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# 1.11: Chapter Test

Difficulty Level: At Grade Created by: CK-12
1. Perform the indicated operations. If possible, simplify all answers.
4+(11)\begin{align*}4 + (-11)\end{align*} 79\begin{align*}-7 -9\end{align*} 7(6)\begin{align*}-7(6)\end{align*} 48÷(4)\begin{align*}-48 \div (-4)\end{align*} 4+(9)+2\begin{align*}4 + (-9) + 2\end{align*}
(35)+(78)\begin{align*}\left ( \frac{3}{5} \right ) + \left ( \frac{7}{8} \right )\end{align*} 3.648÷0.2\begin{align*}3.648 \div -0.2\end{align*} 39÷1310\begin{align*}39 \div 1 \frac{3}{10}\end{align*} (2.476)(6.94)5\begin{align*}(-2.476) - (-6.94) - 5\end{align*} (3.6)(4)(1.7)\begin{align*}(-3.6)(4)(-1.7)\end{align*}
51113\begin{align*}\frac{5}{11} - \frac{1}{3}\end{align*} (0.765)(3.58)+(2.2)\begin{align*}(0.765) - (-3.58) + (2.2)\end{align*} (38)(72)÷(34)\begin{align*}\left ( \frac{3}{8} \right ) \left ( \frac{7}{2} \right ) \div \left ( \frac{3}{4} \right )\end{align*} 16÷22×45\begin{align*}16 \div 2^2 \times 4 - 5\end{align*} (15)÷(13)×(2)\begin{align*}(-15) \div \left ( \frac{1}{3} \right ) \times (-2)\end{align*}
1. State the property of addition or of multiplication that is shown in each example.
15+(8+22)=(15+8)+22\begin{align*}15 + (8+22) = (15 + 8) + 22\end{align*}
37×73=1\begin{align*}\frac{3}{7} \times \frac{7}{3} = 1\end{align*}
6.486+16.39=16.39+6.486\begin{align*}6.486 + 16.39 = 16.39 + 6.486\end{align*}
36+(36)=0\begin{align*}36 + (-36) = 0\end{align*}
44×1=44\begin{align*}44 \times 1 = 44\end{align*}
24×2=48\begin{align*}24 \times 2 = 48\end{align*}
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<x9,x ε W}\begin{align*}\{ x | 4 < x \le 9, x \ \varepsilon \ W \}\end{align*}
2. {x|3x2,x ε I}\begin{align*}\{ x | -3 \le x \le 2, x \ \varepsilon \ I \}\end{align*}
1. Show all the necessary steps to convert 3.246464646 to the form ab\begin{align*}\frac{a}{b}\end{align*}.
2. A box of chicken nuggets weighs 158lb\begin{align*}1 \frac{5}{8}lb\end{align*}. 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 34in\begin{align*}\frac{3}{4}-in\end{align*}. paneling, 58in\begin{align*}\frac{5}{8}-in\end{align*}. fire code sheetrock, 534in\begin{align*}5 \frac{3}{4}-in\end{align*}. studs, 12in\begin{align*}\frac{1}{2}-in\end{align*}. plywood sheathing, 114in\begin{align*}1 \frac{1}{4}-in\end{align*}. insulation board, and 56in\begin{align*}\frac{5}{6}-in\end{align*}. exterior surfacing. What is the total thickness of the wall?

4+(11)\begin{align*}4 + (-11)\end{align*}

-7

79\begin{align*}-7 -9\end{align*}

-16

7(6)\begin{align*}-7(6)\end{align*}

-42

48÷(4)\begin{align*}-48 \div (-4)\end{align*}

12

4+(9)+2\begin{align*}4 + (-9) + 2\end{align*}

-3

(35)+(78)\begin{align*}\left ( \frac{3}{5} \right ) + \left ( \frac{7}{8} \right )\end{align*}

5940=11940\begin{align*}\frac{59}{40} = 1 \frac{19}{40}\end{align*}

3.648÷0.2\begin{align*}3.648 \div -0.2\end{align*}

-18.24

39÷1310\begin{align*}39 \div 1 \frac{3}{10}\end{align*}

30

(2.476)(6.94)5\begin{align*}(-2.476) - (-6.94) - 5\end{align*}

-0.536

(3.6)(4)(1.7)\begin{align*}(-3.6)(4)(-1.7)\end{align*}

24.48

51113\begin{align*}\frac{5}{11} - \frac{1}{3}\end{align*}

433\begin{align*}\frac{4}{33}\end{align*}

(0.765)(3.58)+(2.2)\begin{align*}(0.765) - (-3.58) + (2.2)\end{align*}

6.545

(38)(72)÷(34)\begin{align*}\left ( \frac{3}{8} \right ) \left ( \frac{7}{2} \right ) \div \left ( \frac{3}{4} \right )\end{align*}

74=135\begin{align*}\frac{7}{4} = 1 \frac{3}{5}\end{align*}

16÷22×45\begin{align*}16 \div 2^2 \times 4 - 5\end{align*}

11

(15)÷(13)×(2)\begin{align*}(-15) \div \left ( \frac{1}{3} \right ) \times (-2)\end{align*}

10

15+(8+22)=(15+8)+22\begin{align*}15 + (8+22) = (15 + 8) + 22\end{align*} Associative property of addition
37×73=1\begin{align*}\frac{3}{7} \times \frac{7}{3} = 1\end{align*} Inverse property of multiplication
6.486+16.39=16.39+6.486\begin{align*}6.486 + 16.39 = 16.39 + 6.486\end{align*} Commutative property of addition
36+(36)=0\begin{align*}36 + (-36) = 0\end{align*} Inverse property of addition
44×1=44\begin{align*}44 \times 1 = 44\end{align*} Identity property of multiplication
24×2=48\begin{align*}24 \times 2 = 48\end{align*} Closure property of multiplication
Groceries Price
2×$1.98=$3.96\begin{align*}2 \times \ 1.98 = \ 3.96\end{align*} 2 dozen eggs $1.98/dozen 1×$2.49=2.49\begin{align*}1 \times \ 2.49 = \ 2.49\end{align*} 1 loaf of bread2.49
4×$2.04=$8.16\begin{align*}4 \times \ 2.04 = \ 8.16\end{align*} 4 lb. of ground beef $2.16/lb 2×$1.90=3.80\begin{align*}2 \times \ 1.90 = \ 3.80\end{align*} 2 qt. milk1.90/qt
3×$1.69=$5.07\begin{align*}3 \times \ 1.69 = \ 5.07\end{align*} 3 lb. of apples $1.99/lb 2×$0.79=1.48\begin{align*}2 \times \ 0.79 = \ 1.48\end{align*} 6 lemons0.79 for 3
2.5×$1.49=$3.73\begin{align*}2.5 \times \ 1.49 = \ 3.73\end{align*} 2.5 lb of tomatoes $1.49/lb 1×$3.35=3.35\begin{align*}1 \times \ 3.35 = \ 3.35\end{align*} Dish detergent3.35
2×$3.29=$6.58\begin{align*}2 \times \ 3.29 = \ 6.58\end{align*} 2 bags of potatoes $3.49/bag The total cost of Tom’s groceries is$38.62\begin{align*}\boxed{\38.62}\end{align*}. His change is  $40.0038.92$1.38\begin{align*}& \ \ 40.00\\&\underline{-38.92}\\& \ \ \ 1.38\end{align*}

1. (a) (i){x|4<x9,x ε W}\begin{align*}\{ x | 4 < x \le 9, x \ \varepsilon \ W \}\end{align*} Errors: The dot above the 4 should be an open dot because x>4\begin{align*}x > 4\end{align*}. The dot above the 9 should be a closed dot because x9\begin{align*}x \ge 9\end{align*} The dots should NOT be joined with a line because the variable belongs to the set of whole numbers. {x|4<x9,x ε W}\begin{align*}\{ x | 4 < x \le 9, x \ \varepsilon \ W \}\end{align*} (ii) {x|3x2,x ε I}\begin{align*}\{ x | -3 \le x \le 2, x \ \varepsilon \ I \}\end{align*} 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|3x2,x ε I}\begin{align*}\{ x | -3 \le x \le 2, x \ \varepsilon \ I \}\end{align*}

Let x1000x10x=3.246464646=3246.464646=32.46464646\begin{align*}\text{Let} \ x & = 3.246464646\\ 1000x & = 3246.464646\\ 10x & = 32.46464646\end{align*}

1000x=3246.464646 10x=32.46464646 990x990=3214990x=3214990x=1607495\begin{align*}& 1000x = 3246.464646\\ & \ \underline{-10x = 32.46464646}\\ & \ \frac{990x}{990} = \frac{3214}{990}\\ & \qquad x = \frac{3214}{990}\\ & \qquad x = \frac{1607}{495}\end{align*}

158×12138×121=15681568×201568×201=31208=390 lb.\begin{align*}& 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.\end{align*}

34+58+534+12+114+5634+58+234+12+54+561824+1524+13824+1224+3024+2024=23324=91724 in.\begin{align*}& \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.\end{align*}

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