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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?

Questions & Answers

Aziza is solving this equation-2(1+x)=4x+10
Sechabe Reply
No. 3^32 -1 has exactly two divisors greater than 75 and less than 85 what is their product?
KAJAL Reply
x^2+7x-19=0 has Two solutions A and B give your answer to 3 decimal places
Adedamola Reply
please the answer to the example exercise
Patricia Reply
3. When Jenna spent 10 minutes on the elliptical trainer and then did circuit training for20 minutes, her fitness app says she burned 278 calories. When she spent 20 minutes onthe elliptical trainer and 30 minutes circuit training she burned 473 calories. How manycalories does she burn for each minute on the elliptical trainer? How many calories doesshe burn for each minute of circuit training?
Edwin Reply
.473
Angelita
?
Angelita
John left his house in Irvine at 8:35 am to drive to a meeting in Los Angeles, 45 miles away. He arrived at the meeting at 9:50. At 3:30 pm, he left the meeting and drove home. He arrived home at 5:18.
DaYoungan Reply
p-2/3=5/6 how do I solve it with explanation pls
Adedamola Reply
P=3/2
Vanarith
1/2p2-2/3p=5p/6
James
don't understand answer
Cindy
4.5
Ruth
is y=7/5 a solution of 5y+3=10y-4
Adedamola Reply
yes
James
don't understand answer
Cindy
Lucinda has a pocketful of dimes and quarters with a value of $6.20. The number of dimes is 18 more than 3 times the number of quarters. How many dimes and how many quarters does Lucinda have?
Rhonda Reply
Find an equation for the line that passes through the point P ( 0 , − 4 ) and has a slope 8/9 .
Gabriel Reply
is that a negative 4 or positive 4?
Felix
y = mx + b
Felix
if negative -4, then -4=8/9(0) + b
Felix
-4=b
Felix
if positive 4, then 4=b
Felix
then plug in y=8/9x - 4 or y=8/9x+4
Felix
Macario is making 12 pounds of nut mixture with macadamia nuts and almonds. macadamia nuts cost $9 per pound and almonds cost $5.25 per pound. how many pounds of macadamia nuts and how many pounds of almonds should macario use for the mixture to cost $6.50 per pound to make?
Cherry Reply
Nga and Lauren bought a chest at a flea market for $50. They re-finished it and then added a 350 % mark - up
Makaila Reply
$1750
Cindy
the sum of two Numbers is 19 and their difference is 15
Abdulai Reply
2, 17
Jose
interesting
saw
4,2
Cindy
Felecia left her home to visit her daughter, driving 45mph. Her husband waited for the dog sitter to arrive and left home 20 minutes, or 13 hour later. He drove 55mph to catch up to Felecia. How long before he reaches her?
Rafi Reply
hola saben como aser un valor de la expresión
NAILEA
integer greater than 2 and less than 12
Emily Reply
2 < x < 12
Felix
I'm guessing you are doing inequalities...
Felix
Actually, translating words into algebraic expressions / equations...
Felix
hi
Darianna
hello
Mister
Eric here
Eric
6
Cindy
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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