Topics
5. Expressions
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United States of America
Grade 6

5.05 Substitute into algebraic expressions

Lesson
Practice

Introduction

We have already learned how to  represent algebraic expressions  . We now know what coefficients and variables of each term of an expression are. We will now substitute values in place of variables to evaluate expressions.

Substitution into algebraic expressions

When solving algebraic expressions, we often need to substitute specific values in for the variables .

We can substitute any numbers including whole numbers, decimals, and fractions.

When we substitute a number into an expression and find its value we call this evaluating the expression for the given value. To evaluate an expression, we use the same  order of operations  , often represented by the acronym PEMDAS. Let's work through some examples.

Examples

Example 1

Evaluate 8x+4 when x=2.

Worked Solution
Create a strategy

Substitute the given value for x into the expression, then evaluate using order of operations.

Apply the idea
\displaystyle 8x+4\displaystyle =\displaystyle 8\times 2+4Replace x with 2
\displaystyle =\displaystyle 16+4Evaluate the multiplication
\displaystyle =\displaystyle 20Evaluate the addition

Example 2

Evaluate 6x+4y+6 when x=3 and y=5.

Worked Solution
Create a strategy

Substitute the given values for x and y into the expression, then evaluate using the order of operations.

Apply the idea
\displaystyle 6x+4y+6\displaystyle =\displaystyle 6\times 3+4\times 5+6Replace x with 3, and y with 5
\displaystyle =\displaystyle 18+20+6Evaluate the multiplication
\displaystyle =\displaystyle 44Evaluate the addition

Example 3

Energy can be measured in many forms. A quantity of energy is given in units of Joules (\text{J}). The kinetic energy, E, of an object in motion is calculated using the formula:

E = \dfrac{m v^{2}}{2}

where m is the mass of the object in kilograms and v is the speed of the object in meters per second.

Find the kinetic energy, E, of an object with a mass of 6 \text{ kg}, traveling at a speed of 19 \text{ m/s}.

Worked Solution
Create a strategy

We can calculate the value of E for this object with the formula given by replacing m and v with the correct values.

Apply the idea

Let m=6 and v=19

\displaystyle E = \dfrac{m v^{2}}{2}\displaystyle =\displaystyle \dfrac{6\times (19)^{2}}{2}Substitute the values of m and v
\displaystyle =\displaystyle \dfrac{6\times 361}{2}Evaluate the exponent
\displaystyle =\displaystyle \dfrac{2166}{2}Evaluate the multiplication
\displaystyle =\displaystyle 1083Evaluate the division

The kinetic energy is 1083 J.

Idea summary

We can substitute any numbers including whole numbers, decimals, and fractions into an algebraic expression by replacing the variable. Then we can use the order of operations to evaluate the expression.

Outcomes

6.EE.A.2

Write, read, and evaluate expressions in which letters stand for numbers.

6.EE.A.2.C

Evaluate expressions at specific values for their variables. Include expressions that arise from formulas in real-world problems. Perform arithmetic operations, including those involving whole-number exponents, in the conventional order when there are no parentheses to specify a particular order (order of operations).

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