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Simplify Expressions with Square Roots

In the following exercises, simplify.

Identify Integers, Rational Numbers, Irrational Numbers, and Real Numbers

In the following exercises, write as the ratio of two integers.

5 3.19

5 1 319 100

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12 9.279

−12 1 9297 1000

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In the following exercises, list the rational numbers, irrational numbers

0.75 , 0.22 3 , 1.39174

0.75 , 0.22 3 1.39174

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0.36 , 0.94729 , 2.52 8

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0.4 5 , 1.919293 , 3.59

0.4 5 , 3.59 1.919293

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0.1 3 , 0.42982 , 1.875

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In the following exercises, identify whether each number is rational or irrational.

25 30

rational irrational

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164 169

irrational rational

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In the following exercises, identify whether each number is a real number or not a real number.

81 −121

real number not a real number

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−36 144

not a real number real number

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In the following exercises, list the whole numbers, integers, rational numbers, irrational numbers, real numbers for each set of numbers.

−8 , 0 , 1.95286 , 12 5 , 36 , 9

0 , 36 , 9 −8 , 36 , 9 −8 , 0 , 12 5 , 36 , 9 1.95286 −8 , 0 , 1.95286 , 12 5 , 36 , 9

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−9 , −3 4 9 , 9 , 0.40 9 , 11 6 , 7

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100 , −7 , 8 3 , −1 , 0.77 , 3 1 4

none 100 , −7 , −1 100 , −7 , 8 3 , −1 , 0.77 , 3 1 4 none 100 , −7 , 8 3 , −1 , 0.77 , 3 1 4

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−6 , 5 2 , 0 , 0. 714285 ——— , 2 1 5 , 14

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Locate Fractions on the Number Line

In the following exercises, locate the numbers on a number line.

3 4 , 3 4 , 1 2 3 , −1 2 3 , 5 2 , 5 2

There is a number line shown that runs from negative 4 to 4. From left to right the points read negative 5/2, negative 1 and 2/3, negative 3/4, ¾, 1 and 2/3, and 5/2. The point for negative 5/2 is between negative 3 and negative 2. The point for negative 1 and 2/3 is between negative 2 and negative 1. The point for negative 3/4 is between negative 1 and 0. The point for 3/4 is between 0 and 1. The point for 1 and 2/3 is between 1 and 2. The point for 5/2 is between 2 and 3.

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1 5 , 2 5 , 1 3 4 , −1 3 4 , 8 3 , 8 3

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In the following exercises, order each of the pairs of numbers, using<or>.

Locate Decimals on the Number Line In the following exercises, locate the number on the number line.

In the following exercises, order each pair of numbers, using<or>.

Everyday math

Field trip All the 5th graders at Lincoln Elementary School will go on a field trip to the science museum. Counting all the children, teachers, and chaperones, there will be 147 people. Each bus holds 44 people.

How many busses will be needed?
Why must the answer be a whole number?
Why shouldn’t you round the answer the usual way, by choosing the whole number closest to the exact answer?

4 busses answers may vary answers may vary

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Child care Serena wants to open a licensed child care center. Her state requires there be no more than 12 children for each teacher. She would like her child care center to serve 40 children.

How many teachers will be needed?
Why must the answer be a whole number?
Why shouldn’t you round the answer the usual way, by choosing the whole number closest to the exact answer?

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Writing exercises

In your own words, explain the difference between a rational number and an irrational number.

Answers may vary

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Explain how the sets of numbers (counting, whole, integer, rational, irrationals, reals) are related to each other.

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Self check

After completing the exercises, use this checklist to evaluate your mastery of the objective of this section.

This is a table that has five rows and four columns. In the first row, which is a header row, the cells read from left to right “I can…,” “Confidently,” “With some help,” and “No-I don’t get it!” The first column below “I can…” reads “simplify expressions with square roots,” “identify integers, rational numbers, irrational numbers and real numbers,” locate fractions on the number line,” and “locate decimals on the number line.” The rest of the cells are blank

On a scale of 1 10 , how would you rate your mastery of this section in light of your responses on the checklist? How can you improve this?

Practice Key Terms 6

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Source:  OpenStax, Elementary algebra. OpenStax CNX. Jan 18, 2017 Download for free at http://cnx.org/content/col12116/1.2
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