Absolute Value Symbols
Absolute value symbols in Grade 7 act as symbols of inclusion (like parentheses) in expressions, requiring you to evaluate the expression inside before taking the absolute value. In Saxon Math, Course 2, students follow the order of operations treating absolute value bars as grouping symbols: simplify inside first, then find the absolute value, then continue with remaining operations. For example, 12 + 3|8 - 2| = 12 + 3|6| = 12 + 18 = 30. This understanding ensures correct multi-step computation and prepares students for absolute value in algebraic contexts.
Key Concepts
Property Absolute value symbols may serve as symbols of inclusion. We find the absolute value as the first step of simplifying within the parentheses.
Examples $12 (8 |4 6| + 2) = 12 (8 | 2| + 2) = 12 (8 2 + 2) = 4$ $12 + 3|8 2| = 12 + 3|6| = 12 + 3(6) = 12 + 18 = 30$ $20 |10 5 \cdot 3| = 20 |10 15| = 20 | 5| = 20 5 = 15$.
Explanation These bars are a priority! Solve the math inside them and take the positive result before you do other operations inside the parentheses. It's a special grouping symbol that demands you handle its contents first, turning any result into a positive value for the main calculation.
Common Questions
What role do absolute value symbols play in order of operations?
Absolute value bars act as grouping symbols (like parentheses). You simplify the expression inside the bars first, then evaluate the absolute value, before continuing with multiplication, addition, or other operations.
How do you simplify an expression with absolute value?
Follow order of operations inside the absolute value bars first, then take the absolute value (make the result non-negative), then continue with the remaining operations outside.
Can you show an example with absolute value and other operations?
12 + 3|8 - 2| = 12 + 3|6| = 12 + 3(6) = 12 + 18 = 30. The subtraction inside the bars is done first.
What is the absolute value of a negative number?
The absolute value of a negative number is its positive equivalent. |−5| = 5 because absolute value measures distance from zero, which is always non-negative.
Where are absolute value symbols as grouping tools taught in Saxon Math Course 2?
This use of absolute value is covered in Saxon Math, Course 2, as part of Grade 7 order of operations and integer operations.
How is absolute value different from just removing the negative sign?
Absolute value evaluates the expression inside fully before taking the non-negative value. For example, |10 - 15| = |-5| = 5, not 10 - 15 with sign removed directly.
What common mistakes do students make with absolute value expressions?
Students often evaluate the absolute value before completing operations inside the bars, or mistake absolute value bars for the number 1 in multiplication contexts.