In Saxon Algebra 1, Grade 9 students learn to subtract real numbers by converting subtraction problems into addition of the additive inverse, applying the rule that subtracting a number is equivalent to adding its opposite. The lesson covers the Inverse Property of Addition, subtraction of integers, decimals, and fractions with positive and negative values, and the concept of closure under subtraction for sets such as integers and rational numbers. Students also apply these skills to real-world problems involving depth, temperature, and financial calculations.
Section 1
📘 Foundations of Algebra
Algebra is built on fundamental properties. The Inverse Property of Addition states that for every real number , .
We'll begin by applying these foundational rules to the subtraction of real numbers. Soon, you’ll work through examples showing how opposites make subtraction much simpler.
Section 2
Opposites
For every real number , .
Opposites, like 7 and -7, are numbers with the same distance from zero but on opposite sides. When you add them together, they cancel each other out perfectly, always resulting in zero. Think of it as a perfect mathematical balance.
Section 3
Rules for Subtracting Real Numbers
To subtract a number, add its inverse. Then follow the rules for adding real numbers.
Subtraction is secretly addition! Instead of subtracting, just add the opposite number. This 'Keep-Change-Change' trick turns every tricky subtraction problem into a much simpler addition problem you already know how to solve.
Section 4
Application:Dive Depth
When representing positions relative to a reference point (like the surface of the water), depths below the surface are negative numbers and positions above the surface are positive numbers. Adding or subtracting these values helps determine new positions.
(−23) + (−12) = −35 → 35 meters below the surface ✅
(−15) + 5 = −10 → 10 meters below the surface ✅
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Section 1
📘 Foundations of Algebra
Algebra is built on fundamental properties. The Inverse Property of Addition states that for every real number , .
We'll begin by applying these foundational rules to the subtraction of real numbers. Soon, you’ll work through examples showing how opposites make subtraction much simpler.
Section 2
Opposites
For every real number , .
Opposites, like 7 and -7, are numbers with the same distance from zero but on opposite sides. When you add them together, they cancel each other out perfectly, always resulting in zero. Think of it as a perfect mathematical balance.
Section 3
Rules for Subtracting Real Numbers
To subtract a number, add its inverse. Then follow the rules for adding real numbers.
Subtraction is secretly addition! Instead of subtracting, just add the opposite number. This 'Keep-Change-Change' trick turns every tricky subtraction problem into a much simpler addition problem you already know how to solve.
Section 4
Application:Dive Depth
When representing positions relative to a reference point (like the surface of the water), depths below the surface are negative numbers and positions above the surface are positive numbers. Adding or subtracting these values helps determine new positions.
(−23) + (−12) = −35 → 35 meters below the surface ✅
(−15) + 5 = −10 → 10 meters below the surface ✅
Book overview
Jump across lessons in the current chapter without opening the full course modal.
Continue this chapter