Equations show that two things are equal using an equal sign =.
Each side of an equation is called an expression.
In a balanced equation, the left side, or left expression, is equal to the right side.
If the sides aren't equal, the equation isn't balanced. It's called an inequality.
Tip: Imagine that each side of an equation is like a bowl of marbles. In a balanced equation, both bowls have the same weight.
The simplest an expression can be is just a number, like 4.
Expressions can also be more complex, and have operators like + or -.
You can rewrite any operator between two numbers as just a number. This is called simplifying the expression. Take a look:
Tip: You can swap out any parts of an equation you want as long as they have the same value.
You can even add anything you want to one side of an equation. As long as you add it to both sides, any equation will stay balanced.
You can also subtract anything from both sides of an equation.
Knowing this can come in handy.
Tip: It's like taking the same number of marbles out of two bowls.
Sometimes equations have missing parts. Take a look:
Your teachers may ask you to "balance this equation". That just means to find the value of the unknown part that keeps it balanced.
To find the unknown part, get it alone on one side of the equation.
How do we do that?
1️⃣ First, we simplify anything we can.
Can we simplify the expression on the left? Yes. 3 + 2 = 5.
Now, the left side is as simple as can be.
Next, we need to take away whatever is on the right side to get the unknown part alone.
To do that, we have to take the same number away from both sides to keep the equation balanced.
Tip: It's like taking a marble out of two bowls.
Now, we can simply the left side again to find the value of the unknown part.
Tada! We found the value of the unknown part: 4. ✅
You just learned the basics of what people call algebra.
You also learned that to balance an equation means to get the unknown part alone on one side, so you can see its value.
To do this, you use two math tricks: you simplify, and you add or subtract from both sides.
Awesome!
Let's try balancing one more equation together.
First, we simplify any expression we can.
To simplify means to perform operations until only numbers are left.
Let's simplify the left side.
To get the unknown part alone, we can subtract 89,000 from both sides.
This cancels out the 89,000 on the right side.
The last step is to simplify the left expression, using column form subtraction.
Awesome, we found the answer. The unknown part is 23,800!
Let's check our answer by plugging it back in to the original equation:
The left side is equal to the right side! 👍 The equation is balanced. We found the right answer. ✅
Excellent job learning how to balance equations.
Now, complete the practice. It'll help you master this important skill.