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# 1.11: Chapter Test

Created by: CK-12
1. Perform the indicated operations. If possible, simplify all answers.
$4 + (-11)$ $-7 -9$ $-7(6)$ $-48 \div (-4)$ $4 + (-9) + 2$
$\left ( \frac{3}{5} \right ) + \left ( \frac{7}{8} \right )$ $3.648 \div -0.2$ $39 \div 1 \frac{3}{10}$ $(-2.476) - (-6.94) - 5$ $(-3.6)(4)(-1.7)$
$\frac{5}{11} - \frac{1}{3}$ $(0.765) - (-3.58) + (2.2)$ $\left ( \frac{3}{8} \right ) \left ( \frac{7}{2} \right ) \div \left ( \frac{3}{4} \right )$ $16 \div 2^2 \times 4 - 5$ $(-15) \div \left ( \frac{1}{3} \right ) \times (-2)$
1. State the property of addition or of multiplication that is shown in each example.
$15 + (8+22) = (15 + 8) + 22$
$\frac{3}{7} \times \frac{7}{3} = 1$
$6.486 + 16.39 = 16.39 + 6.486$
$36 + (-36) = 0$
$44 \times 1 = 44$
$24 \times 2 = 48$
1. Tom has $40 to spend for groceries each week. His grocery list is shown below. If he is shopping on “NO TAX DAY”, will he have enough money to buy his groceries? If he has enough money, how much change will he receive? If he doesn’t have enough money, how much more money does he need? Groceries Price 2 dozen eggs$1.98/dozen
1 loaf of bread $2.49 4 lb. of ground beef$2.16/lb
2 qt. milk $1.90/qt 3 lb. of apples$1.99/lb
6 lemons $0.79 for 3 2.5 lb of tomatoes$1.49/lb
Dish detergent $3.35 2 bags of potatoes$3.49/bag
1. In each of the following graphs, find the error(s). Identify each error and explain why each error exists.
2. Draw the correct graph to represent the given set notation.
1. $\{ x | 4 < x \le 9, x \ \varepsilon \ W \}$
2. $\{ x | -3 \le x \le 2, x \ \varepsilon \ I \}$
1. Show all the necessary steps to convert 3.246464646 to the form $\frac{a}{b}$.
2. A box of chicken nuggets weighs $1 \frac{5}{8}lb$. How many pounds will 20 cartons of 12 boxes each weigh?
3. The exterior wall of a small office building under construction is built of $\frac{3}{4}-in$. paneling, $\frac{5}{8}-in$. fire code sheetrock, $5 \frac{3}{4}-in$. studs, $\frac{1}{2}-in$. plywood sheathing, $1 \frac{1}{4}-in$. insulation board, and $\frac{5}{6}-in$. exterior surfacing. What is the total thickness of the wall?

$4 + (-11)$

-7

$-7 -9$

-16

$-7(6)$

-42

$-48 \div (-4)$

12

$4 + (-9) + 2$

-3

$\left ( \frac{3}{5} \right ) + \left ( \frac{7}{8} \right )$

$\frac{59}{40} = 1 \frac{19}{40}$

$3.648 \div -0.2$

-18.24

$39 \div 1 \frac{3}{10}$

30

$(-2.476) - (-6.94) - 5$

-0.536

$(-3.6)(4)(-1.7)$

24.48

$\frac{5}{11} - \frac{1}{3}$

$\frac{4}{33}$

$(0.765) - (-3.58) + (2.2)$

6.545

$\left ( \frac{3}{8} \right ) \left ( \frac{7}{2} \right ) \div \left ( \frac{3}{4} \right )$

$\frac{7}{4} = 1 \frac{3}{5}$

$16 \div 2^2 \times 4 - 5$

11

$(-15) \div \left ( \frac{1}{3} \right ) \times (-2)$

10

$15 + (8+22) = (15 + 8) + 22$ Associative property of addition
$\frac{3}{7} \times \frac{7}{3} = 1$ Inverse property of multiplication
$6.486 + 16.39 = 16.39 + 6.486$ Commutative property of addition
$36 + (-36) = 0$ Inverse property of addition
$44 \times 1 = 44$ Identity property of multiplication
$24 \times 2 = 48$ Closure property of multiplication
Groceries Price
$2 \times \ 1.98 = \ 3.96$ 2 dozen eggs $1.98/dozen $1 \times \ 2.49 = \ 2.49$ 1 loaf of bread$2.49
$4 \times \ 2.04 = \ 8.16$ 4 lb. of ground beef $2.16/lb $2 \times \ 1.90 = \ 3.80$ 2 qt. milk$1.90/qt
$3 \times \ 1.69 = \ 5.07$ 3 lb. of apples $1.99/lb $2 \times \ 0.79 = \ 1.48$ 6 lemons$0.79 for 3
$2.5 \times \ 1.49 = \ 3.73$ 2.5 lb of tomatoes $1.49/lb $1 \times \ 3.35 = \ 3.35$ Dish detergent$3.35
$2 \times \ 3.29 = \ 6.58$ 2 bags of potatoes \$3.49/bag

The total cost of Tom’s groceries is $\boxed{\38.62}$. His change is $& \ \ 40.00\\&\underline{-38.92}\\& \ \ \ 1.38$

1. (a) (i)$\{ x | 4 < x \le 9, x \ \varepsilon \ W \}$ Errors: The dot above the 4 should be an open dot because $x > 4$. The dot above the 9 should be a closed dot because $x \ge 9$ The dots should NOT be joined with a line because the variable belongs to the set of whole numbers. $\{ x | 4 < x \le 9, x \ \varepsilon \ W \}$ (ii) $\{ x | -3 \le x \le 2, x \ \varepsilon \ I \}$ Errors: The line with the arrow should not be on the graph because the variable is between two numbers. The line is only used if the variable belongs to the real number system. $\{ x | -3 \le x \le 2, x \ \varepsilon \ I \}$

$\text{Let} \ x & = 3.246464646\\1000x & = 3246.464646\\10x & = 32.46464646$

$& 1000x = 3246.464646\\& \ \underline{-10x = 32.46464646}\\& \ \frac{990x}{990} = \frac{3214}{990}\\& \qquad x = \frac{3214}{990}\\& \qquad x = \frac{1607}{495}$

$& 1 \frac{5}{8} \times 12\\& \frac{13}{8} \times \frac{12}{1}\\& = \frac{156}{8}\\& \frac{156}{8} \times 20\\& \frac{156}{8} \times \frac{20}{1}\\& = \frac{3120}{8} = 390 \ lb.$

$& \frac{3}{4} + \frac{5}{8} + 5 \frac{3}{4} + \frac{1}{2} + 1 \frac{1}{4} + \frac{5}{6}\\& \frac{3}{4} + \frac{5}{8} + \frac{23}{4} + \frac{1}{2} + \frac{5}{4} + \frac{5}{6}\\& \frac{18}{24} + \frac{15}{24} + \frac{138}{24} + \frac{12}{24} + \frac{30}{24} + \frac{20}{24}\\& = \frac{233}{24} = 9 \frac{17}{24} \ in.$

## Date Created:

Jan 16, 2013

Apr 29, 2014
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