Variables and Algebraic Expressions

Show your work for each problem.

1.
Which of the following is a variable?
1. a)
2. b)
3. c)
4. d)
Answer:
is a variable because it's a letter that can represent any number. is a constant, is an operation, and is the equals sign.
2.
What does mean?
1. a)
2. b)
3. c)
4. d)
Answer:
means (3 multiplied by x). In algebra, when a number is placed directly next to a variable, it indicates multiplication.
3.
Evaluate when .
Answer: 10
Substitute : .
4.
Evaluate when .
Answer: 20
.
5.
Which expression means 'a number decreased by 4'?
1. a)
2. b)
3. c)
4. d)
Answer:
'A number decreased by 4' means we subtract 4 from the number: .
6.
Evaluate when .
Answer: 17
. Multiply first (), then add 5.
7.
Evaluate when and .
Answer: 22
1. Substitute into . What is ? 12
2. Substitute into . What is ? 10
3. Add the two results: 22
8.
Write an expression for: 'twice a number, plus three'
Answer: 2n + 3
1. Choose a variable to represent 'a number'. What letter will you use? n
2. What does 'twice a number' mean in algebra? Write it using n. 2n
3. Now add 'plus three' to your expression. 2n + 3
9.
In the expression , what is the coefficient of ?
1. a)
2. b)
3. c)
4. d)
Answer:
In , the coefficient of is because means . The is a constant (a term without a variable).
10.
Evaluate when .
Answer: 17
.
11.
A gym membership costs 25 euros per month plus a 50 euro joining fee. Write an expression for the total cost after months, then find the cost after 6 months.
Answer: 200
1. What is the monthly cost? 25
2. What is the one-time joining fee? 50
3. Write the expression for total cost after months. 25m + 50
4. Calculate the total cost after 6 months. 200
12.
Evaluate when .
Answer: 7
.
13.
Evaluate when .
Answer: 26
1. Calculate when . What is ? 16
2. Calculate when . What is ? 12
3. Now combine: 26
14.
Which expression represents 'the quotient of a number and 5, increased by 2'?
1. a)
2. b)
3. c)
4. d)
Answer:
'The quotient of a number and 5' = . 'Increased by 2' = . Together: .
15.
Evaluate when .
Answer: 15
1. Substitute inside the parentheses. What is ? 10
2. Now multiply by 2. What is ? 20
3. Finally subtract 5. What is ? 15