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Foundational Concepts Sample Work

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
Field Trip 2
Number of Students
Total Cost
1
20
(12⋅20)+150(12·20)+150open 12 middle dot 20 close plus 150
2
40
(12⋅40)+150(12·40)+150open 12 middle dot 40 close plus 150
3
60
(12⋅60)+150(12·60)+150open 12 middle dot 60 close plus 150
There are no rows in this table
⁠
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)
Whitewater Tours 2
Column 1
Column 2
1
Adult Ticket
$53.00
2
Child Ticket
$32.00
3
Equipment Rental
$5 per hour
There are no rows in this table
⁠
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
Lunch Menu 2
Column 1
Column 2
1
Salad
$6.25
2
Sandwich
$5.50
3
Drink
$2.75
There are no rows in this table
⁠

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)

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