Addition with Two Integers
Addition with two integers in Grade 8 Saxon Math Course 3 teaches students to add positive and negative whole numbers using rules for same-sign and different-sign cases. Students learn to add integers with the same sign by adding their absolute values and keeping the sign, and integers with different signs by subtracting their absolute values and using the sign of the larger absolute value. Proficiency with integer addition is foundational for all algebraic operations.
Key Concepts
Property To find the sum of addends with different signs: 1. Subtract the absolute values of the addends. 2. Take the sign of the addend with the greater absolute value. To find the sum of addends with the same sign: 1. Add the absolute values of the addends. 2. Take the sign of the addends.
Examples Different signs, negative wins: $( 12) + (+3) = 9$. The negative number has a larger absolute value. Same signs, both negative: $( 12) + ( 3) = 15$. The signs are the same, so we add and keep the sign. Different signs, positive wins: $(+12) + ( 3) = 9$. The positive number has a larger absolute value.
Explanation Think of adding integers like a game of tug of war on a number line! When signs are different, the team with the greater absolute value wins and gets to keep its sign, with the final score being the difference between their strengths. When signs are the same, they're on the same team, so just combine their power and keep the sign!
Common Questions
How do you add two integers with the same sign?
Add their absolute values and keep the common sign. For example, (-4) + (-3) = -7 and 4 + 3 = 7.
How do you add two integers with different signs?
Subtract the smaller absolute value from the larger, and use the sign of the integer with the larger absolute value. For example, (-7) + 4 = -3 because 7 > 4 and the result takes the negative sign.
What is the sum of 6 and -6?
The sum is 0. Two numbers with equal absolute values and opposite signs are called opposites, and their sum is always 0 (additive inverse).
How do you use a number line to add integers?
Start at the first integer on the number line. Move right for positive additions and left for negative additions. The endpoint is the sum.
How does Saxon Math Course 3 teach integer addition?
Saxon Math Course 3 introduces integer addition with number lines and sign rules, then applies integer addition in algebraic expressions, equations, and real-world contexts like temperature and elevation.