Topics
3. Numeric & Algebraic Expressions
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United States of AmericaVirginia
Grade 7

3.04 Evaluate algebraic expressions

Lesson
Practice

Evaluate algebraic expressions

A bakery is having a grand opening sale. They are selling cookies for \$1.50 each and muffins for \$2.25 each.

Emily goes to the bakery and buys 4 cookies and 3 muffins. We can represent her purchase like this:

Pictorial representation: $1.50 times 4 cookies + $2.25 times 3 muffins

We can use the expression 1.50c+2.25m to represent the cost for buying different amounts of cookies and muffins.

We can find the cost of Emily's purchase by using substitution. To find the value of (or evaluate) the expression with substitution, we will replace the amount of each item Emily bought with the variables in the the expression. This will look like this: 1.50\left(4\right)+2.25\left(3\right)

Now, we can use what we know about the order of operations and properties of real numbers to evaluate the expression to find the total that Emily spent.

\displaystyle \text{Total Spent}\displaystyle =\displaystyle 1.50\left(4\right)+2.25\left(3\right)Begin with the expression
\displaystyle =\displaystyle 6+6.75Evaluate the multiplication
\displaystyle =\displaystyle 12.75Evaluate the addition

The total cost of Emily's purchase is \$12.75.

Examples

Example 1

Evaluate \dfrac{3}{4}g + 20-\dfrac{1}{2}g-h, when h=7 and g=-8.

Worked Solution
Create a strategy

First, we will substitute the given values for g and h. Next, we will evaluate the expression using the order of operations.

Apply the idea
\displaystyle \frac{3}{4}g + 20-\frac{1}{2}g-h\displaystyle =\displaystyle \frac{3}{4}\left(-8\right) + 20-\frac{1}{2}\left(-8\right)-\left(7\right)Substitute the given values
\displaystyle =\displaystyle -6 + 20-\left(-4\right)-7Evaluate the multiplication
\displaystyle =\displaystyle 14-\left(-4\right)-7Evaluate the addition
\displaystyle =\displaystyle 11Evaluate the subtraction

Example 2

Evaluate\text{ }a\left(b-c\right)−3ac when a = -1.25, b = 13.4, and c = 7.3

Worked Solution
Create a strategy

First we will substitute the given values for a, b, and c. Then we will use the order of operations to decide which operation to perform first.

Apply the idea
\displaystyle a\left(b-c\right)−3ac\displaystyle =\displaystyle -1.25\left(13.4-7.3\right)-3\left(-1.25\right)\left(7.3\right)Substitute the given values
\displaystyle =\displaystyle -1.25\left(6.1\right)-3\left(1.25\right)\left(7.3\right)Evaluate the subtraction inside of the parentheses
\displaystyle =\displaystyle -7.625-\left(-27.375\right) Evaluate the multiplication
\displaystyle =\displaystyle 19.75Evaluate the subtraction

Example 3

The area, A, of a circle is given by the formula: A=\pi r^{2}

where r is the length of its radius.

Find the area of a circle with a radius of 12 \text{ ft}. Use 3.14 for the value of \pi.

Worked Solution
Create a strategy

First, we will substitute the given values into the formula. Then, we will use the order of operations to calculate the area.

Apply the idea
\displaystyle A=\pi r^{2}\displaystyle =\displaystyle \left(3.14\right)\left(12\text{ ft}\right)^{2}Substitute the given values
\displaystyle =\displaystyle \left(3.14\right)\left(144\text{ ft}^{2}\right)Evaluate the exponent
\displaystyle =\displaystyle 452.16\text{ ft}^{2}Evaluate the multiplication
Reflect and check

Remember that \pi is not a variable, it is always equal to the same value (approximately 3.14).

Idea summary

To evaluate expressions for given values, you will first substitute the values into the expression. Next, we use order of operations to evaluate expresion.

Outcomes

7.PFA.2

The student will simplify numerical expressions, simplify and generate equivalent algebraic expressions in one variable, and evaluate algebraic expressions for given replacement values of the variables.

7.PFA.2d

Use the order of operations and apply the properties of real numbers to evaluate algebraic expressions for given replacement values of the variables. Exponents are limited to 1, 2, 3, or 4 and bases are limited to positive integers. Expressions should not include braces { } but may include brackets [ ] and absolute value bars | |. Square roots are limited to perfect squares. Limit the number of replacements to no more than three per expression. Replacement values may be positive or negative rational numbers.

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