### Do you know HOW?

Write an algebraic expression for each phrase.

1. a number n divided by 4

Answer: n/4

2. 2 less than the product of 5 and n

Answer: 5n - 2

3. The table shows how the total cost of a field trip depends on the number of students. What is a rule for the total cost of the tickets? Give the rule in words and as an algebraic expression.

Answer: 12 x n + 150

4. The sign shows the costs associated with a whitewater rafting trip. Write an expression to determine the cost of 3 children and 1 adult renting equipment for a whitewater rafting trip that lasts h hours.

Answer: h*(3x+y)

Simplify each expression.

5. 24÷(3+22)

Answer: 0.96

`6. √144

Answer: 12

Evaluate each expression for the given values of the variables.

7. 3x ⋅ 2 ÷ y; x = 3 and y = 6

Answer: 3

8. (4a)^3 ÷(b−2); a = 2 and b = 4

Answer: 36

9. Name the subset(s) of real numbers to which each number belongs. Then order the numbers from least to greatest. √105,−4, 4/3

Answer: √105 belongs to irrational number

-4 belongs to integers as well as rational numbers

4/3 belongs to rational numbers

10. Estimate √14 to the nearest integer.

Answer: 3.7; 4

11. What property is shown in the following equation? (5+8)+11=5+(8+11)

Answer: Associative property of addition

12. Use the table below. Find the total cost of 2 salads, 1 sandwich, and 2 drinks. Use mental math.

Answer: $23.50

### Do you UNDERSTAND?

13. What word phrases represent the expressions −2 + 3x and 3x + (−2)? Are the two expressions equivalent? Explain.

Answer: yes, both of them equal 2/3 and 0.6 and its called communative property

14. Use grouping symbols to make the following equation true. Use grouping symbols to make the following equation true. 4^2 + 2 ⋅ 3 = 54

Answer: (4^2 + 2) ⋅ 3 18 x 3 = 54

15. Choose the correct word to complete the following sentence: A natural number is (always, sometimes, never) a whole number.

Answer: A natural number is always a whole number

16. How many natural numbers are in the set of numbers from −10 to 10 inclusive? Explain.

Answer: Natural numbers are positive integers

there are 10 terms in the set that are natural

17. What is the simplified form of 3abc/abc ,when abc ≠ 0? Explain using the properties of real numbers.

Answer: 3

3abc/abc simplified is 3 when abc doesn’t equal zero

18. Reasoning Are the associative properties true for all integers? Explain.

Answer: The associative properties of addition and multiplication are true for all integers

19. Use the Commutative Property of Multiplication to rewrite the expression (x ⋅ y) ⋅ z in in two different ways.

Answer: z (x * y)

y ( x * z)