Step-by-step Maths Level 5 Adding and subtracting fractions with the same denominator: check-up and practice test questions

Method. Add the top numbers and keep the bottom number. Simplify if you can.

1. Add the top numbers. The bottom number stays the same, because the parts are the same size.
   2 + 3 = 5
2. Keep the bottom number 6. The total is counted in the same parts.
   5/6
3. Write the answer. This is the simplest form.
   5/6

Check. Check: 5/6 is equal to 5/6.

Watch out. Do not add the bottom numbers too. 2/8 + 3/8 is 5/8, not 5/16.

Method. More than one whole: add the top numbers, then write the whole ones out.

1. Add the top numbers. Keep the bottom number the same.
   4 + 4 = 8
2. Write the total. 8 parts of size 1/5.
   8/5
3. Write as a mixed number. There are 1 whole one and 3/5 left over.
   8/5 = 1 3/5
4. Write the answer. This is the answer in its simplest form.
   1 3/5

Check. Check: 1 3/5 is more than 1, as 8/5 is more than 5/5.

Watch out. A top number bigger than the bottom is more than one whole. Write it as a mixed number.

Method. Subtract the top numbers and keep the bottom number. Simplify if you can.

1. Subtract the top numbers. The bottom number stays the same.
   7 - 4 = 3
2. Keep the bottom number 10. The parts are the same size, so the bottom number does not change.
   3/10
3. Write the answer. This is the simplest form.
   3/10

Check. Check: 3/10 + 4/10 gives 7/10.

Watch out. Do not subtract the bottom numbers. 7/8 - 3/8 is 4/8, which is 1/2.

Method. Add the top numbers and keep the bottom number. Simplify if you can.

1. Add the top numbers. The bottom number stays the same, because the parts are the same size.
   1 + 3 = 4
2. Keep the bottom number 5. The total is counted in the same parts.
   4/5
3. Write the answer. This is the simplest form.
   4/5

Check. Check: 4/5 is equal to 4/5.

Watch out. Do not add the bottom numbers too. 2/8 + 3/8 is 5/8, not 5/16.

Method. Add the top numbers and keep the bottom number. Simplify if you can.

1. Add the top numbers. The bottom number stays the same, because the parts are the same size.
   1 + 3 = 4
2. Keep the bottom number 6. The total is counted in the same parts.
   4/6
3. Simplify. Divide the top and bottom by the same number, which is 2.
   4/6 = 2/3
4. Write the answer. This is the simplest form.
   2/3

Check. Check: 2/3 is equal to 4/6.

Watch out. Do not add the bottom numbers too. 2/8 + 3/8 is 5/8, not 5/16.

Method. More than one whole: add the top numbers, then write the whole ones out.

1. Add the top numbers. Keep the bottom number the same.
   7 + 7 = 14
2. Write the total. 14 parts of size 1/8.
   14/8
3. Write as a mixed number. There are 1 whole one and 3/4 left over.
   7/4 = 1 3/4
4. Write the answer. This is the answer in its simplest form.
   1 3/4

Check. Check: 1 3/4 is more than 1, as 14/8 is more than 8/8.

Watch out. A top number bigger than the bottom is more than one whole. Write it as a mixed number.

Method. With the same denominator, the order is the order of the numerators.

1. Look at the bottom numbers. They are all the same, so compare the top numbers only.
   All are 10ths
2. Order the top numbers. Smallest top number first.
   2, 5, 6, 10
3. Write the fractions in order. Put the fractions back in the same order.
   2/10, 5/10, 6/10, 10/10

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. Divide by the bottom number to find one part, then multiply by the top number.

1. Find one 10th of 90. Share 90 into 10 equal parts.
   90 ÷ 10 = 9
2. Take 9 of those parts. The top number tells us how many parts.
   9 × 9 = 81
3. Write the answer. Keep the unit from the question.
   81 sweets

Check. Check: 9 × 10 = 90, and 9 parts is 81.

Watch out. Divide first, then multiply. Do not multiply by the bottom number.

Method. Multiply the top and bottom by the same number. The fraction stays the same size.

1. Find how many times the bottom number goes into 8. The denominator is multiplied by this number.
   4 × 2 = 8
2. Multiply the top number by the same number. Do the same to the top and bottom, so the fraction stays equal.
   3 × 2 = 6
3. Write the equal fraction. The new fraction has the same value.
   6/8

Check. Check: 6/8 simplifies to 3/4.

Watch out. Multiply the top and the bottom. Do not add the same number to each.

Method. More than one whole: add the top numbers, then write the whole ones out.

1. Add the top numbers. Keep the bottom number the same.
   7 + 4 = 11
2. Write the total. 11 parts of size 1/8.
   11/8
3. Write as a mixed number. There are 1 whole one and 3/8 left over.
   11/8 = 1 3/8
4. Write the answer. This is the answer in its simplest form.
   1 3/8

Check. Check: 1 3/8 is more than 1, as 11/8 is more than 8/8.

Watch out. A top number bigger than the bottom is more than one whole. Write it as a mixed number.

Method. Subtract the top numbers and keep the bottom number. Simplify if you can.

1. Subtract the top numbers. The bottom number stays the same.
   3 - 1 = 2
2. Keep the bottom number 5. The parts are the same size, so the bottom number does not change.
   2/5
3. Write the answer. This is the simplest form.
   2/5

Check. Check: 2/5 + 1/5 gives 3/5.

Watch out. Do not subtract the bottom numbers. 7/8 - 3/8 is 4/8, which is 1/2.

Method. Divide by the bottom number to find one part, then multiply by the top number.

1. Find one 4th of 8. Share 8 into 4 equal parts.
   8 ÷ 4 = 2
2. Take 3 of those parts. The top number tells us how many parts.
   3 × 2 = 6
3. Write the answer. Keep the unit from the question.
   6 cm

Check. Check: 2 × 4 = 8, and 3 parts is 6.

Watch out. Divide first, then multiply. Do not multiply by the bottom number.

Method. Add the top numbers and keep the bottom number. Simplify if you can.

1. Add the top numbers. The bottom number stays the same, because the parts are the same size.
   2 + 1 = 3
2. Keep the bottom number 4. The total is counted in the same parts.
   3/4
3. Write the answer. This is the simplest form.
   3/4

Check. Check: 3/4 is equal to 3/4.

Watch out. Do not add the bottom numbers too. 2/8 + 3/8 is 5/8, not 5/16.

Method. Subtract the top numbers and keep the bottom number. Simplify if you can.

1. Subtract the top numbers. The bottom number stays the same.
   4 - 2 = 2
2. Keep the bottom number 8. The parts are the same size, so the bottom number does not change.
   2/8
3. Simplify. Divide the top and bottom by 2.
   2/8 = 1/4
4. Write the answer. This is the simplest form.
   1/4

Check. Check: 1/4 + 2/8 gives 4/8.

Watch out. Do not subtract the bottom numbers. 7/8 - 3/8 is 4/8, which is 1/2.

Method. Divide by the bottom number to find one part, then multiply by the top number.

1. Find one 8th of 32. Share 32 into 8 equal parts.
   32 ÷ 8 = 4
2. Take 1 of those parts. The top number tells us how many parts.
   1 × 4 = 4
3. Write the answer. Keep the unit from the question.
   4 sweets

Check. Check: 4 × 8 = 32, and 1 parts is 4.

Watch out. Divide first, then multiply. Do not multiply by the bottom number.

Method. Add the top numbers and keep the bottom number. Simplify if you can.

1. Add the top numbers. The bottom number stays the same, because the parts are the same size.
   1 + 4 = 5
2. Keep the bottom number 10. The total is counted in the same parts.
   5/10
3. Simplify. Divide the top and bottom by the same number, which is 5.
   5/10 = 1/2
4. Write the answer. This is the simplest form.
   1/2

Check. Check: 1/2 is equal to 5/10.

Watch out. Do not add the bottom numbers too. 2/8 + 3/8 is 5/8, not 5/16.

Method. More than one whole: add the top numbers, then write the whole ones out.

1. Add the top numbers. Keep the bottom number the same.
   7 + 7 = 14
2. Write the total. 14 parts of size 1/8.
   14/8
3. Write as a mixed number. There are 1 whole one and 3/4 left over.
   7/4 = 1 3/4
4. Write the answer. This is the answer in its simplest form.
   1 3/4

Check. Check: 1 3/4 is more than 1, as 14/8 is more than 8/8.

Watch out. A top number bigger than the bottom is more than one whole. Write it as a mixed number.

Method. Add the top numbers and keep the bottom number. Simplify if you can.

1. Add the top numbers. The bottom number stays the same, because the parts are the same size.
   2 + 1 = 3
2. Keep the bottom number 10. The total is counted in the same parts.
   3/10
3. Write the answer. This is the simplest form.
   3/10

Check. Check: 3/10 is equal to 3/10.

Watch out. Do not add the bottom numbers too. 2/8 + 3/8 is 5/8, not 5/16.

Method. More than one whole: add the top numbers, then write the whole ones out.

1. Add the top numbers. Keep the bottom number the same.
   3 + 7 = 10
2. Write the total. 10 parts of size 1/8.
   10/8
3. Write as a mixed number. There are 1 whole one and 1/4 left over.
   5/4 = 1 1/4
4. Write the answer. This is the answer in its simplest form.
   1 1/4

Check. Check: 1 1/4 is more than 1, as 10/8 is more than 8/8.

Watch out. A top number bigger than the bottom is more than one whole. Write it as a mixed number.

Method. Subtract the top numbers and keep the bottom number. Simplify if you can.

1. Subtract the top numbers. The bottom number stays the same.
   8 - 4 = 4
2. Keep the bottom number 10. The parts are the same size, so the bottom number does not change.
   4/10
3. Simplify. Divide the top and bottom by 2.
   4/10 = 2/5
4. Write the answer. This is the simplest form.
   2/5

Check. Check: 2/5 + 4/10 gives 8/10.

Watch out. Do not subtract the bottom numbers. 7/8 - 3/8 is 4/8, which is 1/2.