1. 6 Chapter Rational Numbers and Proportional Reasoning
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2. 6-2 Addition, Subtraction, and Estimation with Rational Numbers
Mixed Numbers
Properties of Addition for Rational Numbers
Subtraction of Rational Numbers
Estimation with Rational Numbers
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3. Addition of Rational Numbers
Area model
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4. Addition of Rational Numbers
Number-line model
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5. Addition of Rational Numbers with Like Denominators
If are rational numbers, then
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6. Addition of Rational Numbers with Unlike Denominators
If are rational numbers, then
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Example 6-4
Find each of the following sums: a. b.
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Example (continued) c. d.
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Example (continued) e.
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Mixed Numbers
Numbers that are made up of an integer and a fractional part of an integer.
A mixed number is a rational number, and therefore, it can always be written in the form
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Example 6-5
Change each of the following mixed numbers to the form where a and b are integers. a. b.
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Example 6-6
Change to a mixed number.
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13. Properties of Addition for Rational Numbers
Additive Inverse Property
For any rational number , there exists a unique rational number , called the additive inverse of , such that
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14. Properties of Addition for Rational Numbers
Properties of the additive inverse for rational numbers are analogous to those of the additive inverse for integers.
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15. Properties of Addition for Rational Numbers
Addition Property of Equality
If are any rational numbers such that , and if is any rational number, then
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16. Subtraction of Rational Numbers
If are any rational numbers, then is the unique rational number such that
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17. Subtraction of Rational Numbers
If are any rational numbers, then
If are any rational numbers, then
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Example 6-8
Find each difference. a. b.
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Example 6-9
Add or subtract. Write answers in simplest form. a.
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20. Example 6-9 (continued) b.
First, write each fraction in simplest form:
Now add the simplified fractions:
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Example (continued) c.
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22. Copyright © 2013, 2010, and 2007, Pearson Education, Inc.
Example (continued) d.
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23. Estimation with Rational Numbers
Many of the estimation and mental math techniques that are used with whole numbers also work with rational numbers.
Estimation plays an important role in judging the reasonableness of computations.
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Example 6-10
A sixth-grade class is collecting cans to take to the recycling center. Becky’s group brought the following amounts (in pounds). About how many pounds does her group have all together?
Use front-end estimation and then adjust by using 0,
and 1 as reference points.
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Example (continued)
The front-end estimate is = 9.
The adjustment is
The adjusted estimate is = 11.
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26. Copyright © 2013, 2010, and 2007, Pearson Education, Inc.
Example 6-11
Estimate each of the following. a. b.
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