CHECK MY ANSWERS
1. You are given a problem that involves multiplying a positive number and a negative number. Which of the following are reasonable answers? Select all that apply.
6
-3
-2
4
2. Which of the following are reasonable answers for the product of two negative numbers and a positive number? Select all that apply.
-15
45
20
-40
3. What is the simplified form of the expression?
2x^2 + 4y + 3x^2 - 2y + 3y
5x^4 + 5y^2
5x^2y + 5x^2y
5x^2 + 5y
10x^2y
4. Simplify the following expression.
4(12x + 16)
64x + 48
48x + 64
12x + 64
48 x + 16
5. What is the product?
2 x (-7)
-9
-2
-14
14
6. Which property is illustrated? 8(-5/6) = (-5/6)8
Associative Property of Addition
Inverse Property of Multiplication
Commutative Property of Addition
Commutative Property of Multiplication
7. Which property is illustrated?
3.2 + 4 = 4 + 3.2
Associative Property of Addition
Commutative Property of Multiplication
Inverse Property of Multiplication
Commutative Property of Addition
8. Order the following numbers from least to greatest.
√2, -2/3, √11, 0.8, -0.2
√2, -0.2, -2/3, √11, 0.8
-2/3, -0.2, √2, √11, 0.8
-2/3, -0.2, 0.8, √2, √11
√2, √11, -0.2, -2/3, 5.1
9. Which number line can you use to simplify -2 + (-8)?
-2 + (-8) = -10
-2 + (-8) = -10
-2 + (-8) = -10
-2 + (-8) = -10
10. To which subsets of the real number does the number √7 belong?
rational numbers
irrational numbers
whole numbers, integers, rational numbers
whole numbers, natural numbers, integers
11. Which sum or difference is equivalent to the following expression?
15x - 20/5
15x - 4
10x - 15
3x - 4
3x - 20
12. What is the algebraic expression for the following word phrase: "the product of g and 4"?
g - 4
4g
g/4
g + 4
13. What is an algebraic expression for the following word phrase: "the quotient of 8 and the difference of x and m"?
8/x - m
8 - x/m
x - m/8
8 - x / m
14. What is the algebraic expression for the following word phrase: "the quotient of y and 6"?
y + 6
y/6
6y
6 - y
15. What is the difference?
-2 - 6
-8
-4
8
4
16. What is the simplified form of the expression √1/121
1/11
11
1/242
2/121
17. Which property is illustrated?
(wy)z = w(yz)
Associative Property of Multiplication
Commutative Property of Multiplication
Inverse Property of Multiplication
Commutative Property of Addition
18. Evaluate u/z + xy^2, for u = 20, x = 4, y = 7, and z = 10
786
198
294
900
19. What is the product? 4(-2) =
8
-6
2
-8
20. Simplify the expression. (4/7)^3
343/64
12/21
12/49
64/343
21. What word phrase can you use to represent the algebraic expression 3m?
3 plus a number m
3 minus a number m
3 times a number m
3 divided by a number m
22. What is the simplified form of the expression -(8d - 3w)?
8d + 3w
8d - 3w
-8d + 3w
-8d - 3w
23. What is the simplified form of the expression? 12[6^2 / (5^2 - 4^2) + 4]
96
16
148
48
24. Simplify the expression.
3xz/-2x
-3/2z
-3/2x
3/2x
3/2z
25. What is the value of x/y if x = -21 and y = -7?
-3
3
14
-14
1. The reasonable answers when multiplying a positive number and a negative number are -3 and -2. When you multiply a positive number and a negative number, the result is always negative. So, the answer 6 is not reasonable because it is positive, and the answer 4 is not reasonable because it is also positive.
2. The reasonable answers for the product of two negative numbers and a positive number are -15 and -40. When you multiply two negative numbers, the result is always positive. So, the answers 45 and 20 are not reasonable because they are positive.
3. To simplify the expression 2x^2 + 4y + 3x^2 - 2y + 3y, combine the like terms. The terms with x^2 are 2x^2 and 3x^2, which can be combined to give 5x^2. The terms with y are 4y, -2y, and 3y, which can be combined to give 5y. So, the simplified form of the expression is 5x^2 + 5y.
4. To simplify the expression 4(12x + 16), distribute the 4 to each term inside the parentheses. This gives 48x + 64. So, the simplified form of the expression is 48x + 64.
5. To find the product of 2 and -7, multiply the numbers together. This gives -14. So, the product is -14.
6. The property illustrated is the Commutative Property of Multiplication. This property states that the order of multiplication does not affect the result. In this case, 8(-5/6) is the same as (-5/6)8.
7. The property illustrated is the Commutative Property of Addition. This property states that the order of addition does not affect the result. In this case, 3.2 + 4 is the same as 4 + 3.2.
8. The numbers can be ordered from least to greatest as follows: -2/3, -0.2, √2, 0.8, √11.
9. To simplify -2 + (-8), add the two numbers together. This gives -10. So, on the number line, -2 + (-8) is represented as -10.
10. The number √7 belongs to the set of irrational numbers. Irrational numbers are numbers that cannot be expressed as a fraction or a terminating or repeating decimal.
11. The sum or difference that is equivalent to the expression 15x - 20/5 is 3x - 4. To simplify, divide 20 by 5 to get 4.
12. The algebraic expression for "the product of g and 4" is 4g. Since the word "product" indicates multiplication, you multiply g and 4 to get 4g.
13. The algebraic expression for "the quotient of 8 and the difference of x and m" is 8 / (x - m). The word "quotient" indicates division, and the word "difference" indicates subtraction.
14. The algebraic expression for "the quotient of y and 6" is y/6. The word "quotient" indicates division, so you divide y by 6 to get y/6.
15. The difference between -2 and 6 is -8. To find the difference, subtract 6 from -2.
16. The simplified form of the expression √1/121 is 1/11. The square root of 1 is 1, and the square root of 121 is 11.
17. The property illustrated is the Associative Property of Multiplication. This property states that the grouping of factors does not affect the result of multiplication. In this case, (wy)z is the same as w(yz).
18. To evaluate u/z + xy^2 for u = 20, x = 4, y = 7, and z = 10, substitute the values into the expression. This gives 20/10 + 4(7)^2. Simplifying further, we have 2 + 4(49), which equals 2 + 196 and finally equals 198.
19. The product of 4 and -2 is -8. To find the product, multiply 4 and -2.
20. To simplify the expression (4/7)^3, raise the fraction 4/7 to the power of 3. This gives (4/7)^3 = 64/343. So, the simplified expression is 64/343.
21. The word phrase that represents the algebraic expression 3m is "3 times a number m". The word "times" indicates multiplication, so you multiply 3 and m to get 3m.
22. The simplified form of the expression -(8d - 3w) is -8d + 3w. When you distribute the negative sign, it changes the signs of each term inside the parentheses.
23. To simplify the expression 12[6^2 / (5^2 - 4^2) + 4], first perform the operations inside the parentheses using the order of operations (PEMDAS/BODMAS). This gives 12[36 / (25 - 16) + 4], which simplifies further to 12[36 / 9 + 4]. Next, divide 36 by 9 to get 4. Finally, add 4 and 4 to get 8. So, the simplified form of the expression is 12 * 8, which equals 96.
24. To simplify the expression 3xz/-2x, divide 3xz by -2x. The x's cancel out, leaving -3z/2. So, the simplified form of the expression is -3z/2.
25. To find the value of x/y when x = -21 and y = -7, divide -21 by -7. The negative signs cancel out, leaving 3. So, the value of x/y is 3.