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Home / Practice / Maths
Common denominators, mixed numbers, and why you never add the bottoms.
Question 1 of 12
Work out 2/3 + 7/8. Give your answer in its simplest form.
Fractions can only be added when the bottoms match, so the first job is a common denominator. The lowest number both 3 and 8 divide into is 24. 2/3 becomes 16/24 and 7/8 becomes 21/24. Now the tops can be added: 16 + 21 = 37, giving 37/24, which is already in its simplest form and is written 1 13/24 as a mixed number. The bottom never changes during the addition itself — 3 + 8 = 11 is the wrong move, and it is the one most often made. Find the lowest common denominator rather than just multiplying the bottoms together. The numbers stay small and the simplifying is easier.
The answer is A. Fractions can only be added when the bottoms match, so the first job is a common denominator. The lowest number both 3 and 8 divide into is 24. 2/3 becomes 16/24 and 7/8 becomes 21/24. Now the tops can be added: 16 + 21 = 37, giving 37/24, which is already in its simplest form and is written 1 13/24 as a mixed number. The bottom never changes during the addition itself — 3 + 8 = 11 is the wrong move, and it is the one most often made. Find the lowest common denominator rather than just multiplying the bottoms together. The numbers stay small and the simplifying is easier.
Work out 1/4 + 5/7. Give your answer in its simplest form.
Fractions can only be added when the bottoms match, so the first job is a common denominator. The lowest number both 4 and 7 divide into is 28. 1/4 becomes 7/28 and 5/7 becomes 20/28. Now the tops can be added: 7 + 20 = 27, giving 27/28, which is already in its simplest form: 27/28. The bottom never changes during the addition itself — 4 + 7 = 11 is the wrong move, and it is the one most often made. Check the answer looks sensible: adding two fractions under a half should not produce something over one.
The answer is A. Fractions can only be added when the bottoms match, so the first job is a common denominator. The lowest number both 4 and 7 divide into is 28. 1/4 becomes 7/28 and 5/7 becomes 20/28. Now the tops can be added: 7 + 20 = 27, giving 27/28, which is already in its simplest form: 27/28. The bottom never changes during the addition itself — 4 + 7 = 11 is the wrong move, and it is the one most often made. Check the answer looks sensible: adding two fractions under a half should not produce something over one.
Work out 1 4/5 + 3 2/5.
Deal with the whole numbers and the fractions separately. 1 + 3 = 4. The fractions already share a bottom, so add the tops: 4 + 2 = 6, giving 6/5. That is more than a whole one — 5/5 makes 1, leaving 1/5 — so another whole is carried across: 4 + 1 = 5. The answer is 5 1/5. Simplify at the very end, not in the middle. Simplifying early makes the adding harder.
The answer is A. Deal with the whole numbers and the fractions separately. 1 + 3 = 4. The fractions already share a bottom, so add the tops: 4 + 2 = 6, giving 6/5. That is more than a whole one — 5/5 makes 1, leaving 1/5 — so another whole is carried across: 4 + 1 = 5. The answer is 5 1/5. Simplify at the very end, not in the middle. Simplifying early makes the adding harder.
Work out 2 1/6 + 4 5/6.
Deal with the whole numbers and the fractions separately. 2 + 4 = 6. The fractions already share a bottom, so add the tops: 1 + 5 = 6, giving 6/6. That is exactly one whole — 6/6 makes 1 — so it is carried across and no fraction is left: 6 + 1 = 7. The answer is 7. Add the whole numbers first and set them aside. It keeps the fraction part simple.
The answer is B. Deal with the whole numbers and the fractions separately. 2 + 4 = 6. The fractions already share a bottom, so add the tops: 1 + 5 = 6, giving 6/6. That is exactly one whole — 6/6 makes 1 — so it is carried across and no fraction is left: 6 + 1 = 7. The answer is 7. Add the whole numbers first and set them aside. It keeps the fraction part simple.
Work out 3 1/3 + 1 1/3.
Deal with the whole numbers and the fractions separately. 3 + 1 = 4. The fractions already share a bottom, so add the tops: 1 + 1 = 2, giving 2/3. That is less than a whole one, so nothing is carried. The answer is 4 2/3. Simplify at the very end, not in the middle. Simplifying early makes the adding harder.
The answer is A. Deal with the whole numbers and the fractions separately. 3 + 1 = 4. The fractions already share a bottom, so add the tops: 1 + 1 = 2, giving 2/3. That is less than a whole one, so nothing is carried. The answer is 4 2/3. Simplify at the very end, not in the middle. Simplifying early makes the adding harder.
Work out 2 1/3 + 3 1/3.
Deal with the whole numbers and the fractions separately. 2 + 3 = 5. The fractions already share a bottom, so add the tops: 1 + 1 = 2, giving 2/3. That is less than a whole one, so nothing is carried. The answer is 5 2/3. Add the whole numbers first and set them aside. It keeps the fraction part simple.
The answer is A. Deal with the whole numbers and the fractions separately. 2 + 3 = 5. The fractions already share a bottom, so add the tops: 1 + 1 = 2, giving 2/3. That is less than a whole one, so nothing is carried. The answer is 5 2/3. Add the whole numbers first and set them aside. It keeps the fraction part simple.
Work out 1/3 + 2/5. Give your answer in its simplest form.
Fractions can only be added when the bottoms match, so the first job is a common denominator. The lowest number both 3 and 5 divide into is 15. 1/3 becomes 5/15 and 2/5 becomes 6/15. Now the tops can be added: 5 + 6 = 11, giving 11/15, which is already in its simplest form: 11/15. The bottom never changes during the addition itself — 3 + 5 = 8 is the wrong move, and it is the one most often made. Check the answer looks sensible: adding two fractions under a half should not produce something over one.
The answer is A. Fractions can only be added when the bottoms match, so the first job is a common denominator. The lowest number both 3 and 5 divide into is 15. 1/3 becomes 5/15 and 2/5 becomes 6/15. Now the tops can be added: 5 + 6 = 11, giving 11/15, which is already in its simplest form: 11/15. The bottom never changes during the addition itself — 3 + 5 = 8 is the wrong move, and it is the one most often made. Check the answer looks sensible: adding two fractions under a half should not produce something over one.
Work out 3 1/8 + 3 3/8.
Deal with the whole numbers and the fractions separately. 3 + 3 = 6. The fractions already share a bottom, so add the tops: 1 + 3 = 4, giving 4/8. That is less than a whole one, so nothing is carried. The answer is 6 1/2. If the fraction part comes to more than one whole, remember to carry. It is the step most often forgotten.
The answer is A. Deal with the whole numbers and the fractions separately. 3 + 3 = 6. The fractions already share a bottom, so add the tops: 1 + 3 = 4, giving 4/8. That is less than a whole one, so nothing is carried. The answer is 6 1/2. If the fraction part comes to more than one whole, remember to carry. It is the step most often forgotten.
Work out 4/5 + 1/12. Give your answer in its simplest form.
Fractions can only be added when the bottoms match, so the first job is a common denominator. The lowest number both 5 and 12 divide into is 60. 4/5 becomes 48/60 and 1/12 becomes 5/60. Now the tops can be added: 48 + 5 = 53, giving 53/60, which is already in its simplest form: 53/60. The bottom never changes during the addition itself — 5 + 12 = 17 is the wrong move, and it is the one most often made. Find the lowest common denominator rather than just multiplying the bottoms together. The numbers stay small and the simplifying is easier.
The answer is A. Fractions can only be added when the bottoms match, so the first job is a common denominator. The lowest number both 5 and 12 divide into is 60. 4/5 becomes 48/60 and 1/12 becomes 5/60. Now the tops can be added: 48 + 5 = 53, giving 53/60, which is already in its simplest form: 53/60. The bottom never changes during the addition itself — 5 + 12 = 17 is the wrong move, and it is the one most often made. Find the lowest common denominator rather than just multiplying the bottoms together. The numbers stay small and the simplifying is easier.
Work out 7/8 + 2/7. Give your answer in its simplest form.
Fractions can only be added when the bottoms match, so the first job is a common denominator. The lowest number both 8 and 7 divide into is 56. 7/8 becomes 49/56 and 2/7 becomes 16/56. Now the tops can be added: 49 + 16 = 65, giving 65/56, which is already in its simplest form and is written 1 9/56 as a mixed number. The bottom never changes during the addition itself — 8 + 7 = 15 is the wrong move, and it is the one most often made. The denominators tell you the size of the pieces. You cannot add pieces of different sizes until you cut them to match.
The answer is C. Fractions can only be added when the bottoms match, so the first job is a common denominator. The lowest number both 8 and 7 divide into is 56. 7/8 becomes 49/56 and 2/7 becomes 16/56. Now the tops can be added: 49 + 16 = 65, giving 65/56, which is already in its simplest form and is written 1 9/56 as a mixed number. The bottom never changes during the addition itself — 8 + 7 = 15 is the wrong move, and it is the one most often made. The denominators tell you the size of the pieces. You cannot add pieces of different sizes until you cut them to match.
Work out 2 5/6 + 4 5/6.
Deal with the whole numbers and the fractions separately. 2 + 4 = 6. The fractions already share a bottom, so add the tops: 5 + 5 = 10, giving 10/6. That is more than a whole one — 6/6 makes 1, leaving 4/6 — so another whole is carried across: 6 + 1 = 7. The answer is 7 2/3. Simplify at the very end, not in the middle. Simplifying early makes the adding harder.
The answer is B. Deal with the whole numbers and the fractions separately. 2 + 4 = 6. The fractions already share a bottom, so add the tops: 5 + 5 = 10, giving 10/6. That is more than a whole one — 6/6 makes 1, leaving 4/6 — so another whole is carried across: 6 + 1 = 7. The answer is 7 2/3. Simplify at the very end, not in the middle. Simplifying early makes the adding harder.
Work out 2 5/6 + 1 5/6.
Deal with the whole numbers and the fractions separately. 2 + 1 = 3. The fractions already share a bottom, so add the tops: 5 + 5 = 10, giving 10/6. That is more than a whole one — 6/6 makes 1, leaving 4/6 — so another whole is carried across: 3 + 1 = 4. The answer is 4 2/3. Add the whole numbers first and set them aside. It keeps the fraction part simple.
The answer is A. Deal with the whole numbers and the fractions separately. 2 + 1 = 3. The fractions already share a bottom, so add the tops: 5 + 5 = 10, giving 10/6. That is more than a whole one — 6/6 makes 1, leaving 4/6 — so another whole is carried across: 3 + 1 = 4. The answer is 4 2/3. Add the whole numbers first and set them aside. It keeps the fraction part simple.
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