Caution! If we use method 1 to add the mixed numbers in Example 3, the
numbers we encounter are very large. As expected, the result is the same:Write and as improper fractions.The LCD is 63.Note how large the numerators are.Generally speaking, the larger the whole-number parts of the mixed numbers, the
more difficult it becomes to add those mixed numbers using method 1.
Add mixed numbers in vertical form.
We can add mixed numbers quickly when they are written in vertical form by working
in columns. The strategy is the same as in Example 2: Add whole numbers to whole
numbers and fractions to fractions.
2To write the improper fraction as a(^253) mixed number, divide 15,980 by 63.
41
63
Add the numerators and write the sum over the(^) common denominator 63.
15,980
63
10,611
63
5,369
63
1,179
7
9
9
767
9
7
7
(^168 168 3785 29)
3
7
85
2
9
1,179
7
767
9
253 4163.
3.6 Adding and Subtracting Mixed Numbers 273Self Check 3Add:Now TryProblem 21275
1
6
81
3
5
EXAMPLE 3
Add:StrategyWe will write each mixed number as the sum of a whole number and a
fraction. Then we will add the whole numbers and the fractions separately.
WHY If we change each mixed number to an improper fraction, build equivalent
fractions, and add, the resulting numerators will be very large and difficult to work with.
Solution
We will write the solution in horizontalform.
Add the whole numbers.
Prepare to add the fractions.
To build and so that their
denominators are 63, multipy
each by a form of 1. 253 Write the sum as a mixed number.41
63
271 14
41Add the numerators and write
the sum over the common
denominator 63.253
41
63
Multiply the numerators.
Multiply the denominators.253
27
63
14
63
2
93
253 ^37
79
9
2
9
7
7
1681 1 85
253253
3
7
2
9
Use the commutative property
of addition to change the order
of the addition so that the
whole numbers are together
and the fractions are together.168 85
3
7
2
9
Write each mixed number as the sum of(^168) a whole number and a fraction.