Year 4: Adding and subtracting fractions
Part of the Year 4 fractions chapter. Chapter overview · whole chapter on one page · Download worksheet (PDF) · Answers (PDF)
Adding and subtracting fractions
Imagine a chocolate bar cut into 7 equal pieces. Zara eats 2 pieces. Then she eats 3 more pieces. How much has she eaten altogether? She has eaten 2 sevenths and 3 sevenths. That is 5 pieces, so 5 sevenths.
The rule. When the bottom numbers are the same, the pieces are the same size. Add the top numbers and keep the bottom number the same. The same is true for subtraction: subtract the top numbers and keep the bottom number.
Why does the bottom number stay the same? The bottom number names the size of the pieces (sevenths). Adding more pieces does not change their size. 2 apples + 3 apples = 5 apples. 2 sevenths + 3 sevenths = 5 sevenths.
Making a whole. When all the pieces are there, the answer is 1 whole. For example 3 eighths + 5 eighths = 8 eighths = 1 whole. Any fraction with the same top and bottom number equals 1: 4/4 = 1, 10/10 = 1.
This helps with taking a fraction away from 1. Write 1 as a fraction with the same bottom number. For example 1 = 5/5, so 1 − 2/5 = 5/5 − 2/5 = 3/5.
Key words. The numerator is the top number. The denominator is the bottom number. Whole means 1 complete thing.
Key ideas
- Same bottom number: the pieces are the same size.
- Add or subtract the TOP numbers. Keep the bottom number the same.
- When the top number equals the bottom number, the fraction is 1 whole: 6/6 = 1.
- To take a fraction from 1, write 1 as (bottom number)/(bottom number). 1 = 5/5.
- To find what is missing from a whole, subtract the top number from the bottom number.
- Never add the bottom numbers.
Key words. The numerator is the top number. The denominator is the bottom number.
Method. Fractions with the same bottom number are made of equal pieces. Add the top numbers and keep the bottom number the same.
- Check the bottom numbers. They are all 7. That means every piece is the same size (sevenths), so we can add them.
2 7 3 7 - Add the top numbers. The top numbers tell us how many pieces we have. We are counting pieces of the same size.2 + 3 = 5
- Keep the bottom number the same. The pieces are still sevenths. Adding does not change the size of the pieces.
2 7 3 7 5 7
Check. Take away one of the fractions from the answer: 5 − 3 = 2. That is the top of the other fraction. ✓
Watch out. Do not add the bottom numbers. The pieces stay sevenths, so the bottom number stays 7.
Key words. The numerator is the top number. The denominator is the bottom number.
Method. Fractions with the same bottom number are made of equal pieces. Add the top numbers and keep the bottom number the same.
- Check the bottom numbers. They are all 8. That means every piece is the same size (eighths), so we can add them.
3 8 5 8 - Add the top numbers. The top numbers tell us how many pieces we have. We are counting pieces of the same size.3 + 5 = 8
- Keep the bottom number the same. The pieces are still eighths. Adding does not change the size of the pieces.
3 8 5 8 8 8 - Write it as a whole number. 8 eighths make 1 whole.
8 8
Check. Take away one of the fractions from the answer: 8 − 5 = 3. That is the top of the other fraction. ✓
Watch out. Do not add the bottom numbers. The pieces stay eighths, so the bottom number stays 8.
Key words. The numerator is the top number. The denominator is the bottom number.
Method. The pieces are the same size, so take away the top numbers and keep the bottom number the same.
- Check the bottom numbers. They are both 10, so the pieces are the same size (tenths) and we can subtract.
7 10 4 10 - Subtract the top numbers. We start with 7 pieces and take away 4 pieces.7 − 4 = 3
- Keep the bottom number the same. The pieces are still tenths.
7 10 4 10 3 10
Check. Add back: 3 + 4 = 7, so
Watch out. Do not subtract the bottom numbers. The pieces are still tenths.
Key words. The numerator is the top number. The denominator is the bottom number.
Method. Write 1 whole as 5/5. Then subtract.
- Write 1 whole as a fraction. 1 whole is 5 pieces of size
1 5 1 =5 5 - Subtract the top numbers. We take away 3 pieces from 5 pieces.5 − 3 = 2
- Keep the bottom number the same. The pieces are still fifths.1 −
3 5 5 5 3 5 2 5
Check. Add:
Watch out. 1 whole is 5 fifths. It is not 1 fifth.
Key words. The numerator is the top number. The denominator is the bottom number.
Method. The bottom numbers are all the same, so we only need to work out the missing top number.
- Look at the bottom numbers. All are 10, so the pieces are the same size. The missing number is a top number.
3 10 ? 10 8 10 - Use the opposite (inverse) operation. 8 is the total. If we take away 3 from the total, we get the missing top number.8 − 3 = 5
- Write the missing number. The missing number is 5.
Check. 3 + 5 = 8. ✓
Watch out. The missing number goes on top. The bottom number stays the same.
Key words. The numerator is the top number. The denominator is the bottom number.
Method. Fractions with the same bottom number are made of equal pieces. Add the top numbers and keep the bottom number the same.
- Check the bottom numbers. They are all 8. That means every piece is the same size (eighths), so we can add them.
2 8 3 8 - Add the top numbers. The top numbers tell us how many pieces we have. We are counting pieces of the same size.2 + 3 = 5
- Keep the bottom number the same. The pieces are still eighths. Adding does not change the size of the pieces.
2 8 3 8 5 8
Check. Take away one of the fractions from the answer: 5 − 3 = 2. That is the top of the other fraction. ✓
Watch out. Do not add the bottom numbers. The pieces stay eighths, so the bottom number stays 8.
Key words. The numerator is the top number. The denominator is the bottom number.
Method. Write 1 whole as 8/8. Then subtract.
- Write 1 whole as a fraction. 1 whole is 8 pieces of size
1 8 1 =8 8 - Subtract the top numbers. We take away 5 pieces from 8 pieces.8 − 5 = 3
- Keep the bottom number the same. The pieces are still eighths.1 −
5 8 8 8 5 8 3 8
Check. Add:
Watch out. 1 whole is 8 eighths. It is not 1 eighth.
Watch out
Do not add the bottom numbers. 2/5 + 1/5 is 3/5, not 3/10. The pieces are still fifths. To take a fraction away from 1, write 1 as a fraction with the same bottom number: 1 = 5/5 (not 1/1).Exercise 5D Adding and subtracting fractions
Non-calculatorKey words. The numerator is the top number. The denominator is the bottom number.
Method. Fractions with the same bottom number are made of equal pieces. Add the top numbers and keep the bottom number the same.
- Check the bottom numbers. They are all 7. That means every piece is the same size (sevenths), so we can add them.
2 7 3 7 - Add the top numbers. The top numbers tell us how many pieces we have. We are counting pieces of the same size.2 + 3 = 5
- Keep the bottom number the same. The pieces are still sevenths. Adding does not change the size of the pieces.
2 7 3 7 5 7
Check. Take away one of the fractions from the answer: 5 − 3 = 2. That is the top of the other fraction. ✓
Watch out. Do not add the bottom numbers. The pieces stay sevenths, so the bottom number stays 7.
Key words. The numerator is the top number. The denominator is the bottom number.
Method. Fractions with the same bottom number are made of equal pieces. Add the top numbers and keep the bottom number the same.
- Check the bottom numbers. They are all 9. That means every piece is the same size (ninths), so we can add them.
1 9 4 9 - Add the top numbers. The top numbers tell us how many pieces we have. We are counting pieces of the same size.1 + 4 = 5
- Keep the bottom number the same. The pieces are still ninths. Adding does not change the size of the pieces.
1 9 4 9 5 9
Check. Take away one of the fractions from the answer: 5 − 4 = 1. That is the top of the other fraction. ✓
Watch out. Do not add the bottom numbers. The pieces stay ninths, so the bottom number stays 9.
Key words. The numerator is the top number. The denominator is the bottom number.
Method. Fractions with the same bottom number are made of equal pieces. Add the top numbers and keep the bottom number the same.
- Check the bottom numbers. They are all 10. That means every piece is the same size (tenths), so we can add them.
3 10 4 10 - Add the top numbers. The top numbers tell us how many pieces we have. We are counting pieces of the same size.3 + 4 = 7
- Keep the bottom number the same. The pieces are still tenths. Adding does not change the size of the pieces.
3 10 4 10 7 10
Check. Take away one of the fractions from the answer: 7 − 4 = 3. That is the top of the other fraction. ✓
Watch out. Do not add the bottom numbers. The pieces stay tenths, so the bottom number stays 10.
Key words. The numerator is the top number. The denominator is the bottom number.
Method. Fractions with the same bottom number are made of equal pieces. Add the top numbers and keep the bottom number the same.
- Check the bottom numbers. They are all 5. That means every piece is the same size (fifths), so we can add them.
2 5 2 5 - Add the top numbers. The top numbers tell us how many pieces we have. We are counting pieces of the same size.2 + 2 = 4
- Keep the bottom number the same. The pieces are still fifths. Adding does not change the size of the pieces.
2 5 2 5 4 5
Check. Take away one of the fractions from the answer: 4 − 2 = 2. That is the top of the other fraction. ✓
Watch out. Do not add the bottom numbers. The pieces stay fifths, so the bottom number stays 5.
Key words. The numerator is the top number. The denominator is the bottom number.
Method. Fractions with the same bottom number are made of equal pieces. Add the top numbers and keep the bottom number the same.
- Check the bottom numbers. They are all 3. That means every piece is the same size (thirds), so we can add them.
1 3 1 3 - Add the top numbers. The top numbers tell us how many pieces we have. We are counting pieces of the same size.1 + 1 = 2
- Keep the bottom number the same. The pieces are still thirds. Adding does not change the size of the pieces.
1 3 1 3 2 3
Check. Take away one of the fractions from the answer: 2 − 1 = 1. That is the top of the other fraction. ✓
Watch out. Do not add the bottom numbers. The pieces stay thirds, so the bottom number stays 3.
Key words. The numerator is the top number. The denominator is the bottom number.
Method. Fractions with the same bottom number are made of equal pieces. Add the top numbers and keep the bottom number the same.
- Check the bottom numbers. They are all 4. That means every piece is the same size (quarters), so we can add them.
1 4 2 4 - Add the top numbers. The top numbers tell us how many pieces we have. We are counting pieces of the same size.1 + 2 = 3
- Keep the bottom number the same. The pieces are still quarters. Adding does not change the size of the pieces.
1 4 2 4 3 4
Check. Take away one of the fractions from the answer: 3 − 2 = 1. That is the top of the other fraction. ✓
Watch out. Do not add the bottom numbers. The pieces stay quarters, so the bottom number stays 4.
Key words. The numerator is the top number. The denominator is the bottom number.
Method. Fractions with the same bottom number are made of equal pieces. Add the top numbers and keep the bottom number the same.
- Check the bottom numbers. They are all 5. That means every piece is the same size (fifths), so we can add them.
2 5 2 5 - Add the top numbers. The top numbers tell us how many pieces we have. We are counting pieces of the same size.2 + 2 = 4
- Keep the bottom number the same. The pieces are still fifths. Adding does not change the size of the pieces.
2 5 2 5 4 5
Check. Take away one of the fractions from the answer: 4 − 2 = 2. That is the top of the other fraction. ✓
Watch out. Do not add the bottom numbers. The pieces stay fifths, so the bottom number stays 5.
Key words. The numerator is the top number. The denominator is the bottom number.
Method. Fractions with the same bottom number are made of equal pieces. Add the top numbers and keep the bottom number the same.
- Check the bottom numbers. They are all 6. That means every piece is the same size (sixths), so we can add them.
1 6 4 6 - Add the top numbers. The top numbers tell us how many pieces we have. We are counting pieces of the same size.1 + 4 = 5
- Keep the bottom number the same. The pieces are still sixths. Adding does not change the size of the pieces.
1 6 4 6 5 6
Check. Take away one of the fractions from the answer: 5 − 4 = 1. That is the top of the other fraction. ✓
Watch out. Do not add the bottom numbers. The pieces stay sixths, so the bottom number stays 6.
Key words. The numerator is the top number. The denominator is the bottom number.
Method. Fractions with the same bottom number are made of equal pieces. Add the top numbers and keep the bottom number the same.
- Check the bottom numbers. They are all 7. That means every piece is the same size (sevenths), so we can add them.
3 7 4 7 - Add the top numbers. The top numbers tell us how many pieces we have. We are counting pieces of the same size.3 + 4 = 7
- Keep the bottom number the same. The pieces are still sevenths. Adding does not change the size of the pieces.
3 7 4 7 7 7 - Write it as a whole number. 7 sevenths make 1 whole.
7 7
Check. Take away one of the fractions from the answer: 7 − 4 = 3. That is the top of the other fraction. ✓
Watch out. Do not add the bottom numbers. The pieces stay sevenths, so the bottom number stays 7.
Key words. The numerator is the top number. The denominator is the bottom number.
Method. Fractions with the same bottom number are made of equal pieces. Add the top numbers and keep the bottom number the same.
- Check the bottom numbers. They are all 12. That means every piece is the same size (twelfths), so we can add them.
5 12 6 12 - Add the top numbers. The top numbers tell us how many pieces we have. We are counting pieces of the same size.5 + 6 = 11
- Keep the bottom number the same. The pieces are still twelfths. Adding does not change the size of the pieces.
5 12 6 12 11 12
Check. Take away one of the fractions from the answer: 11 − 6 = 5. That is the top of the other fraction. ✓
Watch out. Do not add the bottom numbers. The pieces stay twelfths, so the bottom number stays 12.
Key words. The numerator is the top number. The denominator is the bottom number.
Method. The pieces are the same size, so take away the top numbers and keep the bottom number the same.
- Check the bottom numbers. They are both 4, so the pieces are the same size (quarters) and we can subtract.
3 4 2 4 - Subtract the top numbers. We start with 3 pieces and take away 2 pieces.3 − 2 = 1
- Keep the bottom number the same. The pieces are still quarters.
3 4 2 4 1 4
Check. Add back: 1 + 2 = 3, so
Watch out. Do not subtract the bottom numbers. The pieces are still quarters.
Key words. The numerator is the top number. The denominator is the bottom number.
Method. The pieces are the same size, so take away the top numbers and keep the bottom number the same.
- Check the bottom numbers. They are both 5, so the pieces are the same size (fifths) and we can subtract.
4 5 1 5 - Subtract the top numbers. We start with 4 pieces and take away 1 piece.4 − 1 = 3
- Keep the bottom number the same. The pieces are still fifths.
4 5 1 5 3 5
Check. Add back: 3 + 1 = 4, so
Watch out. Do not subtract the bottom numbers. The pieces are still fifths.
Key words. The numerator is the top number. The denominator is the bottom number.
Method. The pieces are the same size, so take away the top numbers and keep the bottom number the same.
- Check the bottom numbers. They are both 6, so the pieces are the same size (sixths) and we can subtract.
5 6 4 6 - Subtract the top numbers. We start with 5 pieces and take away 4 pieces.5 − 4 = 1
- Keep the bottom number the same. The pieces are still sixths.
5 6 4 6 1 6
Check. Add back: 1 + 4 = 5, so
Watch out. Do not subtract the bottom numbers. The pieces are still sixths.
Key words. The numerator is the top number. The denominator is the bottom number.
Method. The pieces are the same size, so take away the top numbers and keep the bottom number the same.
- Check the bottom numbers. They are both 8, so the pieces are the same size (eighths) and we can subtract.
7 8 2 8 - Subtract the top numbers. We start with 7 pieces and take away 2 pieces.7 − 2 = 5
- Keep the bottom number the same. The pieces are still eighths.
7 8 2 8 5 8
Check. Add back: 5 + 2 = 7, so
Watch out. Do not subtract the bottom numbers. The pieces are still eighths.
Key words. The numerator is the top number. The denominator is the bottom number.
Method. The pieces are the same size, so take away the top numbers and keep the bottom number the same.
- Check the bottom numbers. They are both 10, so the pieces are the same size (tenths) and we can subtract.
9 10 2 10 - Subtract the top numbers. We start with 9 pieces and take away 2 pieces.9 − 2 = 7
- Keep the bottom number the same. The pieces are still tenths.
9 10 2 10 7 10
Check. Add back: 7 + 2 = 9, so
Watch out. Do not subtract the bottom numbers. The pieces are still tenths.
Key words. The numerator is the top number. The denominator is the bottom number.
Method. The pieces are the same size, so take away the top numbers and keep the bottom number the same.
- Check the bottom numbers. They are both 12, so the pieces are the same size (twelfths) and we can subtract.
11 12 4 12 - Subtract the top numbers. We start with 11 pieces and take away 4 pieces.11 − 4 = 7
- Keep the bottom number the same. The pieces are still twelfths.
11 12 4 12 7 12
Check. Add back: 7 + 4 = 11, so
Watch out. Do not subtract the bottom numbers. The pieces are still twelfths.
Key words. The numerator is the top number. The denominator is the bottom number.
Method. Write 1 whole as 7/7. Then find how many more pieces are needed.
- Write 1 whole as a fraction. 1 whole is 7 pieces of size
1 7 1 =7 7 - Find how many more pieces we need. We have 3 pieces and we want 7 pieces.7 − 3 = 4
- Keep the bottom number the same. The pieces are still sevenths.
3 7 7 7 3 7 4 7
Check. Add:
Watch out. 1 whole is 7 sevenths. It is not 1 seventh.
Key words. The numerator is the top number. The denominator is the bottom number.
Method. Write 1 whole as 4/4. Then find how many more pieces are needed.
- Write 1 whole as a fraction. 1 whole is 4 pieces of size
1 4 1 =4 4 - Find how many more pieces we need. We have 1 piece and we want 4 pieces.4 − 1 = 3
- Keep the bottom number the same. The pieces are still quarters.
1 4 4 4 1 4 3 4
Check. Add:
Watch out. 1 whole is 4 quarters. It is not 1 quarter.
Key words. The numerator is the top number. The denominator is the bottom number.
Method. Write 1 whole as 9/9. Then find how many more pieces are needed.
- Write 1 whole as a fraction. 1 whole is 9 pieces of size
1 9 1 =9 9 - Find how many more pieces we need. We have 4 pieces and we want 9 pieces.9 − 4 = 5
- Keep the bottom number the same. The pieces are still ninths.
4 9 9 9 4 9 5 9
Check. Add:
Watch out. 1 whole is 9 ninths. It is not 1 ninth.
Key words. The numerator is the top number. The denominator is the bottom number.
Method. Write 1 whole as 10/10. Then find how many more pieces are needed.
- Write 1 whole as a fraction. 1 whole is 10 pieces of size
1 10 1 =10 10 - Find how many more pieces we need. We have 7 pieces and we want 10 pieces.10 − 7 = 3
- Keep the bottom number the same. The pieces are still tenths.
7 10 10 10 7 10 3 10
Check. Add:
Watch out. 1 whole is 10 tenths. It is not 1 tenth.
Key words. The numerator is the top number. The denominator is the bottom number.
Method. Write 1 whole as 12/12. Then find how many more pieces are needed.
- Write 1 whole as a fraction. 1 whole is 12 pieces of size
1 12 1 =12 12 - Find how many more pieces we need. We have 5 pieces and we want 12 pieces.12 − 5 = 7
- Keep the bottom number the same. The pieces are still twelfths.
5 12 12 12 5 12 7 12
Check. Add:
Watch out. 1 whole is 12 twelfths. It is not 1 twelfth.
Key words. The numerator is the top number. The denominator is the bottom number.
Method. Write 1 whole as 5/5. Then subtract.
- Write 1 whole as a fraction. 1 whole is 5 pieces of size
1 5 1 =5 5 - Subtract the top numbers. We take away 2 pieces from 5 pieces.5 − 2 = 3
- Keep the bottom number the same. The pieces are still fifths.1 −
2 5 5 5 2 5 3 5
Check. Add:
Watch out. 1 whole is 5 fifths. It is not 1 fifth.
Key words. The numerator is the top number. The denominator is the bottom number.
Method. Write 1 whole as 3/3. Then subtract.
- Write 1 whole as a fraction. 1 whole is 3 pieces of size
1 3 1 =3 3 - Subtract the top numbers. We take away 1 piece from 3 pieces.3 − 1 = 2
- Keep the bottom number the same. The pieces are still thirds.1 −
1 3 3 3 1 3 2 3
Check. Add:
Watch out. 1 whole is 3 thirds. It is not 1 third.
Key words. The numerator is the top number. The denominator is the bottom number.
Method. Write 1 whole as 8/8. Then subtract.
- Write 1 whole as a fraction. 1 whole is 8 pieces of size
1 8 1 =8 8 - Subtract the top numbers. We take away 5 pieces from 8 pieces.8 − 5 = 3
- Keep the bottom number the same. The pieces are still eighths.1 −
5 8 8 8 5 8 3 8
Check. Add:
Watch out. 1 whole is 8 eighths. It is not 1 eighth.
Key words. The numerator is the top number. The denominator is the bottom number.
Method. Write 1 whole as 10/10. Then subtract.
- Write 1 whole as a fraction. 1 whole is 10 pieces of size
1 10 1 =10 10 - Subtract the top numbers. We take away 3 pieces from 10 pieces.10 − 3 = 7
- Keep the bottom number the same. The pieces are still tenths.1 −
3 10 10 10 3 10 7 10
Check. Add:
Watch out. 1 whole is 10 tenths. It is not 1 tenth.
Key words. The numerator is the top number. The denominator is the bottom number.
Method. Write 1 whole as 6/6. Then subtract.
- Write 1 whole as a fraction. 1 whole is 6 pieces of size
1 6 1 =6 6 - Subtract the top numbers. We take away 1 piece from 6 pieces.6 − 1 = 5
- Keep the bottom number the same. The pieces are still sixths.1 −
1 6 6 6 1 6 5 6
Check. Add:
Watch out. 1 whole is 6 sixths. It is not 1 sixth.
Key words. The numerator is the top number. The denominator is the bottom number.
Method. The bottom numbers are all the same, so we only need to work out the missing top number.
- Look at the bottom numbers. All are 9, so the pieces are the same size. The missing number is a top number.
? 9 4 9 7 9 - Use the opposite (inverse) operation. 7 is the total. If we take away 4 from the total, we get the missing top number.7 − 4 = 3
- Write the missing number. The missing number is 3.
Check. 3 + 4 = 7. ✓
Watch out. The missing number goes on top. The bottom number stays the same.
Key words. The numerator is the top number. The denominator is the bottom number.
Method. The bottom numbers are all the same, so we only need to work out the missing top number.
- Look at the bottom numbers. All are 10, so the pieces are the same size. The missing number is a top number.
3 10 ? 10 8 10 - Use the opposite (inverse) operation. 8 is the total. If we take away 3 from the total, we get the missing top number.8 − 3 = 5
- Write the missing number. The missing number is 5.
Check. 3 + 5 = 8. ✓
Watch out. The missing number goes on top. The bottom number stays the same.
Key words. The numerator is the top number. The denominator is the bottom number.
Method. The bottom numbers are all the same, so we only need to work out the missing top number.
- Look at the bottom numbers. All are 8, so the pieces are the same size. The missing number is a top number.
7 8 ? 8 2 8 - Think: how many pieces were taken away? We started with 7 pieces and had 2 left, so we took away 7 − 2.7 − 2 = 5
- Write the missing number. The missing number is 5.
Check. 7 − 5 = 2. ✓
Watch out. The missing number goes on top. The bottom number stays the same.
Key words. The numerator is the top number. The denominator is the bottom number.
Method. The bottom numbers are all the same, so we only need to work out the missing top number.
- Look at the bottom numbers. All are 12, so the pieces are the same size. The missing number is a top number.
? 12 5 12 4 12 - Use the opposite (inverse) operation. We took away 5 pieces and had 4 left. So we started with 4 + 5 pieces.4 + 5 = 9
- Write the missing number. The missing number is 9.
Check. 9 − 5 = 4. ✓
Watch out. The missing number goes on top. The bottom number stays the same.
Key words. The numerator is the top number. The denominator is the bottom number.
Method. The bottom numbers are all the same, so we only need to work out the missing top number.
- Look at the bottom numbers. All are 6, so the pieces are the same size. The missing number is a top number.
2 6 ? 6 5 6 - Use the opposite (inverse) operation. 5 is the total. If we take away 2 from the total, we get the missing top number.5 − 2 = 3
- Write the missing number. The missing number is 3.
Check. 2 + 3 = 5. ✓
Watch out. The missing number goes on top. The bottom number stays the same.
Key words. The numerator is the top number. The denominator is the bottom number.
Method. The bottom numbers are all the same, so we only need to work out the missing top number.
- Look at the bottom numbers. All are 10, so the pieces are the same size. The missing number is a top number.
9 10 ? 10 4 10 - Think: how many pieces were taken away? We started with 9 pieces and had 4 left, so we took away 9 − 4.9 − 4 = 5
- Write the missing number. The missing number is 5.
Check. 9 − 5 = 4. ✓
Watch out. The missing number goes on top. The bottom number stays the same.
Key words. The numerator is the top number. The denominator is the bottom number.
Method. Fractions with the same bottom number are made of equal pieces. Add the top numbers and keep the bottom number the same.
- Check the bottom numbers. They are all 9. That means every piece is the same size (ninths), so we can add them.
1 9 2 9 2 9 - Add the top numbers. The top numbers tell us how many pieces we have. We are counting pieces of the same size.1 + 2 + 2 = 5
- Keep the bottom number the same. The pieces are still ninths. Adding does not change the size of the pieces.
1 9 2 9 2 9 5 9
Check. Add the top numbers in a different order: 2 + 2 + 1 = 5. ✓
Watch out. Do not add the bottom numbers. The pieces stay ninths, so the bottom number stays 9.
Key words. The numerator is the top number. The denominator is the bottom number.
Method. Fractions with the same bottom number are made of equal pieces. Add the top numbers and keep the bottom number the same.
- Check the bottom numbers. They are all 10. That means every piece is the same size (tenths), so we can add them.
2 10 1 10 4 10 - Add the top numbers. The top numbers tell us how many pieces we have. We are counting pieces of the same size.2 + 1 + 4 = 7
- Keep the bottom number the same. The pieces are still tenths. Adding does not change the size of the pieces.
2 10 1 10 4 10 7 10
Check. Add the top numbers in a different order: 4 + 1 + 2 = 7. ✓
Watch out. Do not add the bottom numbers. The pieces stay tenths, so the bottom number stays 10.
Key words. The numerator is the top number. The denominator is the bottom number.
Method. Fractions with the same bottom number are made of equal pieces. Add the top numbers and keep the bottom number the same.
- Check the bottom numbers. They are all 5. That means every piece is the same size (fifths), so we can add them.
1 5 1 5 3 5 - Add the top numbers. The top numbers tell us how many pieces we have. We are counting pieces of the same size.1 + 1 + 3 = 5
- Keep the bottom number the same. The pieces are still fifths. Adding does not change the size of the pieces.
1 5 1 5 3 5 5 5 - Write it as a whole number. 5 fifths make 1 whole.
5 5
Check. Add the top numbers in a different order: 3 + 1 + 1 = 5. ✓
Watch out. Do not add the bottom numbers. The pieces stay fifths, so the bottom number stays 5.
Key words. The numerator is the top number. The denominator is the bottom number.
Method. Fractions with the same bottom number are made of equal pieces. Add the top numbers and keep the bottom number the same.
- Check the bottom numbers. They are all 12. That means every piece is the same size (twelfths), so we can add them.
5 12 2 12 - Add the top numbers. The top numbers tell us how many pieces we have. We are counting pieces of the same size.5 + 2 = 7
- Keep the bottom number the same. The pieces are still twelfths. Adding does not change the size of the pieces.
5 12 2 12 7 12
Check. Take away one of the fractions from the answer: 7 − 2 = 5. That is the top of the other fraction. ✓
Watch out. Do not add the bottom numbers. The pieces stay twelfths, so the bottom number stays 12.
Key words. The numerator is the top number. The denominator is the bottom number.
Method. Write 1 whole as 12/12. Then subtract.
- Write 1 whole as a fraction. 1 whole is 12 pieces of size
1 12 1 =12 12 - Subtract the top numbers. We take away 7 pieces from 12 pieces.12 − 7 = 5
- Keep the bottom number the same. The pieces are still twelfths.1 −
7 12 12 12 7 12 5 12
Check. Add:
Watch out. 1 whole is 12 twelfths. It is not 1 twelfth.
Key words. The numerator is the top number. The denominator is the bottom number.
Method. Fractions with the same bottom number are made of equal pieces. Add the top numbers and keep the bottom number the same.
- Check the bottom numbers. They are all 8. That means every piece is the same size (eighths), so we can add them.
3 8 2 8 - Add the top numbers. The top numbers tell us how many pieces we have. We are counting pieces of the same size.3 + 2 = 5
- Keep the bottom number the same. The pieces are still eighths. Adding does not change the size of the pieces.
3 8 2 8 5 8
Check. Take away one of the fractions from the answer: 5 − 2 = 3. That is the top of the other fraction. ✓
Watch out. Do not add the bottom numbers. The pieces stay eighths, so the bottom number stays 8.
Key words. The numerator is the top number. The denominator is the bottom number.
Method. Write 1 whole as 8/8. Then subtract.
- Write 1 whole as a fraction. 1 whole is 8 pieces of size
1 8 1 =8 8 - Subtract the top numbers. We take away 5 pieces from 8 pieces.8 − 5 = 3
- Keep the bottom number the same. The pieces are still eighths.1 −
5 8 8 8 5 8 3 8
Check. Add:
Watch out. 1 whole is 8 eighths. It is not 1 eighth.
Key words. The numerator is the top number. The denominator is the bottom number.
Method. The pieces are the same size, so take away the top numbers and keep the bottom number the same.
- Check the bottom numbers. They are both 10, so the pieces are the same size (tenths) and we can subtract.
9 10 2 10 - Subtract the top numbers. We start with 9 pieces and take away 2 pieces.9 − 2 = 7
- Keep the bottom number the same. The pieces are still tenths.
9 10 2 10 7 10
Check. Add back: 7 + 2 = 9, so
Watch out. Do not subtract the bottom numbers. The pieces are still tenths.
Key words. The numerator is the top number. The denominator is the bottom number.
Method. Add the top numbers and keep the bottom number the same. Ben added both.
- Look at what Ben did. Ben added the top numbers AND the bottom numbers.
2 5 1 5 3 10 - Find the mistake. The pieces are fifths. Adding does not change the size of the pieces, so the bottom number must stay 5. Adding the bottom numbers would make the pieces smaller!
- Do the sum correctly. Add the top numbers and keep the bottom number.2 + 1 = 3, so
2 5 1 5 3 5
Check.
Watch out. When you add pieces of the same size, the size of the piece does not change.
Key words. The numerator is the top number. The denominator is the bottom number.
Method. Add the top numbers in each pair. A pair makes 1 whole when the top numbers add up to the bottom number.
- Add each pair. Check whether the answer has the same top and bottom number.A:
3 8 5 8 8 8
B:2 6 3 6 5 6
C:7 10 3 10 10 10
D:4 9 4 9 8 9 - Choose the two pairs that make 1. A and C
Check. 3 + 5 = 8 and 7 + 3 = 10. The other pairs add up to 5 and 8, not 6 and 9. ✓
Watch out. The answer must have the same top and bottom number to be 1 whole.
Key words. The numerator is the top number. The denominator is the bottom number.
Method. Try some pairs of fractions with the same bottom number. Look for one that is less than 1 and one that is more than 1.
- Try a small pair. Add the top numbers.
1 5 2 5 3 5 - Try a bigger pair. Make the top numbers bigger.
3 5 4 5 7 5 - Decide. One example works and one does not.Sometimes
Check. The answer is less than 1 only when the top numbers add up to less than the bottom number. ✓
Watch out. “Sometimes” needs one example that works and one that does not.
Key words. The numerator is the top number. The denominator is the bottom number.
Method. The bottom numbers are the same, so the top numbers must add up to 7. Find all the pairs of whole numbers above 0 that add to 7.
- Think about the top numbers. The two top numbers must add to 7, because the bottom numbers are the same (ninths).? + ? = 7
- Write the pairs, starting from the smallest top number. We only list each pair once (1 + 6 is the same pair as 6 + 1).1 + 6 = 7, so
1 9 6 9 7 9
2 + 5 = 7, so2 9 5 9 7 9
3 + 4 = 7, so3 9 4 9 7 9 - Count the pairs. 1 and 6, 2 and 5, 3 and 4 (3 pairs)
Check. Each pair adds to 7. ✓
Watch out. List the pairs in order so you do not miss one.