# 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 The hypotenuse of a right triangle is 10cm long. One of the triangle’s legs is three times the length of the other leg. Find the lengths of the three sides of the triangle. Edi Reply Tickets for a show are$70 for adults and $50 for children. For one evening performance, a total of 300 tickets were sold and the receipts totaled$17,200. How many adult tickets and how many child tickets were sold?
A 50% antifreeze solution is to be mixed with a 90% antifreeze solution to get 200 liters of a 80% solution. How many liters of the 50% solution and how many liters of the 90% solution will be used?
June needs 45 gallons of punch for a party and has 2 different coolers to carry it in. The bigger cooler is 5 times as large as the smaller cooler. How many gallons can each cooler hold?
Washing his dad’s car alone, eight-year-old Levi takes 2.5 hours. If his dad helps him, then it takes 1 hour. How long does it take the Levi’s dad to wash the car by himself?
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.
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?
5%
Michael
hey everyone how to do algebra
Felecia answer 1.5 hours before he reaches her
I would like to solve the problem -6/2x
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?
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? Alpha Reply 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? Tsimmuaj Reply 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. Tsimmuaj Reply 26 + 37 = 63 + 8 = 71 gayla 26+37=63+8=71 ziad 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