Year 5: Adding and subtracting fractions

Key words. To add or subtract fractions, the denominators (bottom numbers) must be the same. A common denominator is a bottom number that both denominators go into.

Method. Make sure the denominators are the same. Then add the numerators and keep the denominator.

1. Check the denominators. To add fractions, the parts must be the same size.
   Both denominators are 7, so we can add straight away.
2. Add the numerators. We are adding parts of the same size, so we add the top numbers. The bottom number stays the same.
   27 + 37 = 2 + 37 = 57
3. Write the answer. It is already in its simplest form.
   57

Check. Take away: 57 − 37 = 27. ✓

Watch out. Add the numerators only. The denominator does not get added: 1/4 + 1/4 is 2/4, not 2/8.

Key words. To add or subtract fractions, the denominators (bottom numbers) must be the same. A common denominator is a bottom number that both denominators go into.

Method. Make sure the denominators are the same. Then add the numerators and keep the denominator.

1. Check the denominators. To add fractions, the parts must be the same size.
   Both denominators are 9, so we can add straight away.
2. Add the numerators. We are adding parts of the same size, so we add the top numbers. The bottom number stays the same.
   19 + 49 = 1 + 49 = 59
3. Write the answer. It is already in its simplest form.
   59

Check. Take away: 59 − 49 = 19. ✓

Watch out. Add the numerators only. The denominator does not get added: 1/4 + 1/4 is 2/4, not 2/8.

Key words. To add or subtract fractions, the denominators (bottom numbers) must be the same. A common denominator is a bottom number that both denominators go into.

Method. Make sure the denominators are the same. Then add the numerators and keep the denominator.

1. Check the denominators. To add fractions, the parts must be the same size.
   Both denominators are 12, so we can add straight away.
2. Add the numerators. We are adding parts of the same size, so we add the top numbers. The bottom number stays the same.
   512 + 312 = 5 + 312 = 812
3. Simplify the fraction part. 8 and 12 can both be divided by 4.
   812 = 8 ÷ 412 ÷ 4 = 23
4. Write the answer.
   512 + 312 = 23

Check. Take away: 23 − 312 = 512. ✓

Watch out. Add the numerators only. The denominator does not get added: 1/4 + 1/4 is 2/4, not 2/8.

Key words. To add or subtract fractions, the denominators (bottom numbers) must be the same. A common denominator is a bottom number that both denominators go into.

Method. Make sure the denominators are the same. Then add the numerators and keep the denominator.

1. Check the denominators. To add fractions, the parts must be the same size.
   Both denominators are 10, so we can add straight away.
2. Add the numerators. We are adding parts of the same size, so we add the top numbers. The bottom number stays the same.
   310 + 410 = 3 + 410 = 710
3. Write the answer. It is already in its simplest form.
   710

Check. Take away: 710 − 410 = 310. ✓

Watch out. Add the numerators only. The denominator does not get added: 1/4 + 1/4 is 2/4, not 2/8.

Key words. To add or subtract fractions, the denominators (bottom numbers) must be the same. A common denominator is a bottom number that both denominators go into.

Method. Make sure the denominators are the same. Then subtract the numerators and keep the denominator.

1. Check the denominators. To subtract fractions, the parts must be the same size.
   Both denominators are 9, so we can subtract straight away.
2. Subtract the numerators. We are taking parts of the same size away, so subtract the top numbers. The bottom number stays the same.
   79 − 49 = 7 − 49 = 39
3. Simplify the fraction part. 3 and 9 can both be divided by 3.
   39 = 3 ÷ 39 ÷ 3 = 13
4. Write the answer.
   79 − 49 = 13

Check. Add back: 13 + 49 = 79. ✓

Watch out. Subtract the numerators only. The denominator stays the same.

Key words. To add or subtract fractions, the denominators (bottom numbers) must be the same. A common denominator is a bottom number that both denominators go into.

Method. Make sure the denominators are the same. Then subtract the numerators and keep the denominator.

1. Check the denominators. To subtract fractions, the parts must be the same size.
   Both denominators are 10, so we can subtract straight away.
2. Subtract the numerators. We are taking parts of the same size away, so subtract the top numbers. The bottom number stays the same.
   810 − 310 = 8 − 310 = 510
3. Simplify the fraction part. 5 and 10 can both be divided by 5.
   510 = 5 ÷ 510 ÷ 5 = 12
4. Write the answer.
   810 − 310 = 12

Check. Add back: 12 + 310 = 810. ✓

Watch out. Subtract the numerators only. The denominator stays the same.

Key words. To add or subtract fractions, the denominators (bottom numbers) must be the same. A common denominator is a bottom number that both denominators go into.

Method. Make sure the denominators are the same. Then subtract the numerators and keep the denominator.

1. Check the denominators. To subtract fractions, the parts must be the same size.
   Both denominators are 6, so we can subtract straight away.
2. Subtract the numerators. We are taking parts of the same size away, so subtract the top numbers. The bottom number stays the same.
   56 − 16 = 5 − 16 = 46
3. Simplify the fraction part. 4 and 6 can both be divided by 2.
   46 = 4 ÷ 26 ÷ 2 = 23
4. Write the answer.
   56 − 16 = 23

Check. Add back: 23 + 16 = 56. ✓

Watch out. Subtract the numerators only. The denominator stays the same.

Key words. To add or subtract fractions, the denominators (bottom numbers) must be the same. A common denominator is a bottom number that both denominators go into.

Method. Make sure the denominators are the same. Then subtract the numerators and keep the denominator.

1. Check the denominators. To subtract fractions, the parts must be the same size.
   Both denominators are 12, so we can subtract straight away.
2. Subtract the numerators. We are taking parts of the same size away, so subtract the top numbers. The bottom number stays the same.
   1112 − 712 = 11 − 712 = 412
3. Simplify the fraction part. 4 and 12 can both be divided by 4.
   412 = 4 ÷ 412 ÷ 4 = 13
4. Write the answer.
   1112 − 712 = 13

Check. Add back: 13 + 712 = 1112. ✓

Watch out. Subtract the numerators only. The denominator stays the same.

Key words. To add or subtract fractions, the denominators (bottom numbers) must be the same. A common denominator is a bottom number that both denominators go into.

Method. Make sure the denominators are the same. Then add the numerators and keep the denominator.

1. Check the denominators. To add fractions, the parts must be the same size.
   Both denominators are 4, so we can add straight away.
2. Add the numerators. We are adding parts of the same size, so we add the top numbers. The bottom number stays the same.
   34 + 34 = 3 + 34 = 64
3. The answer is 1 or more, so change it to a mixed number or a whole number. 64 means 6 ÷ 4.
   64 = 124
4. Simplify the fraction part. 2 and 4 can both be divided by 2.
   24 = 2 ÷ 24 ÷ 2 = 12
   So the answer is 112.
5. Write the answer.
   34 + 34 = 112

Check. Take away: 112 − 34 = 34. ✓

Watch out. Add the numerators only. The denominator does not get added: 1/4 + 1/4 is 2/4, not 2/8.

Key words. To add or subtract fractions, the denominators (bottom numbers) must be the same. A common denominator is a bottom number that both denominators go into.

Method. Make sure the denominators are the same. Then add the numerators and keep the denominator.

1. Check the denominators. To add fractions, the parts must be the same size.
   Both denominators are 5, so we can add straight away.
2. Add the numerators. We are adding parts of the same size, so we add the top numbers. The bottom number stays the same.
   45 + 35 = 4 + 35 = 75
3. The answer is 1 or more, so change it to a mixed number or a whole number. 75 means 7 ÷ 5.
   75 = 125
4. Write the answer.
   45 + 35 = 125

Check. Take away: 125 − 35 = 45. ✓

Watch out. Add the numerators only. The denominator does not get added: 1/4 + 1/4 is 2/4, not 2/8.

Key words. To add or subtract fractions, the denominators (bottom numbers) must be the same. A common denominator is a bottom number that both denominators go into.

Method. Make sure the denominators are the same. Then add the numerators and keep the denominator.

1. Check the denominators. To add fractions, the parts must be the same size.
   Both denominators are 8, so we can add straight away.
2. Add the numerators. We are adding parts of the same size, so we add the top numbers. The bottom number stays the same.
   58 + 78 = 5 + 78 = 128
3. The answer is 1 or more, so change it to a mixed number or a whole number. 128 means 12 ÷ 8.
   128 = 148
4. Simplify the fraction part. 4 and 8 can both be divided by 4.
   48 = 4 ÷ 48 ÷ 4 = 12
   So the answer is 112.
5. Write the answer.
   58 + 78 = 112

Check. Take away: 112 − 78 = 58. ✓

Watch out. Add the numerators only. The denominator does not get added: 1/4 + 1/4 is 2/4, not 2/8.

Key words. To add or subtract fractions, the denominators (bottom numbers) must be the same. A common denominator is a bottom number that both denominators go into.

Method. Make sure the denominators are the same. Then add the numerators and keep the denominator.

1. Check the denominators. To add fractions, the parts must be the same size.
   Both denominators are 10, so we can add straight away.
2. Add the numerators. We are adding parts of the same size, so we add the top numbers. The bottom number stays the same.
   710 + 910 = 7 + 910 = 1610
3. The answer is 1 or more, so change it to a mixed number or a whole number. 1610 means 16 ÷ 10.
   1610 = 1610
4. Simplify the fraction part. 6 and 10 can both be divided by 2.
   610 = 6 ÷ 210 ÷ 2 = 35
   So the answer is 135.
5. Write the answer.
   710 + 910 = 135

Check. Take away: 135 − 910 = 710. ✓

Watch out. Add the numerators only. The denominator does not get added: 1/4 + 1/4 is 2/4, not 2/8.

Key words. To add or subtract fractions, the denominators (bottom numbers) must be the same. A common denominator is a bottom number that both denominators go into.

Method. Make sure the denominators are the same. Then add the numerators and keep the denominator.

1. Check the denominators. To add fractions, the parts must be the same size.
   Both denominators are 8, so we can add straight away.
2. Add the numerators. We are adding parts of the same size, so we add the top numbers. The bottom number stays the same.
   38 + 48 = 3 + 48 = 78
3. Write the answer. It is already in its simplest form.
   78

Check. Take away: 78 − 48 = 38. ✓

Watch out. Add the numerators only. The denominator does not get added: 1/4 + 1/4 is 2/4, not 2/8.

Key words. To add or subtract fractions, the denominators (bottom numbers) must be the same. A common denominator is a bottom number that both denominators go into.

Method. Make sure the denominators are the same. Then subtract the numerators and keep the denominator.

1. Check the denominators. To subtract fractions, the parts must be the same size.
   Both denominators are 10, so we can subtract straight away.
2. Subtract the numerators. We are taking parts of the same size away, so subtract the top numbers. The bottom number stays the same.
   710 − 310 = 7 − 310 = 410
3. Simplify the fraction part. 4 and 10 can both be divided by 2.
   410 = 4 ÷ 210 ÷ 2 = 25
4. Write the answer.
   710 − 310 = 25

Check. Add back: 25 + 310 = 710. ✓

Watch out. Subtract the numerators only. The denominator stays the same.

Key words. To add or subtract fractions, the denominators (bottom numbers) must be the same. A common denominator is a bottom number that both denominators go into.

Method. Make sure the denominators are the same. Then add the numerators and keep the denominator.

1. 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
2. Change the fractions to the common denominator. Multiply the top and the bottom by the same number, so each fraction keeps its value.
   12 = 1 × 22 × 2 = 24
3. Add the numerators. We are adding parts of the same size, so we add the top numbers. The bottom number stays the same.
   24 + 14 = 2 + 14 = 34
4. Write the answer.
   12 + 14 = 34

Check. Take away: 34 − 14 = 12. ✓

Watch out. Add the numerators only. The denominator does not get added: 1/4 + 1/4 is 2/4, not 2/8.

Key words. To add or subtract fractions, the denominators (bottom numbers) must be the same. A common denominator is a bottom number that both denominators go into.

Method. Make sure the denominators are the same. Then add the numerators and keep the denominator.

1. 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
2. Change the fractions to the common denominator. Multiply the top and the bottom by the same number, so each fraction keeps its value.
   13 = 1 × 23 × 2 = 26
3. Add the numerators. We are adding parts of the same size, so we add the top numbers. The bottom number stays the same.
   26 + 16 = 2 + 16 = 36
4. Simplify the fraction part. 3 and 6 can both be divided by 3.
   36 = 3 ÷ 36 ÷ 3 = 12
5. Write the answer.
   13 + 16 = 12

Check. Take away: 12 − 16 = 13. ✓

Watch out. Add the numerators only. The denominator does not get added: 1/4 + 1/4 is 2/4, not 2/8.

Key words. To add or subtract fractions, the denominators (bottom numbers) must be the same. A common denominator is a bottom number that both denominators go into.

Method. Make sure the denominators are the same. Then add the numerators and keep the denominator.

1. 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
2. Change the fractions to the common denominator. Multiply the top and the bottom by the same number, so each fraction keeps its value.
   15 = 1 × 25 × 2 = 210
3. Add the numerators. We are adding parts of the same size, so we add the top numbers. The bottom number stays the same.
   310 + 210 = 3 + 210 = 510
4. Simplify the fraction part. 5 and 10 can both be divided by 5.
   510 = 5 ÷ 510 ÷ 5 = 12
5. Write the answer.
   310 + 15 = 12

Check. Take away: 12 − 15 = 310. ✓

Watch out. Add the numerators only. The denominator does not get added: 1/4 + 1/4 is 2/4, not 2/8.

Key words. To add or subtract fractions, the denominators (bottom numbers) must be the same. A common denominator is a bottom number that both denominators go into.

Method. Make sure the denominators are the same. Then add the numerators and keep the denominator.

1. 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
2. Change the fractions to the common denominator. Multiply the top and the bottom by the same number, so each fraction keeps its value.
   13 = 1 × 43 × 4 = 412
3. Add the numerators. We are adding parts of the same size, so we add the top numbers. The bottom number stays the same.
   512 + 412 = 5 + 412 = 912
4. Simplify the fraction part. 9 and 12 can both be divided by 3.
   912 = 9 ÷ 312 ÷ 3 = 34
5. Write the answer.
   512 + 13 = 34

Check. Take away: 34 − 13 = 512. ✓

Watch out. Add the numerators only. The denominator does not get added: 1/4 + 1/4 is 2/4, not 2/8.

Key words. To add or subtract fractions, the denominators (bottom numbers) must be the same. A common denominator is a bottom number that both denominators go into.

Method. Make sure the denominators are the same. Then subtract the numerators and keep the denominator.

1. 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
2. Change the fractions to the common denominator. Multiply the top and the bottom by the same number, so each fraction keeps its value.
   34 = 3 × 24 × 2 = 68
3. Subtract the numerators. We are taking parts of the same size away, so subtract the top numbers. The bottom number stays the same.
   68 − 18 = 6 − 18 = 58
4. Write the answer.
   34 − 18 = 58

Check. Add back: 58 + 18 = 34. ✓

Watch out. Subtract the numerators only. The denominator stays the same.

Key words. To add or subtract fractions, the denominators (bottom numbers) must be the same. A common denominator is a bottom number that both denominators go into.

Method. Make sure the denominators are the same. Then subtract the numerators and keep the denominator.

1. 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
2. Change the fractions to the common denominator. Multiply the top and the bottom by the same number, so each fraction keeps its value.
   13 = 1 × 23 × 2 = 26
3. Subtract the numerators. We are taking parts of the same size away, so subtract the top numbers. The bottom number stays the same.
   56 − 26 = 5 − 26 = 36
4. Simplify the fraction part. 3 and 6 can both be divided by 3.
   36 = 3 ÷ 36 ÷ 3 = 12
5. Write the answer.
   56 − 13 = 12

Check. Add back: 12 + 13 = 56. ✓

Watch out. Subtract the numerators only. The denominator stays the same.

Key words. To add or subtract fractions, the denominators (bottom numbers) must be the same. A common denominator is a bottom number that both denominators go into.

Method. Make sure the denominators are the same. Then subtract the numerators and keep the denominator.

1. 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
2. Change the fractions to the common denominator. Multiply the top and the bottom by the same number, so each fraction keeps its value.
   25 = 2 × 25 × 2 = 410
3. Subtract the numerators. We are taking parts of the same size away, so subtract the top numbers. The bottom number stays the same.
   710 − 410 = 7 − 410 = 310
4. Write the answer.
   710 − 25 = 310

Check. Add back: 310 + 25 = 710. ✓

Watch out. Subtract the numerators only. The denominator stays the same.

Key words. To add or subtract fractions, the denominators (bottom numbers) must be the same. A common denominator is a bottom number that both denominators go into.

Method. Make sure the denominators are the same. Then subtract the numerators and keep the denominator.

1. 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
2. Change the fractions to the common denominator. Multiply the top and the bottom by the same number, so each fraction keeps its value.
   35 = 3 × 25 × 2 = 610
3. Subtract the numerators. We are taking parts of the same size away, so subtract the top numbers. The bottom number stays the same.
   610 − 110 = 6 − 110 = 510
4. Simplify the fraction part. 5 and 10 can both be divided by 5.
   510 = 5 ÷ 510 ÷ 5 = 12
5. Write the answer.
   35 − 110 = 12

Check. Add back: 12 + 110 = 35. ✓

Watch out. Subtract the numerators only. The denominator stays the same.

Key words. To add or subtract fractions, the denominators (bottom numbers) must be the same. A common denominator is a bottom number that both denominators go into. Key words. An improper fraction has a top number that is bigger than (or equal to) the bottom number, like 74. A mixed number is a whole number and a fraction together, like 134.

Method. Make the denominators the same, then subtract. If the fraction you are taking away is bigger, change both numbers to improper fractions first.

1. The first fraction part (0) is smaller than the second (1), so we cannot take them away. Change both numbers to improper fractions. Each whole is worth 4 quarters, so the numbers become fractions over 4.
   104 = 1 × 4 + 04 = 44
   14 = 0 × 4 + 14 = 14
2. Subtract the numerators. Now both numbers are fractions with the same denominator.
   44 − 14 = 4 − 14 = 34
3. Write the answer. It is already in its simplest form.
   34

Check. Add back: 34 + 14 = 1. ✓

Watch out. Never take the smaller number from the bigger one in each column (3⅕ − 1⅗ is not 2⅖). Change to improper fractions when you need to.

Key words. To add or subtract fractions, the denominators (bottom numbers) must be the same. A common denominator is a bottom number that both denominators go into. Key words. An improper fraction has a top number that is bigger than (or equal to) the bottom number, like 74. A mixed number is a whole number and a fraction together, like 134.

Method. Make the denominators the same, then subtract. If the fraction you are taking away is bigger, change both numbers to improper fractions first.

1. The first fraction part (0) is smaller than the second (3), so we cannot take them away. Change both numbers to improper fractions. Each whole is worth 5 fifths, so the numbers become fractions over 5.
   105 = 1 × 5 + 05 = 55
   35 = 0 × 5 + 35 = 35
2. Subtract the numerators. Now both numbers are fractions with the same denominator.
   55 − 35 = 5 − 35 = 25
3. Write the answer. It is already in its simplest form.
   25

Check. Add back: 25 + 35 = 1. ✓

Watch out. Never take the smaller number from the bigger one in each column (3⅕ − 1⅗ is not 2⅖). Change to improper fractions when you need to.

Key words. To add or subtract fractions, the denominators (bottom numbers) must be the same. A common denominator is a bottom number that both denominators go into. Key words. An improper fraction has a top number that is bigger than (or equal to) the bottom number, like 74. A mixed number is a whole number and a fraction together, like 134.

Method. Make the denominators the same, then subtract. If the fraction you are taking away is bigger, change both numbers to improper fractions first.

1. The first fraction part (0) is smaller than the second (7), so we cannot take them away. Change both numbers to improper fractions. Each whole is worth 12 twelfths, so the numbers become fractions over 12.
   1012 = 1 × 12 + 012 = 1212
   712 = 0 × 12 + 712 = 712
2. Subtract the numerators. Now both numbers are fractions with the same denominator.
   1212 − 712 = 12 − 712 = 512
3. Write the answer. It is already in its simplest form.
   512

Check. Add back: 512 + 712 = 1. ✓

Watch out. Never take the smaller number from the bigger one in each column (3⅕ − 1⅗ is not 2⅖). Change to improper fractions when you need to.

Key words. To add or subtract fractions, the denominators (bottom numbers) must be the same. A common denominator is a bottom number that both denominators go into. Key words. An improper fraction has a top number that is bigger than (or equal to) the bottom number, like 74. A mixed number is a whole number and a fraction together, like 134.

Method. Make the denominators the same, then subtract. If the fraction you are taking away is bigger, change both numbers to improper fractions first.

1. The first fraction part (0) is smaller than the second (3), so we cannot take them away. Change both numbers to improper fractions. Each whole is worth 4 quarters, so the numbers become fractions over 4.
   204 = 2 × 4 + 04 = 84
   34 = 0 × 4 + 34 = 34
2. Subtract the numerators. Now both numbers are fractions with the same denominator.
   84 − 34 = 8 − 34 = 54
3. The answer is 1 or more, so change it to a mixed number or a whole number. 54 means 5 ÷ 4.
   54 = 114
4. Write the answer.
   2 − 34 = 114

Check. Add back: 114 + 34 = 2. ✓

Watch out. Never take the smaller number from the bigger one in each column (3⅕ − 1⅗ is not 2⅖). Change to improper fractions when you need to.

Key words. To add or subtract fractions, the denominators (bottom numbers) must be the same. A common denominator is a bottom number that both denominators go into.

Method. Use the inverse (opposite) operation to find the missing number.

1. Choose the operation. We know 25 + ? = 45. The missing number is what is left when we take 25 from 45.
   45 − 25 = 25
2. Check the denominators. To subtract fractions, the parts must be the same size.
   Both denominators are 5, so we can subtract straight away.
3. Subtract the numerators. We are taking parts of the same size away, so subtract the top numbers. The bottom number stays the same.
   45 − 25 = 4 − 25 = 25
4. Write the answer. It is already in its simplest form.
   25

Check. Put it back in: 25 + 25 = 45. ✓

Watch out. The missing number is not always the first or second number. Use the opposite operation.

Key words. To add or subtract fractions, the denominators (bottom numbers) must be the same. A common denominator is a bottom number that both denominators go into.

Method. Use the inverse (opposite) operation to find the missing number.

1. Choose the operation. We know 14 + ? = 58. The missing number is what is left when we take 14 from 58.
   58 − 14 = 38
2. 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
3. Change the fractions to the common denominator. Multiply the top and the bottom by the same number, so each fraction keeps its value.
   14 = 1 × 24 × 2 = 28
4. Subtract the numerators. We are taking parts of the same size away, so subtract the top numbers. The bottom number stays the same.
   58 − 28 = 5 − 28 = 38
5. Write the answer.
   58 − 14 = 38

Check. Put it back in: 14 + 38 = 58. ✓

Watch out. The missing number is not always the first or second number. Use the opposite operation.

Key words. To add or subtract fractions, the denominators (bottom numbers) must be the same. A common denominator is a bottom number that both denominators go into.

Method. Use the inverse (opposite) operation to find the missing number.

1. Choose the operation. We know ? − 14 = 12. To undo the subtraction, add 14 to 12.
   12 + 14 = 34
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
3. Change the fractions to the common denominator. Multiply the top and the bottom by the same number, so each fraction keeps its value.
   12 = 1 × 22 × 2 = 24
4. Add the numerators. We are adding parts of the same size, so we add the top numbers. The bottom number stays the same.
   24 + 14 = 2 + 14 = 34
5. Write the answer.
   12 + 14 = 34

Check. Put it back in: 34 − 14 = 12. ✓

Watch out. The missing number is not always the first or second number. Use the opposite operation.

Key words. To add or subtract fractions, the denominators (bottom numbers) must be the same. A common denominator is a bottom number that both denominators go into.

Method. Use the inverse (opposite) operation to find the missing number.

1. Choose the operation. We know 78 − ? = 38. The missing number is the difference between 78 and 38.
   78 − 38 = 12
2. Check the denominators. To subtract fractions, the parts must be the same size.
   Both denominators are 8, so we can subtract straight away.
3. Subtract the numerators. We are taking parts of the same size away, so subtract the top numbers. The bottom number stays the same.
   78 − 38 = 7 − 38 = 48
4. Simplify the fraction part. 4 and 8 can both be divided by 4.
   48 = 4 ÷ 48 ÷ 4 = 12
5. Write the answer.
   78 − 38 = 12

Check. Put it back in: 78 − 12 = 38. ✓

Watch out. The missing number is not always the first or second number. Use the opposite operation.

Key words. To add or subtract fractions, the denominators (bottom numbers) must be the same. A common denominator is a bottom number that both denominators go into.

Method. Use the inverse (opposite) operation to find the missing number.

1. Choose the operation. We know 1 − ? = 27. The missing number is the difference between 1 and 27.
   1 − 27 = 57
2. The first fraction part (0) is smaller than the second (2), so we cannot take them away. Change both numbers to improper fractions. Each whole is worth 7 sevenths, so the numbers become fractions over 7.
   107 = 1 × 7 + 07 = 77
   27 = 0 × 7 + 27 = 27
3. Subtract the numerators. Now both numbers are fractions with the same denominator.
   77 − 27 = 7 − 27 = 57
4. Write the answer. It is already in its simplest form.
   57

Check. Put it back in: 1 − 57 = 27. ✓

Watch out. The missing number is not always the first or second number. Use the opposite operation.

Key words. To add or subtract fractions, the denominators (bottom numbers) must be the same. A common denominator is a bottom number that both denominators go into.

Method. Make sure the denominators are the same. Then add the numerators and keep the denominator.

1. 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
2. Change the fractions to the common denominator. Multiply the top and the bottom by the same number, so each fraction keeps its value.
   14 = 1 × 24 × 2 = 28
3. Add the numerators. We are adding parts of the same size, so we add the top numbers. The bottom number stays the same.
   28 + 38 = 2 + 38 = 58
4. Write the answer.
   14 + 38 = 58

Check. Take away: 58 − 38 = 14. ✓

Watch out. Add the numerators only. The denominator does not get added: 1/4 + 1/4 is 2/4, not 2/8.

Key words. To add or subtract fractions, the denominators (bottom numbers) must be the same. A common denominator is a bottom number that both denominators go into. Key words. An improper fraction has a top number that is bigger than (or equal to) the bottom number, like 74. A mixed number is a whole number and a fraction together, like 134.

Method. Make the denominators the same, then subtract. If the fraction you are taking away is bigger, change both numbers to improper fractions first.

1. The first fraction part (0) is smaller than the second (5), so we cannot take them away. Change both numbers to improper fractions. Each whole is worth 8 eighths, so the numbers become fractions over 8.
   108 = 1 × 8 + 08 = 88
   58 = 0 × 8 + 58 = 58
2. Subtract the numerators. Now both numbers are fractions with the same denominator.
   88 − 58 = 8 − 58 = 38
3. Write the answer. It is already in its simplest form.
   38

Check. Add back: 38 + 58 = 1. ✓

Watch out. Never take the smaller number from the bigger one in each column (3⅕ − 1⅗ is not 2⅖). Change to improper fractions when you need to.

Key words. To add or subtract fractions, the denominators (bottom numbers) must be the same. A common denominator is a bottom number that both denominators go into.

Method. Make sure the denominators are the same. Then add the numerators and keep the denominator.

1. 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
2. Change the fractions to the common denominator. Multiply the top and the bottom by the same number, so each fraction keeps its value.
   34 = 3 × 24 × 2 = 68
3. Add the numerators. We are adding parts of the same size, so we add the top numbers. The bottom number stays the same.
   68 + 58 = 6 + 58 = 118
4. The answer is 1 or more, so change it to a mixed number or a whole number. 118 means 11 ÷ 8.
   118 = 138
5. Write the answer.
   34 + 58 = 138

Check. Take away: 138 − 58 = 34. ✓

Watch out. Add the numerators only. The denominator does not get added: 1/4 + 1/4 is 2/4, not 2/8.

Key words. To add or subtract fractions, the denominators (bottom numbers) must be the same. A common denominator is a bottom number that both denominators go into.

Method. Make sure the denominators are the same. Then add the numerators and keep the denominator.

1. 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
2. Change the fractions to the common denominator. Multiply the top and the bottom by the same number, so each fraction keeps its value.
   23 = 2 × 23 × 2 = 46
3. Add the numerators. We are adding parts of the same size, so we add the top numbers. The bottom number stays the same.
   46 + 16 = 4 + 16 = 56
4. Write the answer.
   23 + 16 = 56

Check. Take away: 56 − 16 = 23. ✓

Watch out. Add the numerators only. The denominator does not get added: 1/4 + 1/4 is 2/4, not 2/8.

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.

1. Try some examples. Testing numbers helps us see if the statement is true every time.
   14 + 14 = 12, which is less than 1.
2. Look for an example that does not work. One example that breaks the rule is a counter-example.
   34 + 34 = 112, which is more than 1.
3. Decide: always, sometimes or never? It depends on the two fractions. Small fractions add to less than 1 and big ones can add to more than 1.
   Sometimes

Check. We found one of each. ✓

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.

1. Try some examples. Testing numbers helps us see if the statement is true every time.
   1 − 14 = 34, less than 1
   1 − 35 = 25, less than 1
   1 − 910 = 110, less than 1
2. Decide: always, sometimes or never? You take away a part, so there is less than a whole left.
   Always

Check. All the answers are less than 1. ✓

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.