EXAMPLE (^10) Horse Racing In order
to become the Triple Crown Champion, a
thoroughbred horse must win three races: the
Kentucky Derby ( miles long), the Preakness
Stakes ( miles long), and the Belmont
Stakes ( miles long). What is the combined
length of the three races of the Triple Crown?
Analyze
- The Kentucky Derby is miles long.
- The Preakness Stakes is miles long.
- The Belmont Stakes is miles long.
- What is the combined length of the
three races?
(^1 12)
1 163
(^1 14)
(^1 12)
1 163
(^1 14)
3.6 Adding and Subtracting Mixed Numbers 277
Success Tip We can use rounding to check the results when subtracting
mixed numbers. To check the answer from Example 8, we proceed as
follows:
Since is less than , round down to 34.
Since is greater than , round up to 12.
Since 22 is close to 22, it is a reasonable answer.
11
24
(^2312 1123)
81 21 34 81
34
1
8
11
2
3
34 12 22
(^22 1124)
EXAMPLE 9
Subtract:
StrategyWe will write the numbers in vertical form and borrow 1 in the form
of from 419.
WHY In the fraction column, we need to have a fraction from which to subtract
Solution
Write the mixed number in vertical form.
Borrow 1 (in the form of ) from 419.
Then subtract the fractions separately.
Subtract the whole numbers separately.
This also requires borrowing.
The difference is 365
5
16
.
4
3
111
816
16
53
11
16
365
5
16
419 418
16
16
53
11
16
53
11
16
365
5
16
16
1611
16.16
1621
419 53
11
16
Solve application problems by adding
and subtracting mixed numbers.4Self Check 9Subtract:Now TryProblem 452,300 129
31
32
Self Check 10
SALADSA three-bean salad
calls for one can of green beans
( ounces), one can of
garbanzo beans ( ounces),
and one can of kidney beans
( ounces). How many ounces
of beans are called for in the
recipe?
Now TryProblem 89(^15 78)
(^10 34)
(^14 12)
Affirmed,in 1978, was the last
of only 11 horses in history to
win the Triple Crown.
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