When we add mixed numbers, sometimes the sum of the fractions is an improper
fraction.
3.6 Adding and Subtracting Mixed Numbers 275EXAMPLE 6
Add:StrategyWe will write the problem in vertical form. We will make sure that the
fractional part of the answer is in simplest form.
WHY When adding, subtracting, multiplying, or dividing fractions or mixed
numbers, the answer should always be written in simplest form.
Solution
The LCD for and is 15.
Write the mixed numbers in vertical form.
Build and so that their denominators are 15.
Add the fractions separately.
Add the whole numbers
separately.The fractional part of
the answer is greater
than 1.Since we don’t want an improper fraction in the answer, we write as a mixed
number. Then we carry1 from the fraction column to the whole-number column.
142 Carry the 1 and add it to 141 to get 142.7
15
To write the improper fraction as a141 (^1) mixed number divide 22 by 15.
7
15
1
15 22
15
7Write the mixed number as the sum(^141) of a whole number and a fraction.
22
15
141
22
15
22
1545
10
15
96
12
15
141
22
15
45
10
15
96
12
15
22
15
45
2
3
5
5
96
4
5
3
3
45
2
3
96
4
5
4
52
34
5
2
3
45
2
3
96
4
5
Self Check 6Add:Now TryProblem 3376
11
12
49
5
8
Subtract mixed numbers.
Subtracting mixed numbers is similar to adding mixed numbers.
3EXAMPLE 7
Subtract and simplify, if possible:StrategyWe will perform the subtraction in vertical formwith the fractions in a
column and the whole numbers lined up in columns. Then we will subtract the
fractional parts and the whole-number parts separately.
WHY It is often easier to subtract the fractional parts and the whole-number parts
of mixed numbers vertically.
16
7
10
9
8
15
Self Check 7
Subtract and simplify, if possible:Now TryProblem 37