# 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 Macario is making 12 pounds of nut mixture with macadamia nuts and almonds. macadamia nuts cost$9 per pound and almonds cost $5.25 per pound. how many pounds of macadamia nuts and how many pounds of almonds should macario use for the mixture to cost$6.50 per pound to make?
Nga and Lauren bought a chest at a flea market for $50. They re-finished it and then added a 350 % mark - up Makaila Reply the sum of two Numbers is 19 and their difference is 15 Abdulai Reply 2, 17 Jose interesting saw 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 13 hour later. He drove 55mph to catch up to Felecia. How long before he reaches her? Rafi Reply integer greater than 2 and less than 12 Emily Reply 2 < x < 12 Felix I'm guessing you are doing inequalities... Felix Actually, translating words into algebraic expressions / equations... Felix hi Darianna hello Mister Eric here Eric He charges$125 per job. His monthly expenses are $1,600. How many jobs must he work in order to make a profit of at least$2,400?
at least 20
Ayla
what are the steps?
Alicia
6.4 jobs
Grahame
32
Grahame
1600+2400= total amount with expenses. 4000/125= number of jobs needed to make that min profit of 2400. answer is 32
Orlando
He must work 32 jobs to make a profit
POP
what is algebra
repeated addition and subtraction of the order of operations. i love algebra I'm obsessed.
Shemiah
hi
Krekar
Eric here. I'm a parent. 53 years old. I have never taken algebra. I want to learn.
Eric
One-fourth of the candies in a bag of M&M’s are red. If there are 23 red candies, how many candies are in the bag?
they are 92 candies in the bag
POP
rectangular field solutions
What is this?
Donna
t
muqtaar
the proudact of 3x^3-5×^2+3 and 2x^2+5x-4 in z7[x]/ is
?
Choli
a rock is thrown directly upward with an initial velocity of 96feet per second from a cliff 190 feet above a beach. The hight of tha rock above the beach after t second is given by the equation h=_16t^2+96t+190
Usman
Stella bought a dinette set on sale for $725. The original price was$1,299. To the nearest tenth of a percent, what was the rate of discount?
44.19%
Scott
40.22%
Terence
44.2%
Orlando
I don't know
Donna
if you want the discounted price subtract $725 from$1299. then divide the answer by $1299. you get 0.4419... but as percent you get 44.19... but to the nearest tenth... round .19 to .2 and you get 44.2% Orlando you could also just divide$725/$1299 and then subtract it from 1. then you get the same answer. Orlando p mulripied-5 and add 30 to it Tausif Reply p mulripied-5 and add30 Tausif p mulripied-5 and addto30 Tausif how muqtaar Can you explain further Monica Reply p mulripied-5 and add to 30 Tausif -5p+30? Corey p=-5+30 Jacob How do you find divisible numbers without a calculator? Jacob Reply TAKE OFF THE LAST DIGIT AND MULTIPLY IT 9. SUBTRACT IT THE DIGITS YOU HAVE LEFT. IF THE ANSWER DIVIDES BY 13(OR IS ZERO), THEN YOUR ORIGINAL NUMBER WILL ALSO DIVIDE BY 13!IS DIVISIBLE BY 13 BAINAMA When she graduates college, Linda will owe$43,000 in student loans. The interest rate on the federal loans is 4.5% and the rate on the private bank loans is 2%. The total interest she owes for one year was \$1,585. What is the amount of each loan?