Adding and subtracting mixed numbers

Answer 1

Adding and subtracting mixed numbers is similar to adding and subtracting fractions.

Adding and subtracting mixed numbers with like denominators:

1) 5 3/7 + 6 2/7= 11 5/7

a) add the fractions: 3/7 + 2/7 = 5/7

b) add the whole numbers: 5 + 6 = 11

2) 12 3/8 - 2 1/8

a) subtract the fractions and simplify if it is possible: 3/8 - 1/8 = 2/8 = 1/4

b) subtract the whole numbers: 12 - 2 = 10

Adding and subtracting mixed numbers with unlike denominators:

1) 2 3/2 + 5 4/3 = 9 5/6

a) write the fractions as equivalent fractions with a common denominator:

3/2 = (3 x 3)/(2 x 3) = 9/6 and 4/3 = (4 x 2)/(3 x 2) = 8/6

b) add the fractions: 9/6 + 8/6 = 17/6

c) add the whole numbers: 2 + 5 = 7

d) simplify: 7 17/6 = 9 5/6 (since 2 x 6 = 12, and 17 - 12 = 5, then 7 + 2 = 9)

2) 7 1/5 - 5 2/3 = 1 8/15

a) Since 1/5 < 2/3, we borrow 1 (which represents 5/5) form the whole number 7, so we have 6 as a whole number and the fraction 1/5 become:1/5 + 5/5 = 6/5. Now we can subtract as:

6 6/5 - 5 2/3 = 1 8/15

b) write the fractions as equivalent fractions with a common denominator:

6/5 = (6 x 3)/(5 x 3) = 18/15 and 2/3 = (2 x 5)/(3 x 5) = 10/15

b) subtract the fractions: 18/15 - 10/15 = 8/15

c) subtract the whole numbers: 6 - 5 = 1