# 1.10 Systems of measurement  (Page 9/13)

 Page 9 / 13
1. Did you grow up using the U.S. or the metric system of measurement?
2. Describe two examples in your life when you had to convert between the two systems of measurement.

## Self check

After completing the exercises, use this checklist to evaluate your mastery of the objectives of this section. Overall, after looking at the checklist, do you think you are well-prepared for the next Chapter? Why or why not?

## Introduction to Whole Numbers

Use Place Value with Whole Number

In the following exercises find the place value of each digit.

26,915

1
2
9
5
6

tens ten thousands hundreds ones thousands

359,417

9
3
4
7
1

58,129,304

5
0
1
8
2

ten millions tens hundred thousands millions ten thousands

9,430,286,157

6
4
9
0
5

In the following exercises, name each number.

6,104

six thousand, one hundred four

493,068

3,975,284

three million, nine hundred seventy-five thousand, two hundred eighty-four

85,620,435

In the following exercises, write each number as a whole number using digits.

three hundred fifteen

$315$

sixty-five thousand, nine hundred twelve

ninety million, four hundred twenty-five thousand, sixteen

$90,425,016$

one billion, forty-three million, nine hundred twenty-two thousand, three hundred eleven

In the following exercises, round to the indicated place value.

Round to the nearest ten.

407 8,564

$410$ $8,560$

Round to the nearest hundred.

25,846 25,864

In the following exercises, round each number to the nearest hundred thousand ten thousand.

864,951

$865,000$ $865,000$ $860,000$

3,972,849

Identify Multiples and Factors

In the following exercises, use the divisibility tests to determine whether each number is divisible by 2, by 3, by 5, by 6, and by 10.

168

$\text{by}\phantom{\rule{0.2em}{0ex}}2,3,6$

264

375

$\text{by}\phantom{\rule{0.2em}{0ex}}3,5$

750

1430

$\text{by}\phantom{\rule{0.2em}{0ex}}2,5,10$

1080

Find Prime Factorizations and Least Common Multiples

In the following exercises, find the prime factorization.

420

$2·2·3·5·7$

115

225

$3·3·5·5$

2475

1560

$2·2·2·3·5·13$

56

72

$2·2·2·3·3$

168

252

$2·2·3·3·7$

391

In the following exercises, find the least common multiple of the following numbers using the multiples method.

6,15

$30$

60, 75

In the following exercises, find the least common multiple of the following numbers using the prime factors method.

24, 30

120

70, 84

## Use the Language of Algebra

Use Variables and Algebraic Symbols

In the following exercises, translate the following from algebra to English.

$25-7$

25 minus 7, the difference of twenty-five and seven

$5·6$

$45÷5$

45 divided by 5, the quotient of forty-five and five

$x+8$

$42\ge 27$

forty-two is greater than or equal to twenty-seven

$3n=24$

$3\le 20÷4$

3 is less than or equal to 20 divided by 4, three is less than or equal to the quotient of twenty and four

$a\ne 7·4$

In the following exercises, determine if each is an expression or an equation.

$6·3+5$

expression

$y-8=32$

Simplify Expressions Using the Order of Operations

In the following exercises, simplify each expression.

${3}^{5}$

243

${10}^{8}$

In the following exercises, simplify

$6+10\text{/}2+2$

13

$9+12\text{/}3+4$

$20÷\left(4+6\right)·5$

10

$33÷\left(3+8\right)·2$

${4}^{2}+{5}^{2}$

41

${\left(4+5\right)}^{2}$

Evaluate an Expression

In the following exercises, evaluate the following expressions.

$9x+7$ when $x=3$

34

$5x-4$ when $x=6$

${x}^{4}$ when $x=3$

81

${3}^{x}$ when $x=3$

${x}^{2}+5x-8$ when $x=6$

58

He charges $125 per job. His monthly expenses are$1,600. How many jobs must he work in order to make a profit of at least $2,400? Alicia Reply at least 20 Ayla what are the steps? Alicia 6.4 jobs Grahame 32 Grahame what is algebra Azhar Reply repeated addition and subtraction of the order of operations. i love algebra I'm obsessed. Shemiah hi Krekar One-fourth of the candies in a bag of M&M’s are red. If there are 23 red candies, how many candies are in the bag? Leanna Reply rectangular field solutions Navin Reply What is this? Donna the proudact of 3x^3-5×^2+3 and 2x^2+5x-4 in z7[x]/ is anas Reply ? Choli a rock is thrown directly upward with an initial velocity of 96feet per second from a cliff 190 feet above a beach. The hight of tha rock above the beach after t second is given by the equation h=_16t^2+96t+190 Usman Stella bought a dinette set on sale for$725. The original price was $1,299. To the nearest tenth of a percent, what was the rate of discount? Manhwa Reply 44.19% Scott 40.22% Terence 44.2% Orlando I don't know Donna if you want the discounted price subtract$725 from $1299. then divide the answer by$1299. you get 0.4419... but as percent you get 44.19... but to the nearest tenth... round .19 to .2 and you get 44.2%
Orlando
you could also just divide $725/$1299 and then subtract it from 1. then you get the same answer.
Orlando
p mulripied-5 and add 30 to it
Tausif
Tausif
Can you explain further
p mulripied-5 and add to 30
Tausif
-5p+30?
Corey
p=-5+30
Jacob
How do you find divisible numbers without a calculator?
TAKE OFF THE LAST DIGIT AND MULTIPLY IT 9. SUBTRACT IT THE DIGITS YOU HAVE LEFT. IF THE ANSWER DIVIDES BY 13(OR IS ZERO), THEN YOUR ORIGINAL NUMBER WILL ALSO DIVIDE BY 13!IS DIVISIBLE BY 13
BAINAMA
When she graduates college, Linda will owe $43,000 in student loans. The interest rate on the federal loans is 4.5% and the rate on the private bank loans is 2%. The total interest she owes for one year was$1,585. What is the amount of each loan?
Sean took the bus from Seattle to Boise, a distance of 506 miles. If the trip took 7 2/3 hours, what was the speed of the bus?
66miles/hour
snigdha
How did you work it out?
Esther
s=mi/hr 2/3~0.67 s=506mi/7.67hr = ~66 mi/hr
Orlando
hello, I have algebra phobia. Subtracting negative numbers always seem to get me confused.
what do you need help in?
Felix
Heather
look at the numbers if they have different signs, it's like subtracting....but you keep the sign of the largest number...
Felix
for example.... -19 + 7.... different signs...subtract.... 12 keep the sign of the "largest" number 19 is bigger than 7.... 19 has the negative sign... Therefore, -12 is your answer...
Felix
—12
Thanks Felix.l also get confused with signs.
Esther
Thank you for this
Shatey
ty
Graham
think about it like you lost $19 (-19), then found$7(+7). Totally you lost just $12 (-12) Annushka I used to struggle a lot with negative numbers and math in general what I typically do is look at it in terms of money I have -$5 in my account I then take out 5 more dollars how much do I have in my account well-\$10 ... I also for a long time would draw it out on a number line to visualize it
Meg
practicing with smaller numbers to understand then working with larger numbers helps too and the song/rhyme same sign add and keep opposite signs subtract keep the sign of the bigger # then you'll be exact
Meg
Bruce drives his car for his job. The equation R=0.575m+42 models the relation between the amount in dollars, R, that he is reimbursed and the number of miles, m, he drives in one day. Find the amount Bruce is reimbursed on a day when he drives 220 miles
168.50=R
Heather
john is 5years older than wanjiru.the sum of their years is27years.what is the age of each
46
mustee
j 17 w 11
Joseph
john is 16. wanjiru is 11.
Felix
27-5=22 22÷2=11 11+5=16
Joyce
I don't see where the answers are.
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