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1. Add any two mixed numbers2. Add any group of mixed numbers3. Subtract any two mixed numbers4. Solve an application that involves mixed number
addition or subtraction
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Once you know how to add fractions, adding mixed numbers should be no problem if youkeep in mind that addition involves combining groups of the same kind of objects. Becausemixed numbers consist of two parts—a whole number and a fraction—we could work withthe whole numbers and the fractions separately. Generally, it is easier to rewrite mixednumbers as improper fractions, then do the addition.
This suggests the following general rule.
518
53�
512
56
The sum of the The sum of thefractional parts
�
partswhole-number
�
�
or 3
Step 1 Change the mixed numbers to improper fractions.Step 2 Add the fractions.Step 3 Rewrite the result as a mixed number if required.
Step by Step: To Add Mixed Numbers
NOTE Step 2 requires that thefractional parts have the samedenominator.
262 CHAPTER 3 ADDING AND SUBTRACTING FRACTIONS
Our first example illustrates the use of this rule.
The LCD of the fractions is 24. Renamethem with that denominator.
�19
6�
19
83
1
6� 2
3
8
C H E C K Y O U R S E L F 1
Add � Write the result as a mixed number.3
410
.2
310
When the fractional portions of the mixed numbers have different denominators, wemust rename these fractions as equivalent fractions with the least common denominator toperform the addition in step 2. Consider Example 2.
C H E C K Y O U R S E L F 2
Add � Write the result as a mixed number.3
56
.5
710
NOTE 5
12013
24B133
You follow the same procedure if more than two mixed numbers are involved in theproblem.
ADDING AND SUBTRACTING MIXED NUMBERS SECTION 3.4 263
Using Your Calculator to Addand Subtract Mixed Numbers
We have already seen how to add, multiply, and divide fractions using our calculators. Nowwe will use our calculators to add and subtract mixed numbers.
Scientific Calculator
To enter a mixed number on a scientific calculator, press the fraction key between both the
whole number and the numerator and denominator. For example, to enter , press
3 7 12a b/ca b/c
3
7
12
271
Example 1
Adding Mixed Numbers
Add.
The keystroke sequence is
3 7 12 2 11 16
The result is
Graphing Calculator
As with multiplying and dividing fractions, when using a graphing calculator, you must
choose the fraction option from the math menu before pressing .
For the problem in Example 1, the keystroke sequence is
Units AnalysisEvery denominate number with a fractional unit, such as
25
has a dual denominate number, which is the reciprocal number and thereciprocal units. In this case we have
The 25 indicates that we can drive 25 miles on 1 gallon. The
indicates that we use of a gallon for each mile.
Examples
Denominate Number Dual
55
minpage
32
pagemin
23
hmi
155
mih
125
125
galmi
migal
125
galmi
migal
Of all the skills you develop in the study of arithmetic, perhaps the most useful is that ofestimation. Every day, you have occasion to estimate. Here are a few estimation exercisesthat you may have gone through this morning.
How much flour should I put in the pancakes?
How much cash am I likely to need today?
How long will it take me to walk to the bus stop?
How long is the ride to school?
How many miles can I get on just over tank of gas?
Although you may not think of these as arithmetic problems, they are. As your estima-tion skills improve, so will your ability to come up with good answers to everydayproblems.
1
4
274 CHAPTER 3 ADDING AND SUBTRACTING FRACTIONS
Estimating Measurements
Based on the gauge, is the gas tank closer to or full?
At slightly more than , the gauge indicates close to of a tank remains.2
A recipe calls for cup of flour, but you have only a 1 cup, a cup, and a cup
measure. How should you proceed?
13
23
34
Almost every shopping trip presents many estimation opportunities. Whether you are esti-mating the impact of car payments on your monthly budget, or estimating the number ofbananas you can buy for $3, you are practicing your arithmetic skills. Example 3 providesan opportunity to practice these skills.
Estimating Total Cost
Dog food is on special at three cans for a dollar. Your puppy eats about can per day. How
much should you budget for dog food over the next semester (almost 5 months)?
First, estimate the number of days in the semester. At 30 days per month, we’ll use
30 � 5 months � 150 days
Next, estimate the amount of food to be consumed. We could try using can per day, whichyields
� 150 days � 75 cans
but remember that this is a puppy, so we will assume his food intake will increase over thenext 5 months. To be safe, we will add 25 cans and estimate the total to be 100 cans.
Finally, we can estimate the total cost. If we buy all of the food today, we can buy it at
9. Mark wants to make $300 by selling cupcakes at a bake sale, and his mother hasoffered to pay for the ingredients. He plans to sell them for $5 per dozen. A boxof cake mix makes about 50 cupcakes. Approximately how many boxes shouldMark buy?
10. Amy is traveling to a city 418 miles away at a speed of roughly 55 miles per hour.About how long should her trip take?
11. The map tells Manuel that it is 423 miles from Eastwick to West Goshen. He knowsthat, with mixed city and freeway driving, he can average about 50 miles per hour. Heis currently in Eastwick and needs to be in West Goshen by noon. Make a roughestimate of the time that Manuel should leave Eastwick.
12. Sam works in a shipping department for a manufacturer. He is filling a customer’sorder for several small items. The items ordered weigh 21 ounces, 23 ounces,18 ounces, and 7 ounces. The company policy is to use a stronger box to shipproducts totaling more than 3 pounds. Knowing 16 ounces is 1 pound, estimatewhether Sam should use the stronger box.
13. Lauren is a contractor for a roofing job. She estimates that she will need about 4800roofing nails. According to a handbook, the roofing nails that are needed count out atabout 189 nails per pound. Estimate how many pounds Lauren will need for the job.
14. Julio works as a quality control expert in a beverage factory. The assembly line thathe monitors produces about 20,000 bottles in a 24-hour period. Julio samples about
120 bottles an hour and rejects the line if he finds more than of the sample to be
defective. About how many defective bottles should Julio allow before rejecting the entire line?
15. Based on the amount of liquid in the pitcher, is the pitcher closer to or full?
16. Lunch meat sells for about $3 per pound. You use about pound per day for
sandwiches. How much should you budget for lunch meat over the next month (about20 work days)?