How to Add and Subtract Mixed Numbers

Fractions can be proper, improper or mixed. A fraction is proper if the numerator is less than the denominator (1/2, 3/4). A fraction is improper if the numerator is greater than the denominator (7/5, 9/7). A mixed number consists of an integer followed by a proper fraction (4 1/2).

Instructions

1. Take an example problem: 4 1/2 + 3 1/3. Here we are adding two mixed numbers.

2. Add the integers from the first and second number: 4 + 3 = 7.

3. Find a common denominator for 1/2 + 1/3. To find the least common denominator, look at the multiples for each denominator. Multiples of 2 are 2, 4, 6, 8, 10 and 12 up to infinity. Multiples of 3 are 3, 6, 9, 12, 15, 18, 21 and 24 up to infinity. You will see that 6 is the lowest number that appears in both lists. So 6 is the lowest common denominator.

4. Convert the fractions to the new denominator; 1/2 = 3/6 because 1x3 = 3 and 2x3 = 6; 1/3 = 2/6 because 1x2 =2 and 3x2 = 6.

5. Add the new fractions; 3/6 + 2/6 = 5/6. So 7 + 5/6 = 7 5/6. This is the final answer.

6. Take another example: 4 2/3 + 3 3/4.

7. Add the integers from the first and second number: 4 + 3 = 7.

8. Find a common denominator for 2/3 + 3/4. To find the least common denominator, look at the multiples of each denominator. Multiples of 3 are 3, 6, 9, 12, 15, 18, 21 and 24 up to infinity. Multiples of 4 are 4, 8, 12, 16, 20 and 24 up to infinity. You will see that 12 is the lowest number that appears in both lists. So 12 is the lowest common denominator.

9. Convert the fractions to the new denominator; 2/3 = 8/12 because 2x4 = 8 and 3x4 = 12; 3/4 = 9/12 because 3x3 = 9 and 4 x 3 = 12.

10. Add the new fractions; 8/12 + 9/12 = 17/12.

11. Here you have the improper fraction 17/12. Convert 17/12 into a mixed number--17 divided by 12 is 1 with a remainder of 5. 17/12 = 1 5/12.

12. Add the sum of the integers to the new mixed number: 7 + 1 5/12 = 8 5/12. So 4 2/3 + 3 3/4 = 8 5/12. This is the final answer.

13. Take another example: 5 2/3 -- 3 1/4. Here you are subtracting mixed numbers.

14. Subtract the integers from the first and second number: 5 -3 = 2.

15. Find the common denominator of: 2/3 -- 1/4. To find the least common denominator, look at the multiples of each denominator. Multiples of 3 are 3, 6, 9, 12, 15, 18, 21 and 24 up to infinity. Multiples of 4 are 4, 8, 12, 16, 20 and 24 up to infinity. You will see that 12 is the lowest number that appears in both lists. So 12 is the lowest common denominator.

16. Convert the fractions to the new denominator; 2/3 = 8/12 because 2x4 = 8 and 3x4 = 12. 1/4 = 3/12 because 1x3 = 3 and 4x3 = 12.

17. Subtract the new fractions: 8/12 -- 3/12 = 5/12. So 5 2/3 -- 3 1/4 = 2 5/12. This is the final answer.

18. Take another example: 5 1/4 - 3 2/3. Here you are also subtracting mixed numbers. The difference is that here the fraction in the second number is greater than the fraction in the first.

19. In order to be able to subtract the fraction, you have to borrow 1 from the 5, so 5 1/4 = 4 + 1 + 1/4 = 4 + 4/4 + 1/4 = 4 5/4.

20. Replace 5 1/4 with 4 /54. Now the equation reads as 4 5/4 -- 3 2/3.

21. Subtract the integer from the second number from the integer in the first: 4 -- 3 = 1.

22. Find the common denominator for 5/4 -- 2/3. To find the common denominator, look at the multiples of each denominator. Multiples of 4 are 4, 8, 12, 16, 20 and 24 up to infinity. Multiples of 3 are 3, 6, 9, 12, 15, 18, 21 and 24 up to infinity. You will see that 12 is the lowest number that appears in both lists. So 12 is the lowest common denominator.

23. Convert the fractions to the new denominator. 5/4 = 15/12 because 5x3 = 15 and 4x3 = 12. 2/3 = 8/12 because 2x4 = 8 and 3x4 = 12.

24. Subtract the new fractions: 15/12 - 8/12 = 7/12. So 5 1/4 - 3 2/3 = 1 7/12. This is the final answer.

Resources

• Math.com: Adding and Subtracting Mixed Numbers