Key Concepts
 To evaluate an algebraic expression, use substitution to replace the variable with a number.
 Evaluate algebraic expression with whole numbers
 Evaluate algebraic equations with decimals
 Evaluate algebraic expressions with fractions
Solve & Discuss It!
A bike shop charges by the hour to rent a bike. Related items are rented for flat fees. Write an expression that represents how much it will cost to rent a bike and helmet for h hours. How much would it cost to rent a bike and a helmet for 3 hours?
Expression for cost of renting a bike and helmet for h hours
Rent for bike per hour = $12.50
Rent for helmet per helmet = $5.25
Rent for h hours = h x 12.50 + h x 5.25
= h (12.50 + 5.25)
Rent for 3 hours = 3(12.50 + 5.25)
= 3(17.25)
=$53.25
Rent for bike and helmet for 3 hours is $53.25.
Model with Math
You can write an algebraic expression with decimals in the same way you do with whole numbers.
Essential Question
How can you evaluate an algebraic expression?
Example 1:
Erik collects miniature cars. He has one large case that has 20 cars.
He also has 3 samesize, smaller cases filled with cars.
Solution:
Let n = the number of cars in each smaller case.
How many miniature cars does Erik have if each
smaller case holds 10 cars? 12 cars? 14 cars?
To evaluate an algebraic expression, use substitution to replace the variable with a number.
Evaluate 20 + 3n when n equals 10, 12 and 14.
n = 10
20 + 3n = 20 + 3(10)
=20 + 30
= 50
If each smaller case holds 10 cars, Erik has 50 cars.
n = 12
20 + 3n = 20 + 3(12)
=20 + 36
=56
If each smaller case holds 12 cars, Erik has 56 cars.
n = 14
20 + 3n = 20 + 3(14)
=20 + 42
=62
If each smaller case holds 14 cars, Erik has 62 cars.
Try it!
Evaluate the expression 40 – t when t equals 10, 20, or 25. Then complete the table to show the values.
Solution:
Example 2:
Julie’s family took a 4day trip. Julie’s mother wrote an equation to calculate their gas mileage, m, in miles per gallon. Let d = the number of total miles driven on the trip. Let g = the total number of gallons of gas used for the trip.
m = d/g. What was the gas mileage for the 4day trip?
Solution:
Step 1
Identify the values of the variables d and g.
d = 476 + 439 + 382 + 263 = 1560
g = 15 + 13.5 + 15.4 +16.1 = 60
Step 2
Substitute the values of the
variables into the equation and
evaluate.
m = 1560/60 = 26
The gas mileage was 26 miles per gallon.
Try it!
Evaluate the expression 3.4 + 12a – 4 for a = 10.
Solution:
Given expression is 3.4 +12a – 4
The value of a = 10
3.4 + 12a – 4 = 3.4 + 12 (10) – 4
= 3.4 + 120 – 4
= 123.4 – 4
= 119.4
The value of the expression 3.4 + 12a – 4 when a = 10 is 119.4
Example 2
Mr. Grant wants to tile a 27squarefoot area with square tiles. Let s = the side length, in feet, of a square tile. Use the expression 27÷ s^{2}
to find the number of tiles Mr. Grant needs to buy.
Solution:
Step 1:
27 ÷ s^{2} =
27÷ ( 1/3)^{ 2}
= 27÷ ( 1/3. 1/3)
= 27÷ 1/9
Step 2:
Evaluate the expression
27÷ 1/9 = 27 × 9/1
= 243
Mr Grant needs to buy 243 tiles.
Try it
Suppose Mr. Grant decides to buy square tiles that have side lengths of 3/4 foot. How many tiles will he need to buy?
Solution:
27 ÷ s^{2} = 27÷ (3/4)^{2}
= 27 ÷ (3/4 × 3/4)
= 27 ÷ 9/16
Evaluate the expression
27 ÷ 9/16 = 27× 16/9
= 48
Mr. grant needs to buy 48 tiles if the side lengths are 3/4 foot.
Key concept:
An algebraic expression can be written to represent a situation with an unknown quantity. Use a variable to represent the unknown quantity. An algebraic expression can be evaluated by substituting a value for the variable and performing the operations.
Then use the order of operations to simplify
Practice & Problem Solving
 The density, d, of an object can be found by using the formula d = m/v, where m is the mass of the object and visits volume. What is the density of an object that has a mass of 73,430 kilograms and a volume of 7 m³ ?
Solution:
Given that,
Mass of the object = 73,430 kg
Volume of the object = 7m³
Density = m/v
= 73,430 kg/ 7m³
= 10,490kg per m³
∴The density of the given object is 10,490 kg per m³
 Tamara is making a mediumlength necklace. Write an expression that shows how much it will cost Tamara for the chain pendant and b beads that cost $0.25 each. Then find the total cost of the necklace if Tamara uses 30 beads.
Given that,
Cost of each bead = $0.25
No. of beads used = 30
Total cost of medium necklace = $1.80 + 30 x $0.25 + $3.72
= $1.80 + $7.5 + $3.72
= $13.02
∴ The total cost of medium necklace is $13.02.
 The formula V=s3 can be used to find the volume of a cube. Use the formula to find the volume, V, of a cubeshaped bin with side lengths of 2/3 yards.
Solution:
Given that,
Length of the side of cubeshaped bin = 2/3 yards
Volume of the cube = s³
= (2/3)³
= 2/3 x 2/3 x 23
= 8/27 cubic yards
∴ The volume of the cubeshaped bin is 8/27 cubic yards
Let’s check our knowledge:
 Evaluate each expression for t = 8, w = 1212 and x = 3
i. 3t – 8. ii. 6w ÷ x + 9.
 Evaluate each expression for the value given.
i. z÷4, z = 824. ii. 6÷9 – 22, t=60.
 Evaluate the given expression for x = 1.8, x = 5, and x = 6.4.
2x + 3.1
 Evaluate the given expression for the value given 8 – g ÷ 7878 when g = 5656 .
 Katie is evaluating the expression 15.75 ÷p+ 3p when p= 3.15. Explain each step that she should follow.
Answers:
 Given that,
t = 8, w =1/2 and x = 3
i. 3t – 8 = 3 (8) – 8
= 24 – 8
= 16
ii. 6w ÷ x + 9 = 6(1/2) ÷ 3 + 9
= 3 ÷ 3 + 9
= 1 + 9
= 10

i. Given that,
z = 824
z ÷ 4 = 824 ÷ 4
= 206
ii. Given that,
t=60
6t÷9 – 22 = 6(60) ÷ 9 – 22
= 360 ÷ 9 – 22
= 40 – 22
= 18
 Given that,
Case 1
x = 1.8
2x + 3.1 = 2(1.8) + 3.1
=6.7
Case 2
x = 5
2x + 3.1 = 2(5) + 3.1
= 10 + 3.1
= 13.1
Case 3
x = 6.4
2x + 3.1 = 2(6.4) + 3.1
= 15.9
 Given that,
g = 5/ 6
8 – g ÷ 7/8 = 8 – 5/6 ÷ 7/8
= 8 – 5/6 x 8/7
= 8 – 20/21
= 168 −20/21
= 148/21
 Given that,
p= 3.15
Step 1
15.75 ÷p+ 3p = 15.75 ÷ 3.15 + 3(3.15) (Substitute the value of p in expression)
Step 2
15.75 ÷ 3.15 + 3(3.15) = 15.75 ÷ 3.15 + 9.45 (Simplify all terms)
Step 3
15.75 ÷ 3.15 + 9.45 = 5 + 9.45 (Use order of operations)
=14.45
Exercise
 Evaluate 30 + 4n when n equals 15, 16, or 17.
 Evaluate the expression 20 – 3t when t equals 20, 26, or 34.
 Mr. John wants to tile a 36 square foot area with square tiles. Let s= the side length in feet of a square tile. Use the expression 36+s^{2 }to find the number of tiles Mr. John needs to buy.
 Evaluate the expression for t=8, w= ½ , and x=3.
t^{2 }– 12w + x  Evaluate the expression for the value given.
z÷4: z=824  Evaluate the expression for w=5, x=3, y=4, and z=8.
W^{2}+2÷48÷2z  Evaluate the expression for x=1.8, x= 5 and x=6.4.
2x+3.1  Evaluate the expression for the value given.
J+ ⅜ ; J =¾  Evaluate the expression for the value of b=8.9.
b (3) + 20.4
Concept Map:
Related topics
Addition and Multiplication Using Counters & BarDiagrams
Introduction: We can find the solution to the word problem by solving it. Here, in this topic, we can use 3 methods to find the solution. 1. Add using counters 2. Use factors to get the product 3. Write equations to find the unknown. Addition Equation: 8+8+8 =? Multiplication equation: 3×8=? Example 1: Andrew has […]
Read More >>Dilation: Definitions, Characteristics, and Similarities
Understanding Dilation A dilation is a transformation that produces an image that is of the same shape and different sizes. Dilation that creates a larger image is called enlargement. Describing Dilation Dilation of Scale Factor 2 The following figure undergoes a dilation with a scale factor of 2 giving an image A’ (2, 4), B’ […]
Read More >>How to Write and Interpret Numerical Expressions?
Write numerical expressions What is the Meaning of Numerical Expression? A numerical expression is a combination of numbers and integers using basic operations such as addition, subtraction, multiplication, or division. The word PEMDAS stands for: P → Parentheses E → Exponents M → Multiplication D → Division A → Addition S → Subtraction Some examples […]
Read More >>System of Linear Inequalities and Equations
Introduction: Systems of Linear Inequalities: A system of linear inequalities is a set of two or more linear inequalities in the same variables. The following example illustrates this, y < x + 2…………..Inequality 1 y ≥ 2x − 1…………Inequality 2 Solution of a System of Linear Inequalities: A solution of a system of linear inequalities […]
Read More >>
Comments: