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

 Page 7 / 10

## 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 In 10 years, the population of Detroit fell from 950,000 to about 712,500. Find the percent decrease. Jenise Reply how do i set this up Jenise 25% Melissa 25 percent Muzamil 950,000 - 712,500 = 237,500. 237,500 / 950,000 = .25 = 25% Melissa I've tried several times it won't let me post the breakdown of how you get 25%. Melissa Subtract one from the other to get the difference. Then take that difference and divided by 950000 and you will get .25 aka 25% Melissa Finally 👍 Melissa one way is to set as ratio: 100%/950000 = x% / 712500, which yields that 712500 is 75% of the initial 950000. therefore, the decrease is 25%. bruce twenty five percent... Jeorge thanks melissa Jeorge 950000-713500 *100 and then divide by 950000 = 25 Muzamil Jeannette has$5 and $10 bills in her wallet. The number of fives is three more than six times the number of tens. Let t represent the number of tens. Write an expression for the number of fives. jamie Reply 6t+3 Melissa 6t +3 Bollywood Tricia got a 6% raise on her weekly salary. The raise was$30 per week. What was her original salary?
let us suppose her original salary is 'm'. so, according to the given condition, m*(6/100)=30 m= (30*100)/6 m= 500 hence, her original salary is $500. Simply 28.50 Toi thanks Jeorge How many pounds of nuts selling for$6 per pound and raisins selling for $3 per pound should Kurt combine to obtain 120 pounds of trail mix that cost him$5 per pound?
Amber wants to put tiles on the backsplash of her kitchen counters. She will need 36 square feet of tiles. She will use basic tiles that cost $8 per square foot and decorator tiles that code$20 per square foot. How many square feet of each tile should she use so that the overal cost of he backsplash will be $10 per square foot? Nia Reply I need help with maths can someone help me plz.. is there a wats app group? Cindy Reply WY need Fernando How did you get$750?
if y= 2x+sinx what is dy÷dx
does it teach you how to do algebra if you don't know how
Liam borrowed a total of $35,000 to pay for college. He pays his parents 3% interest on the$8,000 he borrowed from them and pays the bank 6.8% on the rest. What average interest rate does he pay on the total \$35,000? (Round your answer to the nearest tenth of a percent.)
exact definition of length by bilbao
the definition of length
literal meaning of length
francemichael
exact meaning of length
francemichael
exact meaning of length
francemichael
how many typos can we find...?
5
Joseph
In the LCM Prime Factors exercises, the LCM of 28 and 40 is 280. Not 420!
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