# 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

4x+7y=29,x+3y=11 substitute method of linear equation
substitute method of linear equation
Srinu
Solve one equation for one variable. Using the 2nd equation, x=11-3y. Substitute that for x in first equation. this will find y. then use the value for y to find the value for x.
bruce
I want to learn
Elizebeth
help
Elizebeth
I want to learn. Please teach me?
Wayne
1) Use any equation, and solve for any of the variables. Since the coefficient of x (the number in front of the x) in the second equation is 1 (it actually isn't shown, but 1 * x = x), use that equation. Subtract 3y from both sides (this isolates the x on the left side of the equal sign).
bruce
2) This results in x=11-3y. x is note in terms of y. Use that as the value of x and substitute for all x in the first equation. The first equation becomes 4(11-3y)+7y =29. Note that the only variable left in the first equation is the y. If you have multiple variable, then something is wrong.
bruce
3) Distribute (multiply) the 4 across 11-3y to get 44-12y. Add this to the 7y. So, the equation is now 44-5y=29.
bruce
4) Solve 44-5y=29 for y. Isolate the y by subtracting 44 from birth sides, resulting in -5y=-15. Now, divide birth sides by -5 (since you have -5y). This results in y=3. You now have the value of one variable.
bruce
5) The last step is to take the value of y from Step 4) and substitute into the 2nd equation. Therefore: x+3y=11 becomes x+3(3)=11. Then multiplying, x+9=11. Finally, solve for x by subtracting 9 from both sides. Therefore, x=2.
bruce
6) The ordered pair of (2, 3) is the proposed solution. To check, substitute those values into either equation. If the result is true, then the solution is correct. 4(2)+7(3)=8+21=29. TRUE! Finished.
bruce
At 1:30 Marlon left his house to go to the beach, a distance of 5.625 miles. He rose his skateboard until 2:15, and then walked the rest of the way. He arrived at the beach at 3:00. Marlon's speed on his skateboard is 1.5 times his walking speed. Find his speed when skateboarding and when walking.
divide 3x⁴-4x³-3x-1 by x-3
how to multiply the monomial
Two sisters like to compete on their bike rides. Tamara can go 4 mph faster than her sister, Samantha. If it takes Samantha 1 hours longer than Tamara to go 80 miles, how fast can Samantha ride her bike? Got questions? Get instant answers now!
how do u solve that question
Seera
Two sisters like to compete on their bike rides. Tamara can go 4 mph faster than her sister, Samantha. If it takes Samantha 1 hours longer than Tamara to go 80 miles, how fast can Samantha ride her bike?
Seera
Speed=distance ÷ time
Tremayne
x-3y =1; 3x-2y+4=0 graph
Brandon has a cup of quarters and dimes with a total of 5.55\$. The number of quarters is five less than three times the number of dimes
app is wrong how can 350 be divisible by 3.
June needs 48 gallons of punch for a party and has two different coolers to carry it in. The bigger cooler is five times as large as the smaller cooler. How many gallons can each cooler hold?
Susanna if the first cooler holds five times the gallons then the other cooler. The big cooler holda 40 gallons and the 2nd will hold 8 gallons is that correct?
Georgie
@Susanna that person is correct if you divide 40 by 8 you can see it's 5 it's simple
Ashley
@Geogie my bad that was meant for u
Ashley
Hi everyone, I'm glad to be connected with you all. from France.
I'm getting "math processing error" on math problems. Anyone know why?
Can you all help me I don't get any of this
4^×=9
Did anyone else have trouble getting in quiz link for linear inequalities?
operation of trinomial