Grade 6 Fractions: Subtracting Mixed Numbers

Worked examples

Real problems from the practice worksheets, solved one step at a time.

1. Example 1

   8 3/4 − 7 7/12 = ?

   1. The fraction parts have different denominators, so rename them with a common denominator, 12: 3/4 = 9/12 and 7/12 = 7/12. Now it is 8 9/12 − 7 7/12.
   2. Subtract the fraction parts: 9/12 − 7/12 = 2/12.
   3. Subtract the whole numbers: 8 − 7 = 1.
   4. Put them together: 1 2/12.
   5. The greatest number that divides both 2 and 12 is 2.
   6. Divide the top and bottom by 2: 2 ÷ 2 = 1 and 12 ÷ 2 = 6, so 2/12 = 1/6.
   7. So 8 3/4 − 7 7/12 = 1 1/6.

   Answer: 1 1/6

2. Example 2

   9 5/8 − 6 1/2 = ?

   1. The fraction parts have different denominators, so rename them with a common denominator, 8: 5/8 = 5/8 and 1/2 = 4/8. Now it is 9 5/8 − 6 4/8.
   2. Subtract the fraction parts: 5/8 − 4/8 = 1/8.
   3. Subtract the whole numbers: 9 − 6 = 3.
   4. Put them together: 3 1/8.
   5. So 9 5/8 − 6 1/2 = 3 1/8.

   Answer: 3 1/8

3. Example 3

   9 5/6 − 8 1/12 = ?

   1. The fraction parts have different denominators, so rename them with a common denominator, 12: 5/6 = 10/12 and 1/12 = 1/12. Now it is 9 10/12 − 8 1/12.
   2. Subtract the fraction parts: 10/12 − 1/12 = 9/12.
   3. Subtract the whole numbers: 9 − 8 = 1.
   4. Put them together: 1 9/12.
   5. The greatest number that divides both 9 and 12 is 3.
   6. Divide the top and bottom by 3: 9 ÷ 3 = 3 and 12 ÷ 3 = 4, so 9/12 = 3/4.
   7. So 9 5/6 − 8 1/12 = 1 3/4.

   Answer: 1 3/4