C2.2 Evaluate algebraic expressions that involve whole numbers and decimal numbers.
Skill: Evaluating Algebraic Expressions Involving Whole Numbers and Decimal Numbers
To evaluate an algebraic expression, the variables are replaced with numerical values and calculations are performed based on the order of operations.
When students are working 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(7.2) when m = 7.2. The operation between 4.5 and (7.2) is understood to be multiplication.
Source: The Ontario Curriculum. Mathematics, Grades 1-8 Ontario Ministry of Education, 2020.
Example
Evaluate the following algebraic expressions, if x = 2.25 and a = 1.5.
Evaluate the Algebraic Expression With the Help of an Illustration
To evaluate this expression, I place a group of 3x plus the variable a, minus 1. Later, I replace the variable x with the value of 2.25 and the variable a with the value of 1.5. Having all my values in the expression, I can now solve the expression.
2 equations:3 squares are marked with an ‘x’, plus, one square marked ‘a’, minus, one square marked one.3 squares are marked 2 decimal 25, plus, one square marked one decimal 5, minus, one square marked one. Here are the calculations:2 decimal 25, plus, 2 decimal 25, plus, 2 decimal 25, plus, one decimal 50, minus, one, equals, 6 decimal 75, plus, one decimal 5, minus, one.Equals 8 decimal 25, minus one.Equals 7 decimal 25.
Evaluate the Algebraic Expression Symbolically
\(\begin{align} 3x+ a- 1 &= 3 (2.25) + 1.5 - 1 \\ &= 6.75 + 1.5 - 1 \\ &= 8.25 - 1 \\ &= 7.25 \end{align}\)Source : En avant, les maths!, 6e, CM, Algèbre, p. 3-4.