Learn How To Evaluate Algebraic Expression

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:

1. What is the value of  when x= 0.5?
2. What is the value of 7.4 n – 3.6 when n= 4 and p= 4?
3. Evaluate expression.
   4d – 5
   d = 1.3        
4. Evaluate the expression.
   i. 0.4f- 3.4g
   ii. f= 10; g= 2
5. Evaluate 2t–5 when t=6.
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?
7. 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.
8. 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.
9. 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.
10. Evaluate the given expression for m = 13.
    m² + 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