# 1.10 Systems of measurement  (Page 11/13)

 Page 11 / 13

the sum of $-4$ and $-17$ , increased by 32

$\left(-4+\left(-17\right)\right)+32;11$

the difference of 15 and $-7$ subtract 15 from $-7$

the quotient of $-45$ and $-9$

$\frac{-45}{-9};5$

the product of $-12$ and the difference of $c\phantom{\rule{0.2em}{0ex}}\text{and}\phantom{\rule{0.2em}{0ex}}d$

Use Integers in Applications

In the following exercises, solve.

Temperature The high temperature one day in Miami Beach, Florida, was $76\text{°}$ . That same day, the high temperature in Buffalo, New York was $\text{−}8\text{°}$ . What was the difference between the temperature in Miami Beach and the temperature in Buffalo?

84 degrees

Checking Account Adrianne has a balance of $\text{−}22$ in her checking account. She deposits $301 to the account. What is the new balance? ## Visualize Fractions Find Equivalent Fractions In the following exercises, find three fractions equivalent to the given fraction. Show your work, using figures or algebra. $\frac{1}{4}$ $\frac{2}{8},\frac{3}{12},\frac{4}{16}$ answers may vary $\frac{1}{3}$ $\frac{5}{6}$ $\frac{10}{12},\frac{15}{18},\frac{20}{24}$ answers may vary $\frac{2}{7}$ Simplify Fractions In the following exercises, simplify. $\frac{7}{21}$ $\frac{1}{3}$ $\frac{8}{24}$ $\frac{15}{20}$ $\frac{3}{4}$ $\frac{12}{18}$ $-\phantom{\rule{0.2em}{0ex}}\frac{168}{192}$ $-\phantom{\rule{0.2em}{0ex}}\frac{7}{8}$ $-\phantom{\rule{0.2em}{0ex}}\frac{140}{224}$ $\frac{11x}{11y}$ $\frac{x}{y}$ $\frac{15a}{15b}$ Multiply Fractions In the following exercises, multiply. $\frac{2}{5}·\frac{1}{3}$ $\frac{2}{15}$ $\frac{1}{2}·\frac{3}{8}$ $\frac{7}{12}\left(-\phantom{\rule{0.2em}{0ex}}\frac{8}{21}\right)$ $-\phantom{\rule{0.2em}{0ex}}\frac{2}{9}$ $\frac{5}{12}\left(-\phantom{\rule{0.2em}{0ex}}\frac{8}{15}\right)$ $-28p\left(-\phantom{\rule{0.2em}{0ex}}\frac{1}{4}\right)$ $7p$ $-51q\left(-\phantom{\rule{0.2em}{0ex}}\frac{1}{3}\right)$ $\frac{14}{5}\left(-15\right)$ $-42$ $-1\left(-\phantom{\rule{0.2em}{0ex}}\frac{3}{8}\right)$ Divide Fractions In the following exercises, divide. $\frac{1}{2}÷\frac{1}{4}$ 2 $\frac{1}{2}÷\frac{1}{8}$ $-\phantom{\rule{0.2em}{0ex}}\frac{4}{5}÷\frac{4}{7}$ $-\phantom{\rule{0.2em}{0ex}}\frac{7}{5}$ $-\phantom{\rule{0.2em}{0ex}}\frac{3}{4}÷\frac{3}{5}$ $\frac{5}{8}÷\frac{a}{10}$ $\frac{25}{4a}$ $\frac{5}{6}÷\frac{c}{15}$ $\frac{7p}{12}÷\frac{21p}{8}$ $\frac{2}{9}$ $\frac{5q}{12}÷\frac{15q}{8}$ $\frac{2}{5}÷\left(-10\right)$ $-\phantom{\rule{0.2em}{0ex}}\frac{1}{25}$ $-18÷-\left(\frac{9}{2}\right)$ In the following exercises, simplify. $\frac{\frac{2}{3}}{\frac{8}{9}}$ $\frac{3}{4}$ $\frac{\frac{4}{5}}{\frac{8}{15}}$ $\frac{-\phantom{\rule{0.2em}{0ex}}\frac{9}{10}}{3}$ $-\phantom{\rule{0.2em}{0ex}}\frac{3}{10}$ $\frac{2}{\frac{5}{8}}$ $\frac{\frac{r}{5}}{\frac{s}{3}}$ $\frac{3r}{5s}$ $\frac{-\phantom{\rule{0.2em}{0ex}}\frac{x}{6}}{-\phantom{\rule{0.2em}{0ex}}\frac{8}{9}}$ Simplify Expressions Written with a Fraction Bar In the following exercises, simplify. $\frac{4+11}{8}$ $\frac{15}{8}$ $\frac{9+3}{7}$ $\frac{30}{7-12}$ $-6$ $\frac{15}{4-9}$ $\frac{22-14}{19-13}$ $\frac{4}{3}$ $\frac{15+9}{18+12}$ $\frac{5·8}{-10}$ $-4$ $\frac{3·4}{-24}$ $\frac{15·5-{5}^{2}}{2·10}$ $\frac{5}{2}$ $\frac{12·9-{3}^{2}}{3·18}$ $\frac{2+4\left(3\right)}{-3-{2}^{2}}$ $-2$ $\frac{7+3\left(5\right)}{-2-{3}^{2}}$ Translate Phrases to Expressions with Fractions In the following exercises, translate each English phrase into an algebraic expression. the quotient of c and the sum of d and 9. $\frac{c}{d+9}$ the quotient of the difference of h and k , and $-5$ . ## Add and Subtract Fractions Add and Subtract Fractions with a Common Denominator In the following exercises, add. $\frac{4}{9}+\frac{1}{9}$ $\frac{5}{9}$ $\frac{2}{9}+\frac{5}{9}$ $\frac{y}{3}+\frac{2}{3}$ $\frac{y+2}{3}$ $\frac{7}{p}+\frac{9}{p}$ $-\phantom{\rule{0.2em}{0ex}}\frac{1}{8}+\left(-\phantom{\rule{0.2em}{0ex}}\frac{3}{8}\right)$ $-\phantom{\rule{0.2em}{0ex}}\frac{1}{2}$ $-\phantom{\rule{0.2em}{0ex}}\frac{1}{8}+\left(-\phantom{\rule{0.2em}{0ex}}\frac{5}{8}\right)$ In the following exercises, subtract. $\frac{4}{5}-\phantom{\rule{0.2em}{0ex}}\frac{1}{5}$ $\frac{3}{5}$ $\frac{4}{5}-\phantom{\rule{0.2em}{0ex}}\frac{3}{5}$ $\frac{y}{17}-\phantom{\rule{0.2em}{0ex}}\frac{9}{17}$ $\frac{y-9}{17}$ $\frac{x}{19}-\phantom{\rule{0.2em}{0ex}}\frac{8}{19}$ $-\phantom{\rule{0.2em}{0ex}}\frac{8}{d}-\phantom{\rule{0.2em}{0ex}}\frac{3}{d}$ $-\phantom{\rule{0.2em}{0ex}}\frac{11}{d}$ $-\phantom{\rule{0.2em}{0ex}}\frac{7}{c}-\phantom{\rule{0.2em}{0ex}}\frac{7}{c}$ Add or Subtract Fractions with Different Denominators In the following exercises, add or subtract. $\frac{1}{3}+\frac{1}{5}$ $\frac{8}{15}$ $\frac{1}{4}+\frac{1}{5}$ $\frac{1}{5}-\left(-\phantom{\rule{0.2em}{0ex}}\frac{1}{10}\right)$ $\frac{3}{10}$ $\frac{1}{2}-\left(-\phantom{\rule{0.2em}{0ex}}\frac{1}{6}\right)$ $\frac{2}{3}+\frac{3}{4}$ $\frac{17}{12}$ $\frac{3}{4}+\frac{2}{5}$ $\frac{11}{12}-\phantom{\rule{0.2em}{0ex}}\frac{3}{8}$ $\frac{13}{24}$ $\frac{5}{8}-\phantom{\rule{0.2em}{0ex}}\frac{7}{12}$ $-\phantom{\rule{0.2em}{0ex}}\frac{9}{16}-\left(-\phantom{\rule{0.2em}{0ex}}\frac{4}{5}\right)$ $\frac{19}{80}$ $-\phantom{\rule{0.2em}{0ex}}\frac{7}{20}-\left(-\phantom{\rule{0.2em}{0ex}}\frac{5}{8}\right)$ $1+\frac{5}{6}$ $\frac{11}{6}$ $1-\phantom{\rule{0.2em}{0ex}}\frac{5}{9}$ Use the Order of Operations to Simplify Complex Fractions In the following exercises, simplify. $\frac{{\left(\frac{1}{5}\right)}^{2}}{2+{3}^{2}}$ $\frac{1}{275}$ $\frac{{\left(\frac{1}{3}\right)}^{2}}{5+{2}^{2}}$ $\frac{\frac{2}{3}+\frac{1}{2}}{\frac{3}{4}-\phantom{\rule{0.2em}{0ex}}\frac{2}{3}}$ 14 $\frac{\frac{3}{4}+\frac{1}{2}}{\frac{5}{6}-\phantom{\rule{0.2em}{0ex}}\frac{2}{3}}$ Evaluate Variable Expressions with Fractions In the following exercises, evaluate. $x+\frac{1}{2}$ when $x=-\phantom{\rule{0.2em}{0ex}}\frac{1}{8}$ $x=-\phantom{\rule{0.2em}{0ex}}\frac{1}{2}$ $\frac{3}{8}$ 0 $x+\frac{2}{3}$ when $x=-\phantom{\rule{0.2em}{0ex}}\frac{1}{6}$ $x=-\phantom{\rule{0.2em}{0ex}}\frac{5}{3}$ $4{p}^{2}q$ when $p=-\phantom{\rule{0.2em}{0ex}}\frac{1}{2}$ and $q=\frac{5}{9}$ $\frac{5}{9}$ $5{m}^{2}n$ when $m=-\phantom{\rule{0.2em}{0ex}}\frac{2}{5}$ and $n=\frac{1}{3}$ $\frac{u+v}{w}$ when $u=-4,v=-8,w=2$ $-6$ $\frac{m+n}{p}$ when $m=-6,n=-2,p=4$ ## Decimals Name and Write Decimals In the following exercises, write as a decimal. Eight and three hundredths 8.03 Nine and seven hundredths One thousandth 0.001 Nine thousandths In the following exercises, name each decimal. 7.8 seven and eight tenths 5.01 0.005 five thousandths 0.381 Round Decimals In the following exercises, round each number to the nearest hundredth tenth whole number. 5.7932 5.79 5.8 6 3.6284 12.4768 12.48 12.5 12 25.8449 Add and Subtract Decimals In the following exercises, add or subtract. $18.37+9.36$ 27.73 $256.37-85.49$ $15.35-20.88$ −5.53 #### Questions & Answers 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. Dojzae Reply LeBron needs 150 milliliters of a 30% solution of sulfuric acid for a lab experiment but only has access to a 25% and a 50% solution. How much of the 25% and how much of the 50% solution should he mix to make the 30% solution? Xona Reply 5% Michael hey everyone how to do algebra The Reply Felecia answer 1.5 hours before he reaches her Adriana Reply I would like to solve the problem -6/2x rachel Reply 12x Andrew how Christian Does the x represent a number or does it need to be graphed ? latonya -3/x Venugopal -3x is correct Atul Arnold invested$64,000, some at 5.5% interest and the rest at 9%. How much did he invest at each rate if he received $4,500 in interest in one year? Stephanie Reply Tickets for the community fair cost$12 for adults and $5 for children. On the first day of the fair, 312 tickets were sold for a total of$2204. How many adult tickets and how many child tickets were sold?
220
gayla
Three-fourths of the people at a concert are children. If there are 87 children, what is the total number of people at the concert?
Erica earned a total of $50,450 last year from her two jobs. The amount she earned from her job at the store was$1,250 more than four times the amount she earned from her job at the college. How much did she earn from her job at the college?
Tsimmuaj
Erica earned a total of $50,450 last year from her two jobs. The amount she earned from her job at the store was$1,250 more than four times the amount she earned from her job at the college. How much did she earn from her job at the college?
Tsimmuaj
? Is there anything wrong with this passage I found the total sum for 2 jobs, but found why elaborate on extra If I total one week from the store *4 would = the month than the total is = x than x can't calculate 10 month of a year
candido
what would be wong
candido
87 divided by 3 then multiply that by 4. 116 people total.
Melissa
the actual number that has 3 out of 4 of a whole pie
candido
was having a hard time finding
Teddy
use Matrices for the 2nd question
Daniel
One number is 11 less than the other number. If their sum is increased by 8, the result is 71. Find the numbers.
26 + 37 = 63 + 8 = 71
gayla
26+37=63+8=71
11+52=63+8=71
Thisha
how do we know the answer is correct?
Thisha
23 is 11 less than 37. 23+37=63. 63+8=71. that is what the question asked for.
gayla
23 +11 = 37. 23+37=63 63+8=71
Gayla
by following the question. one number is 11 less than the other number 26+11=37 so 26+37=63+8=71
Gayla
your answer did not fit the guidelines of the question 11 is 41 less than 52.
gayla
71-8-11 =52 is this correct?
Ruel
let the number is 'x' and the other number is "x-11". if their sum is increased means: x+(x-11)+8 result will be 71. so x+(x-11)+8=71 2x-11+8=71 2x-3=71 2x=71+3 2x=74 1/2(2x=74)1/2 x=37 final answer
tesfu
just new
Muwanga
Amara currently sells televisions for company A at a salary of $17,000 plus a$100 commission for each television she sells. Company B offers her a position with a salary of $29,000 plus a$20 commission for each television she sells. How televisions would Amara need to sell for the options to be equal?
yes math
Kenneth
company A 13 company b 5. A 17,000+13×100=29,100 B 29,000+5×20=29,100
gayla
need help with math to do tsi test
Toocute
me too
Christian
have you tried the TSI practice test ***tsipracticetest.com
gayla
DaMarcus and Fabian live 23 miles apart and play soccer at a park between their homes. DaMarcus rode his bike for 34 of an hour and Fabian rode his bike for 12 of an hour to get to the park. Fabian’s speed was 6 miles per hour faster than DaMarcus’s speed. Find the speed of both soccer players.
?
Ann
DaMarcus: 16 mi/hr Fabian: 22 mi/hr
Sherman
Joy is preparing 20 liters of a 25% saline solution. She has only a 40% solution and a 10% solution in her lab. How many liters of the 40% solution and how many liters of the 10% solution should she mix to make the 25% solution?
15 and 5
32 is 40% , & 8 is 10 % , & any 4 letters is 5%.
Karen
It felt that something is missing on the question like: 40% of what solution? 10% of what solution?
Jhea
its confusing
Sparcast
3% & 2% to complete the 25%
Sparcast
because she already has 20 liters.
Sparcast
ok I was a little confused I agree 15% & 5%
Sparcast
8,2
Karen
Jim and Debbie earned $7200. Debbie earned$1600 more than Jim earned. How much did they earned
5600
Gloria
1600
Gloria
Bebbie: 4,400 Jim: 2,800
Jhea
A river cruise boat sailed 80 miles down the Mississippi River for 4 hours. It took 5 hours to return. Find the rate of the cruise boat in still water and the rate of the current.
A veterinarian is enclosing a rectangular outdoor running area against his building for the dogs he cares for. He needs to maximize the area using 100 feet of fencing. The quadratic equation A=x(100−2x) gives the area, A , of the dog run for the length, x , of the building that will border the dog run. Find the length of the building that should border the dog run to give the maximum area, and then find the maximum area of the dog run.
ggfcc
Mike