Subtraction of mixed numbers (like subtraction of whole numbers) sometimes
involves borrowing. When the fraction we are subtracting is greater than the fraction
we are subtracting it from, it is necessary to borrow.276 Chapter 3 Fractions and Mixed Numbers
SolutionThe LCD for and is 30.Write the mixed numbers in vertical form.
Build and so that their denominators are 30.
Subtract the fractions separately.
Subtract the whole numbers
separately.The difference is 7.1
6
16
21
30
9
16
30
7
5
30
16
21
30
9
16
30
5
30
16
7
10
3
3
9
8
15
2
2
16
7
10
9
8
15
8
157
108
15
7
10
Simplify:305 ^5.1
51 6 1
6EXAMPLE 8
Subtract:
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.
SolutionThe LCD for and is 24.
Write the mixed number in vertical form.
Build and so that their denominators are 24.Note that is greater than.
Since is greater than , borrow 1
(in the form of ) from 34 and add it to to get.
Subtract the fractions separately.
Subtract the whole numbers separately.The difference is 22.11
24
33
27
24
11
16
24
22
11
24
33
27
24
11
16
24
11
24
34
(^33)
24
24
24
11
16
24
27
243
2424
243
2416
243
2416
2434
3
24
11
16
24
34
1
8
3
3
11
2
3
8
8
34
1
8
11
2
3
2
31
8
2
3
1
8
34
1
8
11
2
3
Self Check 8Subtract:Now TryProblem 41