Do not add the same number to each.
Method. With the same denominator, the order is the order of the numerators.
- Look at the bottom numbers. They are all the same, so compare the top numbers only.All are 8ths
- Order the top numbers. Smallest top number first.1, 3, 6, 8
- Write the fractions in order. Put the fractions back in the same order.1/8, 3/8, 6/8, 8/8
Check. Check: the first fraction has the fewest parts, and the last has the most.
Watch out. The fractions are the same size if the top numbers are equal. Use the top numbers to order them.
Method. With the same denominator, the order is the order of the numerators.
- Look at the bottom numbers. They are all the same, so compare the top numbers only.All are 10ths
- Order the top numbers. Smallest top number first.5, 7, 8, 9
- Write the fractions in order. Put the fractions back in the same order.5/10, 7/10, 8/10, 9/10
Check. Check: the first fraction has the fewest parts, and the last has the most.
Watch out. The fractions are the same size if the top numbers are equal. Use the top numbers to order them.
Method. Multiply the top and bottom by the same number. The fraction stays the same size.
- Find how many times the bottom number goes into 8. The denominator is multiplied by this number.2 × 4 = 8
- Multiply the top number by the same number. Do the same to the top and bottom, so the fraction stays equal.1 × 4 = 4
- Write the equal fraction. The new fraction has the same value.4/8
Check. Check: 4/8 simplifies to 1/2.
Watch out. Multiply the top and the bottom. Do not add the same number to each.
Method. With the same denominator, compare the numerators.
- Look at the bottom numbers. Both fractions have the same bottom number, so the parts are the same size.Both are 4ths
- Compare the top numbers. With the same size of part, the bigger top number is the bigger fraction.1 and 2
- Choose the greater fraction. The fraction with more parts is greater.2/4
Check. Check: 2 parts is more than 1 parts of the same size.
Watch out. Do not compare the bottom numbers. The bigger the bottom number, the smaller each part.
Method. Multiply the top and bottom by the same number. The fraction stays the same size.
- Find how many times the bottom number goes into 6. The denominator is multiplied by this number.3 × 2 = 6
- Multiply the top number by the same number. Do the same to the top and bottom, so the fraction stays equal.2 × 2 = 4
- Write the equal fraction. The new fraction has the same value.4/6
Check. Check: 4/6 simplifies to 2/3.
Watch out. Multiply the top and the bottom. Do not add the same number to each.
Method. Multiply the top and bottom by the same number. The fraction stays the same size.
- Find how many times the bottom number goes into 12. The denominator is multiplied by this number.3 × 4 = 12
- Multiply the top number by the same number. Do the same to the top and bottom, so the fraction stays equal.1 × 4 = 4
- Write the equal fraction. The new fraction has the same value.4/12
Check. Check: 4/12 simplifies to 1/3.
Watch out. Multiply the top and the bottom. Do not add the same number to each.
Method. With the same denominator, compare the numerators.
- Look at the bottom numbers. Both fractions have the same bottom number, so the parts are the same size.Both are 4ths
- Compare the top numbers. With the same size of part, the bigger top number is the bigger fraction.3 and 2
- Choose the greater fraction. The fraction with more parts is greater.3/4
Check. Check: 3 parts is more than 2 parts of the same size.
Watch out. Do not compare the bottom numbers. The bigger the bottom number, the smaller each part.
Method. Multiply the top and bottom by the same number. The fraction stays the same size.
- Find how many times the bottom number goes into 8. The denominator is multiplied by this number.4 × 2 = 8
- Multiply the top number by the same number. Do the same to the top and bottom, so the fraction stays equal.2 × 2 = 4
- Write the equal fraction. The new fraction has the same value.4/8
Check. Check: 4/8 simplifies to 2/4.
Watch out. Multiply the top and the bottom. Do not add the same number to each.
Method. With the same denominator, the order is the order of the numerators.
- Look at the bottom numbers. They are all the same, so compare the top numbers only.All are 8ths
- Order the top numbers. Smallest top number first.3, 4, 6, 8
- Write the fractions in order. Put the fractions back in the same order.3/8, 4/8, 6/8, 8/8
Check. Check: the first fraction has the fewest parts, and the last has the most.
Watch out. The fractions are the same size if the top numbers are equal. Use the top numbers to order them.
Method. Multiply the top and bottom by the same number. The fraction stays the same size.
- Find how many times the bottom number goes into 12. The denominator is multiplied by this number.4 × 3 = 12
- Multiply the top number by the same number. Do the same to the top and bottom, so the fraction stays equal.2 × 3 = 6
- Write the equal fraction. The new fraction has the same value.6/12
Check. Check: 6/12 simplifies to 2/4.
Watch out. Multiply the top and the bottom. Do not add the same number to each.
Method. With the same denominator, compare the numerators.
- Look at the bottom numbers. Both fractions have the same bottom number, so the parts are the same size.Both are 4ths
- Compare the top numbers. With the same size of part, the bigger top number is the bigger fraction.1 and 3
- Choose the greater fraction. The fraction with more parts is greater.3/4
Check. Check: 3 parts is more than 1 parts of the same size.
Watch out. Do not compare the bottom numbers. The bigger the bottom number, the smaller each part.
Method. With the same denominator, the order is the order of the numerators.
- Look at the bottom numbers. They are all the same, so compare the top numbers only.All are 6ths
- Order the top numbers. Smallest top number first.2, 3, 4, 6
- Write the fractions in order. Put the fractions back in the same order.2/6, 3/6, 4/6, 6/6
Check. Check: the first fraction has the fewest parts, and the last has the most.
Watch out. The fractions are the same size if the top numbers are equal. Use the top numbers to order them.