C2.2 Evaluate algebraic expressions that involve whole numbers and decimal tenths.
Skill: Evaluating Algebraic Expressions Involving Whole Numbers and Decimal Tenths
To evaluate an algebraic expression, variables are replaced with numerical values and calculations are performed according to the order of operations.
When students work with formulas, they are evaluating expressions.
Replacing the variables with numerical values often requires the use of brackets. For example, the expression 4.5m becomes 4.5(m) and then 4.5(7) when m = 7. The operation between 4.5 and (7) is understood to be multiplication.
Source: Ontario Curriculum, Mathematics Curriculum, Grades 1-8, 2020, Ontario Ministry of Education.
Example
Evaluate the algebraic expression below if \(x = 2.25\) and \(a = 1.5\).
Evaluate the Algebraic Expression With an Illustration
To evaluate this expression, I place a group of 3x plus the variable a, minus 1. Then, I replace the variable x with the value of 2 and the variable a with the value of 1.5. Having all my values in the expression, I can now evaluate the expression.
Here are my calculations:
\(\displaylines{\begin{align} \color{blue} 2 \color{black} + \color{blue} 2 \ \color{black} + \color{blue} \ 2 \color{black} + \color{red} 1,5 \color{black} - 1 &= \color{blue} 6 \color{black}+ \color{red} 1.5 \color{black} \ - \ 1 \\ &= \color{black}7.5 \ - \ 1 \\ &= 6.5 \end{align}}\)
Evaluate the Algebraic Expression Symbolically
\(\displaylines{\begin{align} 3x+a \ - \ 1 &= 3 \ (2) + 1,5 \ - \ 1 \\ &= 6 + 1.5 \ - \ 1 \\ &= 7.5 \ - \ 1 \\ &= 6.5 \end{align}}\)
Source: inspired by and translated from En avant, les maths!, 6e année, CM, Algèbre, Évaluation d'expressions algébriques, p. 3-4.
Knowledge: Expression
An expression is a numeric or algebraic representation of a quantity. An expression may include numbers, variables, and operations. Specifically, an expression such as 3 + n + 4 is an algebraic expression, since it contains numbers and symbols.
Note: An expression containing only numbers is a numeric expression, for example 5 - 2.
Source: Ontario Curriculum, Mathematics Curriculum, Grades 1-8, 2020, Ontario Ministry of Education.