Adapted from Wentworth's Elementary Algebra for MathDoctor.net
In the last chapter, we learned that a Term is a chunk of math joined by multiplication. In this chapter, we learn how to add and subtract them. The golden rule of Algebra is: You can only add or subtract terms if they are exactly the same type.
Think of variables as objects. If you have 3 iPhones and someone gives you 2 more iPhones, you have 5 iPhones. In Algebra, we write that as:
3i + 2i = 5i
However, if you have 3 iPhones and 2 Androids, you cannot say you have "5 iPhone-Androids." You just have 3 iPhones and 2 Androids. In Algebra:
3x + 2y remains 3x + 2y
Simplify the following expressions by combining like terms:
Example 1: Social Media
You have f followers on Monday. You gain 10 more on Tuesday, and then 5 more on Wednesday.
Expression: f + 10 + 5
Simplified: f + 15
Example 2: App Subscriptions
A company pays for 8 z (Zoom) licenses and 5 s (Slack) licenses. Later, they cancel 3 z licenses.
Expression: 8z + 5s - 3z
Simplified: 5z + 5s
Example 3: Complex Grouping
Simplify: 10x + 4y - 3x + y
Step 1 (Group x): 10x - 3x = 7x
Step 2 (Group y): 4y + y = 5y
Final Answer: 7x + 5y
A very common mistake is trying to "over-simplify." Remember:
Do not combine numbers with variables!
The expression 5x + 10 cannot be turned into 15x. One is a variable term, and one is a constant. They must stay separate, like oil and water.
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In this chapter, we learned that you can't add an x to a y any more than you can add an apple to an orange. To really "see" these boundaries, nothing beats a physical model.
Magnetic Algebra Tiles are the gold standard for tactile learning. They allow you to physically group your "x-blocks" together and your "unit-blocks" together, making the logic of combining like terms second nature before you ever pick up a pencil.
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