# 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 where's the answers? Ed Reply I don't see where the answers are. Ed Cindy and Richard leave their dorm in Charleston at the same time. Cindy rides her bicycle north at a speed of 18 miles per hour. Richard rides his bicycle south at a speed of 14 miles per hour. How long will it take them to be 96 miles apart? Maddy Reply 3 Christopher 18t+14t=96 32t=96 32/96 3 Christopher show that a^n-b^2n is divisible by a-b Florence Reply What does 3 times your weight right now Cherokee Reply Use algebra to combine 39×5 and the half sum of travel of 59+30 Cherokee What is the segment of 13? Explain Cherokee my weight is 49. So 3 times is 147 Cherokee kg to lbs you goin to convert 2.2 or one if the same unit your going to time your body weight by 3. example if my body weight is 210lb. what would be my weight if I was 3 times as much in kg. that's you do 210 x3 = 630lb. then 630 x 2.2= .... hope this helps tyler How to convert grams to pounds? paul What is the lcm of 340 Kendra Reply Yes Cherokee How many numbers each equal to y must be taken to make 15xy Malik Reply 15x Martin 15x Asamoah 15x Hugo 1y Tom 1y x 15y Tom find the equation whose roots are 1 and 2 Adda Reply (x - 2)(x -1)=0 so equation is x^2-x+2=0 Ranu I believe it's x^2-3x+2 NerdNamedGerg because the X's multiply by the -2 and the -1 and than combine like terms NerdNamedGerg find the equation whose roots are -1 and 4 Adda Ans = ×^2-3×+2 Gee find the equation whose roots are -2 and -1 Adda (×+1)(×-4) = x^2-3×-4 Gee Quadratic equations involving factorization Winner Reply there's a chatting option in the app wow Nana That's cool cool Nana Nice to meet you all Nana you too. Joan 😃 Nana Hey you all there are several Free Apps that can really help you to better solve type Equations. Debra Debra, which apps specifically. ..? Nana am having a course in elementary algebra ,any recommendations ? samuel Samuel Addai, me too at ucc elementary algebra as part of my core subjects in science Nana me too as part of my core subjects in R M E Ken at ABETIFI COLLEGE OF EDUCATION Ken ok great. Good to know. Joan 5x + 1/3= 2x + 1/2 sanam Plz solve this sanam 5x - 3x = 1/2 - 1/3 2x = 1/6 x = 1/12 Ranu Thks ranu sanam a trader gains 20 rupees loses 42 rupees and then gains ten rupees Express algebraically the result of his transactions vinaya Reply a trader gains 20 rupees loses 42 rupees and then gains 10 rupees Express algebraically the result of his three transactions vinaya a trader gains 20 rupees loses 42 rupees and then gains 10 rupees Express algebraically the result of his three transactions vinaya a trader gains 20 rupees loses 42 rupees and then gains 10 rupees Express algebraically the result of his three transactions vinaya Kim is making eight gallons of punch from fruit juice and soda. The fruit juice costs$6.04 per gallon and the soda costs $4.28 per gallon. How much fruit juice and how much soda should she use so that the punch costs$5.71 per gallon?
(a+b)(p+q+r)(b+c)(p+q+r)(c+a) (p+q+r)
4x-7y=8 2x-7y=1 what is the answer?
x=7/2 & y=6/7
Pbp
x=7/2 & y=6/7 use Elimination
Debra
true
bismark
factoriz e
usman
4x-7y=8 X=7/4y+2 and 2x-7y=1 x=7/2y+1/2
Peggie
Frank
thanks
Ramil
copy and complete the table. x. 5. 8. 12. then 9x-5. to the 2nd power+4. then 2xto the second power +3x
What is c+4=8
2
Letha
4
Lolita
4
Rich
4
thinking
C+4=8 -4 -4 C =4
thinking
I need to study
Letha
4+4=8
William
During two years in college, a student earned $9,500. The second year, she earned$500 more than twice the amount she earned the first year.
9500=500+2x
Debra
9500-500=9000 9000÷2×=4500 X=4500
Debra
X + Y = 9500....... & Y = 500 + 2X so.... X + 500 + 2X = 9500, them X = 3000 & Y = 6500
Pbp  By   By Rhodes By By  By 