Quiz Preview! Lessons 5-1 To 5-3

1) What is the absolute value of -27?

-27

27

The absolute value of a number is its distance from zero on the number line. Since -27 is 27 units away from zero in the negative direction, the absolute value of -27 is 27.

Explanation

The absolute value of a number is its distance from zero on the number line. Since -27 is 27 units away from zero in the negative direction, the absolute value of -27 is 27.

2) -5.68 - 1.2 =

-6.88

6.88

-4.48

4.48

Remember - Leave it, change it, change it. Leave the first number alone, change the subtraction to addition, and change the sign of the second number.

Explanation

Remember - Leave it, change it, change it. Leave the first number alone, change the subtraction to addition, and change the sign of the second number.

3) What property says that a + b = b + a?

Betweenness property

Commutative property

Associative property

Angle addition property

The commutative property states that the order of addition does not affect the result. In other words, for any two numbers a and b, a + b is equal to b + a. This property holds true for addition in mathematics.

Explanation

The commutative property states that the order of addition does not affect the result. In other words, for any two numbers a and b, a + b is equal to b + a. This property holds true for addition in mathematics.

4) 28 + (-34)

62

6

-6

-62

The signs are different, so subtract and keep the sign of the number with the largest absolute value.

Explanation

The signs are different, so subtract and keep the sign of the number with the largest absolute value.

5) A recipe calls for t cups of cheese, k cups of coffee, and m cups of green beans, for a total of g cups of ingredients. Write an equation relating t, k, m and g.

T - k - m = g

T + k + g = m

T + k + m = g

The equation t + k + m = g represents the relationship between the number of cups of cheese (t), cups of coffee (k), and cups of green beans (m) needed in a recipe, which together make up the total number of cups of ingredients (g).

Explanation

The equation t + k + m = g represents the relationship between the number of cups of cheese (t), cups of coffee (k), and cups of green beans (m) needed in a recipe, which together make up the total number of cups of ingredients (g).

6) Rewrite the expression m - n, using the algebraic definition of subtraction.

-m - (-n)

M - (-n)

-m + n

M + -n

The correct answer is m + -n because the algebraic definition of subtraction states that subtracting a number is the same as adding its opposite. In this case, subtracting n is the same as adding -n. Therefore, rewriting m - n using the algebraic definition of subtraction gives us m + -n.

Explanation

The correct answer is m + -n because the algebraic definition of subtraction states that subtracting a number is the same as adding its opposite. In this case, subtracting n is the same as adding -n. Therefore, rewriting m - n using the algebraic definition of subtraction gives us m + -n.

7) If you have a clockwise 60 degree turn followed by a 240 degree counterclockwise turn, followed by a clockwise 20 degree turn, what is the result?

-160 degrees

160 degrees

320 degrees

-320 degrees

The result of the given sequence of turns can be found by adding up the angles in a clockwise direction and subtracting the angles in a counterclockwise direction. In this case, we have a clockwise 60 degree turn followed by a 240 degree counterclockwise turn, which cancels out the initial clockwise turn. Finally, we have a clockwise 20 degree turn. Adding up all the clockwise turns, we get 60 + 20 = 80 degrees. Since there are no counterclockwise turns remaining, the final result is 80 degrees in a clockwise direction. Therefore, the correct answer is 160 degrees.

Explanation

The result of the given sequence of turns can be found by adding up the angles in a clockwise direction and subtracting the angles in a counterclockwise direction. In this case, we have a clockwise 60 degree turn followed by a 240 degree counterclockwise turn, which cancels out the initial clockwise turn. Finally, we have a clockwise 20 degree turn. Adding up all the clockwise turns, we get 60 + 20 = 80 degrees. Since there are no counterclockwise turns remaining, the final result is 80 degrees in a clockwise direction. Therefore, the correct answer is 160 degrees.