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4 Algebra
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Australia
Year 8

4.06 Substitution

Lesson
Worksheet
Practice
Lesson

Substitution

We've seen how to substitute numerical values for pronumerals before. We follow the same process when the numerical values are negative.

Examples

Example 1

Find the value of m+n when m=6 and n=-4.

Worked Solution
Create a strategy

Replace m with 6 and n with -4.

Apply the idea
\displaystyle m+n\displaystyle =\displaystyle 6+(-4)Substitute the values
\displaystyle =\displaystyle 2Evaluate

Example 2

Find the value of \dfrac{p}{2q} when p=-28 and q=-7.

Worked Solution
Create a strategy

Replace p with -28 and q with -7.

Apply the idea
\displaystyle \dfrac{p}{2q}\displaystyle =\displaystyle \dfrac{-28}{2\times (-7)}Substitute the values
\displaystyle =\displaystyle \dfrac{-28}{-14}Evaluate the denominator
\displaystyle =\displaystyle 2Evaluate the quotient

Example 3

Find the value of k^2 when k=-7.

Worked Solution
Create a strategy

Replace k with -7.

Apply the idea
\displaystyle k^2\displaystyle =\displaystyle (-7)^2Substitute the values
\displaystyle =\displaystyle 49Evaluate the power
Reflect and check

When substituting a negative, it is important to use brackets to make sure that we apply the operation to both the negative sign and the number.

If we had not used brackets in this example, we could have forgotten to square the negative and gotten the wrong answer:

\displaystyle k^2\displaystyle =\displaystyle -7^2Forgot to use brackets
\displaystyle =\displaystyle -49Incorrect answer
Idea summary

It is important that when we substitute values, the value that we substitute fits into exactly the same position as the pronumeral, and that we follow the order of operations.

Outcomes

ACMNA192

Simplify algebraic expressions involving the four operations

ACMNA193

Plot linear relationships on the Cartesian plane with and without the use of digital technologies

ACMNA194

Solve linear equations using algebraic and graphical techniques. Verify solutions by substitution

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