1.9 Review

  1. Evaluate.

    a) –3 – 6 + 9 b) 6 – (–8) c) 12 + (–4) + 7
    d) 25 – 5 – (–10)

     

    		 e) –9 + (–8) + 1

     

    		 f) –60 – 4 + (–3) – (–10)

     

  2. Multiply.

    a) –5 \times –9 \times –2 b) 6(–2)(–9) c) –6 \times 0
    d) –(–15)(–2)

     

    		 e) 4 \bullet 10 \bullet –1

     

    		 f) (–8)(–1)(–1)(–1)(–8)

     

  3. Divide.

    a) \frac{-49}{7} b) 0\div-10 c) \frac{17}{-1}
    d) 75\div5 e) \frac{341}{0} f) -10 000\div-100

  4. Simplify.

    a) 8 + 3 \times (4^2 - 6)

     

     

     

    		 b) 5 \times (2 + 3)^2 - 4 \div 2

     

     

     
    c) 12 \div 4 + 6 \times (2 + 3)

     

     

     

    		 d) 7 + 3 \times 2^3 - 4

     

     

     
    e) (5 + 2)^2 - 3 \times 4

     

     

     

     

    		 f) 3 + 6 \div 2 \times \sqrt{25}

     

     

     

     

  5. Add or subtract.

    a) \dfrac{4}{9}+\dfrac{1}{9}

     

    		 b) \dfrac{2}{9}+\dfrac{5}{9}

     

    		 c) -\dfrac{1}{8}+\left(-\dfrac{3}{8}\right)

     
    d) -\dfrac{1}{8}+\left(-\dfrac{5}{8}\right)

     

     

    		 e) \dfrac{4}{5}-\dfrac{1}{5}

     

     

    		 f) \dfrac{4}{5}-\dfrac{3}{5}

     

     
    g) \dfrac{1}{3}+\dfrac{1}{5}

     

     

     

    		 h) \dfrac{1}{5}-\left(-\dfrac{1}{10}\right)

     

     

     

    		 i) \dfrac{2}{3}+\dfrac{3}{4}

     

     

     
    j) \dfrac{11}{12}-\dfrac{3}{8}

     

     

     

    		 k) -\dfrac{9}{16}-\left(-\dfrac{4}{5}\right)

     

     

     

    		 l) 1+\dfrac{5}{6}

     

     

     

  6. Find the product.

    a) \frac{3}{7} \bullet \frac{2}{5}

     

     

    		 b) -\frac{8}{10} \bullet \frac{3}{4}

     

     

    		 c) \frac{5}{6} \bullet \left(-\frac{7}{9}\right)

     

     
    d) \frac{-6}{12} \bullet \frac{3}{8}

     

     

    		 e) \frac{4}{9} \bullet \left(-\frac{6}{15}\right)

     

     

    		 f) \frac{3}{5} \bullet \left(-\frac{2}{7}\right)

     

     
    g) \frac{-10}{20} \bullet \frac{4}{9}

     

     

    		 h) \frac{8}{12} \bullet \frac{-5}{15}

     

     

    		 i) \frac{7}{11} \bullet \left(-\frac{3}{4}\right)

     

     
    j) \frac{-9}{16} \bullet \frac{2}{5}

     

     

    		 k) \frac{-12}{20} \bullet \frac{-5}{6}

     

     

    		 l) \frac{5}{9} \bullet \frac{7}{15}

     

     

  7. Evaluate for the quotient.

    a) \frac{3}{5} \div \frac{2}{7}

     

     

     

    		 b) \frac{-2}{9} \div \frac{3}{8}

     

     

     

    		 c) \frac{4}{7} \div \left(-\frac{3}{5}\right)

     

     

     
    d) \frac{-3}{4} \div \frac{-6}{7}

     

     

     

    		 e) \frac{5}{8} \div \frac{1}{3}

     

     

     

    		 f) \frac{-6}{11} \div \frac{2}{5}

     

     

     
    g) \frac{9}{14} \div \left(-\frac{3}{7}\right)

     

     

     

    		 h) \frac{7}{12} \div \frac{5}{6}

     

     

     

    		 i) \frac{8}{15} \div \frac{-4}{9}

     

     

     
    j) \frac{-5}{12} \div \frac{2}{3}

     

     

     

    		 k) \frac{6}{12} \div 2

     

     

     

    		 l) \frac{-6}{15} \div \left(-\frac{2}{3}\right)

     

     

     

  8. Solve.

    a) y+2=-6

     

     

    		 b) n+3.6=5.1

     

     

    		 c) x-9=-4

     

     
    d) p-4.8=14

     

     

    		 e) y+16=-9

     

     

    		 f) d-3.9=8.2

     

     
    g) a+\frac{1}{3}=\frac{5}{3}

     

     

     

    		 h) c-\frac{3}{11}=\frac{9}{11}

     

     

     

    		 i) 13a=-65

     

     

     
    j) -y=4

     

     

     

    		 k) \frac{y}{-10}=30

     

     

     

    		 l) \frac{5}{8}u=\frac{15}{16}

     

     

     
    m) \frac{c}{9}=36

     

     

     

    		 n) \frac{11}{12}=\frac{2}{3}y

     

     

     
    o) 10w-5=65

     

     

     

    		 p) 32=-4-9n

     

     

     
    q) 0.05p-0.01p=2+0.24

     

     

     

     

    		 r) 4x-\frac{3}{8}=3x

     

     

     

     
    s) 4x-17=3x+2

     

     

     

     

    		 t) 9c+7=-2c-37

     

     

     

     
    u) 6y-3y+12y=-43+28

     

     

     

     

    		 v) -18-7=5t-9t-6t

     

     

     

     
    w) -4\left(n-2\right)-8=24

     

     

     

     

    		 x) -6\left(n-2\right)-12=30

     

     

     

     
    y) 4\left(z+2\right)=2\left(z+20\right)

     

     

     

     

    		 z) 0.06x+0.02=0.25x-1.5

     

     

     

     
    aa) c+\frac{3}{4}=\frac{c}{2}-\frac{1}{4}

     

     

     

     

    		 bb) 6=\frac{1}{2}\phantom{\rule{0.1em}{0ex}}v+\frac{2}{5}\phantom{\rule{0.1em}{0ex}}v-\frac{3}{4}\phantom{\rule{0.1em}{0ex}}v

     

     

     

     
    cc) -11=\frac{1}{2}\left(6p+2\right)

     

     

     

     

    		 dd) \frac{1}{5}\left(n+3\right)=\frac{1}{4}\left(n+2\right)

     

     

     

     

  9. Solve.

    a) One tree is three-fourths as tall as another tree. If the taller tree is 34 m, how tall is the shorter tree?

     

     

     

    		 b) The difference of a number and 12 is 3. Find the number.

     

     

     
    c) The difference of twice a number and 7 is 17. Find the number.

     

     

     

    		 d) The sum of two numbers is 20. One number is 4 less than the other. Find the numbers.

     

     

     
    e) Phil pays $1 620 in rent every month. This amount is $120 more than twice what his friend Andres pays for rent. How much does Andres pay for rent?

     

     

     

    		 f) Mayyada paid $1 166.40 for a new refrigerator, including $86.40 tax. What was the price of the refrigerator?

     

     

     
    g) There are 18 Cub Scouts in Pack 645. The number of scouts is 3 more than five times the number of adult leaders. Find the number of adult leaders.

     

     

     

    		 h) Ishani 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 three times the amount she earned from her job at the college. How much did she earn from her job at the college?

     

     

Answers

1.

a) 0 b) 14 c) 15 d) 30 e) –16 f) –57

2.

a) –90 b) 108 c) 0 d) –30 e) –40 f) –64

3.

a) –7 b) 0 c) –17 d) 15 e) undefined f) 100

4.

a) 38 b) 123 c) 33 d) 27 e) 37 f) 18

5.

a) \frac{5}{9} b) \frac{7}{9} c) \frac{-1}{2} d) \frac{-3}{4} e) \frac{3}{5} f) \frac{1}{5}
g) \frac{8}{15} h) \frac{3}{10} i) \frac{17}{12} j) \frac{13}{24} k) \frac{19}{80} l) \frac{11}{6}

6.

a) \frac{6}{35} b) -\frac{3}{5} c) -\frac{35}{54} d) -\frac{3}{16} e) -\frac{8}{45} f) -\frac{6}{35}
g) -\frac{2}{9} h) -\frac{2}{9} i) \frac{-21}{44} j) -\frac{9}{40} k) \frac{1}{2} l) \frac{7}{27}

7.

a) \frac{21}{10} b) \frac{-16}{27} c) \frac{-20}{21} d) \frac{7}{8} e) \frac{15}{8} f) \frac{-15}{11}
g) \frac{-3}{2} h) \frac{7}{10} i) \frac{-6}{5} j) \frac{-5}{8} k) \frac{1}{4} l) \frac{3}{5}

8.

a) –8 b) 1.5 c) 5 d) 16 e) –25 f) 12.1
g) \frac{4}{3} h) \frac{12}{11} i) –5 j) –4 k) –300 l) \frac{3}{2}
m) 324 n) \frac{11}{8} o) 7 p) –4 q) 56 r) \frac{3}{8}
s) 19 t) –4 u) –1 v) \frac{5}{2} w) –6 x) –5
y) 16 z) 8 aa) –2 bb) 40 cc) –4 dd) 2

9.

a) 25.5 m b) 15 c) 12 d) 8, 12
e) $750 f) $1 080 g) 3 h) $12 300

Attribution

Unless otherwise indicated, material on this page has been adapted from the following resource:

Mazur, I. (2021). Introductory algebra. BCcampus. https://collection.bccampus.ca/textbooks/intermediate-algebra-bccampus-412/, licensed under CC BY 4.0

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