# 1.3 Add and subtract integers  (Page 7/10)

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## Practice makes perfect

Use Negatives and Opposites of Integers

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

$9___4$
$-3___6$
$-8___-2$
$1___-10$

> < < >

$-7___3$
$-10___-5$
$2___-6$
$8___9$

In the following exercises, find the opposite of each number.

2
$-6$

$-2$ 6

9
$-4$

In the following exercises, simplify.

$\text{−}\left(-4\right)$

4

$\text{−}\left(-8\right)$

$\text{−}\left(-15\right)$

15

$\text{−}\left(-11\right)$

In the following exercises, evaluate.

$\text{−}c$ when
$c=12$
$c=-12$

$-12$ 12

$\text{−}d$ when
$d=21$
$d=-21$

Simplify Expressions with Absolute Value

In the following exercises, simplify.

$|-32|$
$|0|$
$|16|$

32 0 16

$|0|$
$|-40|$
$|22|$

In the following exercises, fill in<,>, or $=$ for each of the following pairs of numbers.

$-6___|-6|$
$\text{−}|-3|___-3$

< $=$

$|-5|___\text{−}|-5|$
$9___\text{−}|-9|$

In the following exercises, simplify.

$\text{−}\left(-5\right)\phantom{\rule{0.2em}{0ex}}\text{and}\phantom{\rule{0.2em}{0ex}}\text{−}|-5|$

$5,-5$

$\text{−}|-9|\phantom{\rule{0.2em}{0ex}}\text{and}\phantom{\rule{0.2em}{0ex}}\text{−}\left(-9\right)$

$8|-7|$

56

$5|-5|$

$|15-7|-|14-6|$

0

$|17-8|-|13-4|$

$18-|2\left(8-3\right)|$

8

$18-|3\left(8-5\right)|$

In the following exercises, evaluate.

$\text{−}|p|\phantom{\rule{0.2em}{0ex}}\text{when}\phantom{\rule{0.2em}{0ex}}p=19$
$\text{−}|q|\phantom{\rule{0.2em}{0ex}}\text{when}\phantom{\rule{0.2em}{0ex}}q=-33$

$-19$ $-33$

$\text{−}|a|\phantom{\rule{0.2em}{0ex}}\text{when}\phantom{\rule{0.2em}{0ex}}a=60$
$\text{−}|b|\phantom{\rule{0.2em}{0ex}}\text{when}\phantom{\rule{0.2em}{0ex}}b=-12$

In the following exercises, simplify each expression.

$-21+\left(-59\right)$

$-80$

$-35+\left(-47\right)$

$48+\left(-16\right)$

32

$34+\left(-19\right)$

$-14+\left(-12\right)+4$

$-22$

$-17+\left(-18\right)+6$

$135+\left(-110\right)+83$

108

6 $-38+27+\left(-8\right)+126$

$19+2\left(-3+8\right)$

29

$24+3\left(-5+9\right)$

Subtract Integers

In the following exercises, simplify.

$8-2$

6

$-6-\left(-4\right)$

$-5-4$

$-9$

$-7-2$

$8-\left(-4\right)$

12

$7-\left(-3\right)$

$44-28$
$44+\left(-28\right)$

16 16

$35-16$
$35+\left(-16\right)$

$27-\left(-18\right)$
$27+18$

45 45

$46-\left(-37\right)$
$46+37$

In the following exercises, simplify each expression.

$15-\left(-12\right)$

27

$14-\left(-11\right)$

$48-87$

$-39$

$45-69$

$-17-42$

$-59$

$-19-46$

$-103-\left(-52\right)$

$-51$

$-105-\left(-68\right)$

$-45-\left(54\right)$

9

$-58-\left(-67\right)$

$8-3-7$

$-2$

$9-6-5$

$-5-4+7$

$-2$

$-3-8+4$

$-14-\left(-27\right)+9$

22

$64+\left(-17\right)-9$

$\left(2-7\right)-\left(3-8\right)\left(2\right)$

0

$\left(1-8\right)-\left(2-9\right)$

$\text{−}\left(6-8\right)-\left(2-4\right)$

4

$\text{−}\left(4-5\right)-\left(7-8\right)$

$25-\left[10-\left(3-12\right)\right]$

6

$32-\left[5-\left(15-20\right)\right]$

$6.3-4.3-7.2$

$-8$

$5.7-8.2-4.9$

${5}^{2}-{6}^{2}$

$-11$

${6}^{2}-{7}^{2}$

## Everyday math

Elevation The highest elevation in the United States is Mount McKinley, Alaska, at 20,320 feet above sea level. The lowest elevation is Death Valley, California, at 282 feet below sea level.

Use integers to write the elevation of:

Mount McKinley.
Death Valley.

20,329 $-282$

Extreme temperatures The highest recorded temperature on Earth was $58\text{°}$ Celsius, recorded in the Sahara Desert in 1922. The lowest recorded temperature was $90\text{°}\phantom{\rule{0.2em}{0ex}}\text{below}\phantom{\rule{0.2em}{0ex}}0\text{°}$ Celsius, recorded in Antarctica in 1983.

Use integers to write the:

1. highest recorded temperature.
2. lowest recorded temperature.

State budgets In June, 2011, the state of Pennsylvania estimated it would have a budget surplus of $540 million. That same month, Texas estimated it would have a budget deficit of$27 billion.

Use integers to write the budget of:

Pennsylvania.
Texas.

$540 million $\text{−}27$ billion College enrollments Across the United States, community college enrollment grew by 1,400,000 students from Fall 2007 to Fall 2010. In California, community college enrollment declined by 110,171 students from Fall 2009 to Fall 2010. Use integers to write the change in enrollment: 1. in the U.S. from Fall 2007 to Fall 2010. 2. in California from Fall 2009 to Fall 2010. Stock Market The week of September 15, 2008 was one of the most volatile weeks ever for the US stock market. The closing numbers of the Dow Jones Industrial Average each day were:  Monday $-504$ Tuesday $+142$ Wednesday $-449$ Thursday $+410$ Friday $+369$ What was the overall change for the week? Was it positive or negative? $-32$ Stock Market During the week of June 22, 2009, the closing numbers of the Dow Jones Industrial Average each day were:  Monday $-201$ Tuesday $-16$ Wednesday $-23$ Thursday $+172$ Friday $-34$ What was the overall change for the week? Was it positive or negative? ## Writing exercises Give an example of a negative number from your life experience. Answers may vary What are the three uses of the $\text{“}-\text{”}$ sign in algebra? Explain how they differ. Explain why the sum of $-8$ and 2 is negative, but the sum of 8 and $-2$ is positive. Answers may vary Give an example from your life experience of adding two negative numbers. ## Self check After completing the exercises, use this checklist to evaluate your mastery of the objectives of this section. What does this checklist tell you about your mastery of this section? What steps will you take to improve? #### Questions & Answers how to square Fiona Reply easiest way to find the square root of a large number? Jackie the accompanying figure shows known flow rates of hydrocarbons into and out of a network of pipes at an oil refinery set up a linear system whose solution provides the unknown flow rates (b) solve the system for the unknown flow rates (c) find the flow rates and directions of flow if x4=50and x6=0 Sabee Reply What is observation adeyemi Reply I'm confused by the question. Can you describe or explain the math question it pertains to? Melissa there is no math to it because all you use is your vision or gaze to the sorrounding areas Cesarp Teegan likes to play golf. He has budgeted$60 next month for the driving range. It costs him $10.55 for a bucket of balls each time he goes. What is the maximum number of times he can go to the driving range next month? Sunnyshay Reply 5 times max Anton 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 1/3 hour later. He drove 55mph to catch up to Felecia. How long before he reaches her? Sophia Reply 35 min Debra Carmen wants to tile the floor of his house. He will need 1,000 square feet of tile. He will do most of the floor with a tile that costs$1.50 per square foot, but also wants to use an accent tile that costs $9.00 per square foot. How many square feet of each tile should he plan to use if he wants the overall cost to be$3 per square foot?
what you wanna get
Cesar
800 sq. ft @ $1.50 & 200 sq. ft @$9.00
Marco
Geneva treated her parents to dinner at their favorite restaurant. The bill was $74.25. Geneva wants to leave 16 % of the total - bill as a tip. How much should the tip be? 74.25 × .16 then get the total and that will be your tip David$74.25 x 0.16 = $11.88 total bill:$74.25 + $11.88 =$86.13
ericka
yes and tip 16% will be $11.88 David what is the shorter way to do it Cesar Reply Priam has dimes and pennies in a cup holder in his car. The total value of the coins is$4.21. The number of dimes is three less than four times the number of pennies. How many dimes and how many pennies are in the cup?
Uno de los ángulos suplementario es 4° más que 1/3 del otro ángulo encuentra las medidas de cada uno de los angulos
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?
I hope this is correct, x=cooler 1 5x=cooler 2 x + 5x = 48 6x=48 ×=8 gallons 5×=40 gallons
ericka
Priam has pennies and dimes in a cup holder in his car. The total value of the coins is $4.21 . The number of dimes is three less than four times the number of pennies. How many pennies and how many dimes are in the cup? Cecilia Reply Arnold invested$64,000 some at 5.5% interest and the rest at 9% interest how much did he invest at each rate if he received $4500 in interest in one year Heidi Reply List five positive thoughts you can say to yourself that will help youapproachwordproblemswith a positive attitude. You may want to copy them on a sheet of paper and put it in the front of your notebook, where you can read them often. Elbert Reply Avery and Caden have saved$27,000 towards a down payment on a house. They want to keep some of the money in a bank account that pays 2.4% annual interest and the rest in a stock fund that pays 7.2% annual interest. How much should they put into each account so that they earn 6% interest per year?
324.00
Irene
1.2% of 27.000
Irene
i did 2.4%-7.2% i got 1.2%
Irene
I have 6% of 27000 = 1620 so we need to solve 2.4x +7.2y =1620
Catherine
I think Catherine is on the right track. Solve for x and y.
Scott
next bit : x=(1620-7.2y)/2.4 y=(1620-2.4x)/7.2 I think we can then put the expression on the right hand side of the "x=" into the second equation. 2.4x in the second equation can be rewritten as 2.4(rhs of first equation) I write this out tidy and get back to you...
Catherine