Question 1

Find an equivalent expression with the given denominator.
-$$\frac { 2 } { 5 x } = \frac { ? } { 5 x y }$$

Accepted Answer

A)  $\frac { 2 y } { 5 x y }$ 
B)  $\frac { y } { 5 x y }$ 
C)  $\frac { 10 y } { 5 x y }$ 
D)  $\frac { 2 x y } { 5 x y }$ 
A)  $\frac { 2 y } { 5 x y }$ 
B)  $\frac { y } { 5 x y }$ 
C)  $\frac { 10 y } { 5 x y }$ 
D)  $\frac { 2 x y } { 5 x y }$

Question 2

Add. Do not use a number line except as a check.
--9.3 + 5.2

Accepted Answer

A) 14.5 
B) -14.5 
C) -4.1 
D) 4.1 
A) 14.5 
B) -14.5 
C) -4.1 
D) 4.1

Question 3

Add. Do not use a number line except as a check.
-$$- 98 + \left( - \frac { 5 } { 9 } \right) + 49 + \left( - \frac { 4 } { 9 } \right)$$

Accepted Answer

A)  $- 50$ 
B)  $- \frac { 58 } { 9 }$ 
C)  48 
D)  $- 48$ 
A)  $- 50$ 
B)  $- \frac { 58 } { 9 }$ 
C)  48 
D)  $- 48$

Question 4

Find the absolute value.
-$$| - 24.6 |$$

Accepted Answer

A) 49.2 
B) 24.6 
C) 0 
D) -24.6 
A) 49.2 
B) 24.6 
C) 0 
D) -24.6

Question 5

Multiply.
-(-1)6

Accepted Answer

A) 1 
B) -1 
C) -6 
D) 6 
A) 1 
B) -1 
C) -6 
D) 6

Question 6

Solve the problem.
-The stock market gained 57 points on Tuesday and lost 45 points on Wednesday. It had closed on Monday at 2783 points. Where did the market close on Wednesday?

Accepted Answer

A) 2795 points 
B) 2885 points 
C) 2681 points 
D) 2771 points 
A) 2795 points 
B) 2885 points 
C) 2681 points 
D) 2771 points

Question 7

Find an equivalent expression with the given denominator.
-$$\frac { 5 } { 6 } = \frac { ? } { 6 y }$$

Accepted Answer

A)  $\frac { 5 y } { 6 y }$ 
B)  $\frac { y } { 6 y }$ 
C)  $\frac { 5 } { 6 y }$ 
D)  $\frac { 30 } { 6 y }$ 
A)  $\frac { 5 y } { 6 y }$ 
B)  $\frac { y } { 6 y }$ 
C)  $\frac { 5 } { 6 y }$ 
D)  $\frac { 30 } { 6 y }$

Question 8

Insert  to write a true statement.
-

Accepted Answer

A) - 5 > 6 B) $- 5 < 6$ A) - 5 > 6 B) $- 5 < 6$

Question 9

Find the reciprocal, if it exists.
-$\frac { 5 b } { - 8 a }$

Accepted Answer

A)  $- \frac { 8 a } { 5 b }$ 
B)  $- \frac { 5 b } { 8 a }$ 
C)  $- \frac { 8 b } { 5 a }$ 
D)  $- \frac { 5 a } { 8 b }$ 
A)  $- \frac { 8 a } { 5 b }$ 
B)  $- \frac { 5 b } { 8 a }$ 
C)  $- \frac { 8 b } { 5 a }$ 
D)  $- \frac { 5 a } { 8 b }$

Question 10

Add. Do not use a number line except as a check.
-53 + (-26)

Accepted Answer

A) -79 
B) 27 
C) 79 
D) -27 
A) -79 
B) 27 
C) 79 
D) -27

Question 11

Remove parentheses and simplify.
--7.6(3r + 9)+ 8.5(4r + 6)

Accepted Answer

A) -4.6r + 1.4 
B) 11.2r + 9 
C) 11.2r - 17.4 
D) -91.2r 
A) -4.6r + 1.4 
B) 11.2r + 9 
C) 11.2r - 17.4 
D) -91.2r

Question 12

Evaluate the expression for the given value of x.
-$2 x ^ { 3 } , x = - 1$

Accepted Answer

A)  $- 8$ 
B)  $- 6$ 
C)  2 
D)  $- 2$ 
A)  $- 8$ 
B)  $- 6$ 
C)  2 
D)  $- 2$

Question 13

Factor. Check by multiplying.
-$10 + 5 w + 25 y$

Accepted Answer

A)  $10 ( 1 + 5 w + 25 y )$ 
B)  $5 ( 2 + w + 5 y )$ 
C)  $5 ( 2 + w + 25 y )$ 
D)  $5 ( 2 + 5 w + 25 y )$ 
A)  $10 ( 1 + 5 w + 25 y )$ 
B)  $5 ( 2 + w + 5 y )$ 
C)  $5 ( 2 + w + 25 y )$ 
D)  $5 ( 2 + 5 w + 25 y )$

Question 14

Rewrite the division as a multiplication.
-$\frac { 28.2 } { - 2.5 }$

Accepted Answer

A)  $28.2 \cdot \left( - \frac { 1 } { 2.5 } \right)$ 
B)  $- 28.2 \cdot 2.5$ 
C)  $28.2 \cdot 2.5$ 
D)  $28.2 \left( \frac { 1 } { 2.5 } \right)$ 
A)  $28.2 \cdot \left( - \frac { 1 } { 2.5 } \right)$ 
B)  $- 28.2 \cdot 2.5$ 
C)  $28.2 \cdot 2.5$ 
D)  $28.2 \left( \frac { 1 } { 2.5 } \right)$

Question 15

Use the commutative and/or associative laws to rewrite the given expression. Label each step with a reason.
-(6 + y)+ 6 as y + 12

Accepted Answer

The answer of Use the commutative and/or associative laws to...

Question 16

Write an equivalent expression. Use an associative law.
-r + (7 + s)

Accepted Answer

A) (7 + s)+ r 
B) r(7 + s) 
C) r + (s + 7) 
D) (r + 7)+ s 
A) (7 + s)+ r 
B) r(7 + s) 
C) r + (s + 7) 
D) (r + 7)+ s

Question 17

Evaluate -(-x) for the given value of x.
-$$x = \frac { 1 } { 2 }$$

Accepted Answer

A)  0 
B)  2 
C)  $\frac { 1 } { 2 }$ 
D)  $- \frac { 1 } { 2 }$ 
A)  0 
B)  2 
C)  $\frac { 1 } { 2 }$ 
D)  $- \frac { 1 } { 2 }$

Question 18

Add. Do not use a number line except as a check.
--46 + 7.7 + (-12.4)+ (-21)+ 52

Accepted Answer

A) -10.3 
B) 6.9 
C) -19.7 
D) -35.1 
A) -10.3 
B) 6.9 
C) -19.7 
D) -35.1

Question 19

Solve the problem.
-If a roll of wallpaper costs $36, how much will 8 rolls cost?

Accepted Answer

A) $288 
B) $50 
C) $44 
D) $294 
A) $288 
B) $50 
C) $44 
D) $294

Question 20

Find the reciprocal, if it exists.
-$\frac { - 1 } { 7 y }$

Accepted Answer

A)  $- \frac { y } { 7 }$ 
B)  $- \frac { 7 } { y }$ 
C)  $7 \mathrm { y }$ 
D)  $- 7 \mathrm { y }$ 
A)  $- \frac { y } { 7 }$ 
B)  $- \frac { 7 } { y }$ 
C)  $7 \mathrm { y }$ 
D)  $- 7 \mathrm { y }$

Find an equivalent expression with the given denominator. - $\frac { 2 } { 5 x } = \frac { ? } { 5 x y }$

Add. Do not use a number line except as a check. --9.3 + 5.2

Add. Do not use a number line except as a check. - $- 98 + \left( - \frac { 5 } { 9 } \right) + 49 + \left( - \frac { 4 } { 9 } \right)$

Find the absolute value. - $| - 24.6 |$

Multiply. -(-1)⁶

Solve the problem. -The stock market gained 57 points on Tuesday and lost 45 points on Wednesday. It had closed on Monday at 2783 points. Where did the market close on Wednesday?

Find an equivalent expression with the given denominator. - $\frac { 5 } { 6 } = \frac { ? } { 6 y }$

Insert < or > to write a true statement. -

Find the reciprocal, if it exists. - $\frac { 5 b } { - 8 a }$

Add. Do not use a number line except as a check. -53 + (-26)

Remove parentheses and simplify. --7.6(3r + 9)+ 8.5(4r + 6)

Evaluate the expression for the given value of x. - $2 x ^ { 3 } , x = - 1$

Factor. Check by multiplying. - $10 + 5 w + 25 y$

Rewrite the division as a multiplication. - $\frac { 28.2 } { - 2.5 }$

Use the commutative and/or associative laws to rewrite the given expression. Label each step with a reason. -(6 + y)+ 6 as y + 12

Write an equivalent expression. Use an associative law. -r + (7 + s)

Evaluate -(-x) for the given value of x. - $x = \frac { 1 } { 2 }$

Add. Do not use a number line except as a check. --46 + 7.7 + (-12.4)+ (-21)+ 52

Solve the problem. -If a roll of wallpaper costs $36, how much will 8 rolls cost?

Find the reciprocal, if it exists. - $\frac { - 1 } { 7 y }$

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Exam 1: Introduction to Real Numbers and Algebraic Expressions

Find an equivalent expression with the given denominator. - 25x=?5xy\frac { 2 } { 5 x } = \frac { ? } { 5 x y }5x2​=5xy?​