### Key Concepts

- Write expression to represent situations
- Evaluate expressions
- Write and evaluate expressions

**4.1 Write and evaluate algebraic expressions**

## What is meant by algebraic expressions?

An algebraic expression (or) a variable expression is a combination of terms by the operations such as addition, subtraction, multiplication, division, etc.

Thus, we can say that 5x + 7 is an example of an algebraic expression.

Evaluate 5x + 8 when x=3.

**4.1.1 Write expression to represent situations**

Kelvin started with $217 in her bank account. He deposits $25.50 each week and never withdraws any money. What expression can Kelvin use to determine his account balance after *w* weeks?

**Solution:**

Draw a bar diagram to represent the amount of money in his account balance after *w* weeks.

Use the bar diagram to write an expression to represent the amount of money in the balance after *w* days.

Kelvin can use the expression $ 217 + $ 25.50w to determine the amount of money in her account balance after *w* weeks.

**4.1.2 Evaluate expressions**

The cost to rent a scooter is $15.50 per hour and the cost to rent a watercraft is $22.80 per hour.

Use the expression $15.5s+22.8w to determine how much it would cost to rent a scooter for 3½

hours and a watercraft for 1¾ hours.

**Solution:**

Evaluate expression for the given values.

$ 15.5. s+22.8w

15.5(3 1/2 ) +22.8 (1 3/4 )

54.25 + 39.9

94.15

It cost $94.15 to rent a scooter for (3½) hours and Watercraft for (1¾) hours.

**4.1.3 Write and evaluate expressions**

**Example1:**

Ria earns $8.74 per hour plus a gas allowance of $3.50 per day at her job. How much does Ria job pay in a day when she works 5½ hours? Write an expression and evaluate for 5½ hours.

**Solution:**

Write an expression to represent how much Ria earns. Evaluate the expression for the given values.

5 ½(h)+ 3.50

= 5½ (8.74) +3.50

=11/2(8.74) +3.50

=48.07 +3.50

=51.57

Ria’s job pays $51.57 in a day.

**Example2:**

Mark bought a new sweater for $27 plus sales tax *t*. Tax was $1.76, what is the total cost of the sweater?

**Solution:**

Write an expression to represent the total cost of the sweater.

$ 27.00+ t

$ 27.00 + $ 1.76

$ 28.76

The total cost of the sweater was $ 28.76.

## Exercise:

- What is the value of when x= 0.5?
- What is the value of 7.4 n – 3.6 when n= 4 and p= 4?
- Evaluate expression.

4d – 5

d = 1.3 - Evaluate the expression.

i. 0.4f- 3.4g

ii. f= 10; g= 2 - Evaluate 2t–5 when t=6.
- Pizza Place bases its pizza prices on the size of the pizza and the number of toppings. The price of a medium pizza, in dollars, is 9+2t, where ‘t’ is the number of toppings. What is the price of a medium pizza with 3 toppings?
- James is an electrician. He charges $45 per hour and spends $20 a day on gasoline.

Write an algebraic expression to represent his earnings for one day. - A movie streaming service charges a one-time membership fee of $4 plus $13 per month. Write an expression to represent the cost of the streaming service for
*m*months. - The rent cost for a bike is $15 plus $2 for each hour the bike is used. How much will it cost if you rent the bike for a certain number of hours? Write the expression that would give you the cost.
- Evaluate the given expression for m = 13.

m^{2}+ m – 54

### Concept Map

### What have we learned:

- Understand algebraic expressions.
- Write expressions to represent situations.
- Understand how to evaluate expressions.
- Write and evaluate expressions