In this Grade 9 Saxon Algebra 1 lesson, students learn to find the absolute value of integers, decimals, and fractions by measuring distance from zero on a number line. They then apply the rules for adding real numbers with the same sign and different signs, using absolute values to determine the sum and its sign. The lesson also introduces the concept of closure under addition for sets of integers and real numbers.
Section 1
🎯 Starting Point: Absolute Value
Absolute value measures a number's distance from zero on a number line. Since distance can't be negative, the absolute value is always a positive number or zero. For example, and .
First, we'll master finding the absolute value of any number. Then, we'll use that skill to learn the rules for adding real numbers—a fundamental skill for all of algebra.
Section 2
📘 The Language of Algebra
Algebra is a universal language that uses symbols, variables, and consistent rules to explore relationships and solve for unknown values.
This course is your guide to fluency. We'll start with the fundamental grammar: worked examples on finding absolute value and adding real numbers.
Section 3
Absolute Value
The absolute value of a number is the distance from to 0 on a number line. and .
Think of absolute value as a number's 'distance license'—it tells you how far you are from zero, but not which direction. Since distance can't be negative, the absolute value is always a positive number or zero. It’s like asking 'How many steps?' not 'Which way?'—so the answer is always positive!
Section 4
Adding Numbers With the Same Sign
To add numbers with the same sign, add their absolute values. The sum will have the same sign as the addends.
Imagine you're on a team. If you're on the 'Negative Team' and you add more negative players, your team just gets more negative! Just add up everyone's strength (their absolute values) and stick with your team's sign. You're either building a taller tower or digging a deeper hole together.
Section 5
Adding Numbers With Different Signs
To add numbers with different signs, find the difference of their absolute values. The sum will have the sign of the addend with the greater absolute value.
This is a tug-of-war between the Positive Team and the Negative Team! Find the difference in their strengths by subtracting the smaller absolute value from the larger one. The team with the bigger muscle (greater absolute value) wins the tug-of-war and gets to decide if the final answer is positive or negative.
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Section 1
🎯 Starting Point: Absolute Value
Absolute value measures a number's distance from zero on a number line. Since distance can't be negative, the absolute value is always a positive number or zero. For example, and .
First, we'll master finding the absolute value of any number. Then, we'll use that skill to learn the rules for adding real numbers—a fundamental skill for all of algebra.
Section 2
📘 The Language of Algebra
Algebra is a universal language that uses symbols, variables, and consistent rules to explore relationships and solve for unknown values.
This course is your guide to fluency. We'll start with the fundamental grammar: worked examples on finding absolute value and adding real numbers.
Section 3
Absolute Value
The absolute value of a number is the distance from to 0 on a number line. and .
Think of absolute value as a number's 'distance license'—it tells you how far you are from zero, but not which direction. Since distance can't be negative, the absolute value is always a positive number or zero. It’s like asking 'How many steps?' not 'Which way?'—so the answer is always positive!
Section 4
Adding Numbers With the Same Sign
To add numbers with the same sign, add their absolute values. The sum will have the same sign as the addends.
Imagine you're on a team. If you're on the 'Negative Team' and you add more negative players, your team just gets more negative! Just add up everyone's strength (their absolute values) and stick with your team's sign. You're either building a taller tower or digging a deeper hole together.
Section 5
Adding Numbers With Different Signs
To add numbers with different signs, find the difference of their absolute values. The sum will have the sign of the addend with the greater absolute value.
This is a tug-of-war between the Positive Team and the Negative Team! Find the difference in their strengths by subtracting the smaller absolute value from the larger one. The team with the bigger muscle (greater absolute value) wins the tug-of-war and gets to decide if the final answer is positive or negative.
Book overview
Jump across lessons in the current chapter without opening the full course modal.
Continue this chapter