We've already learned how to balance addition, subtraction, and multiplication equations.
In this lesson, we will learn how to balance division equations.
An equation shows two sides that are equal.
Each side of an equation is called an expression. An expression can have numbers or operators.
Whenever we balance an equation, we make sure that the left side and the right side have the same values.
Are these two expressions equal?
We figure it out by simplifying the expressions.
To simplify means to find the number value of an expression by performing the operations in it.
Let's simplify the left side of the equation above.
8 ÷ 4 = 2
Now let's simplify the right side.
6 ÷ 3 = 2
Is our equation balanced?
Yes! It's balanced because the value of both sides is 2. ✅
Let's try a few more examples.
Balance the equation by finding the missing number.
First, simplify the expression on the left.
We divide 20 by 5.
Now, we want to get the unknown part alone on one side of the equals sign, so we can see exactly what it equals.
One way to do that is to multiply both sides by 4. Check it out:
4 = ___ ÷ 4
4 × 4 = ___ ÷ 4 × 4
Remember: You can add, subtract, multiply, or divide any number to one side of an equation, and as long as you do it to the other side too, the equation stays balanced.
Tip: It's like taking the same number of marbles out of two bowls that weight the same.
So, after we multiply by 4 on both sides, we cancel out the division on the right side, and we get our answer.
4 × 4 = ___ ÷ 4 × 4
4 × 4 = ___÷ 4 × 416 = ___
The missing number is 16! ✅
Let's check if we got the right answer by plugging it back in to the problem:
We simplify the numbers on the left.
20 ÷ 5 = 4
Then, we simplify the numbers on the right.
16 ÷ 4 = 4
Both sides are equal. So yes, the equation is balanced.
Great job! 👏
Let's balance this equation:
The first step is to simplify the expression on the right side.
When we divide 36 by 3, we get 12.
This means the value on the left should also be 12.
Earlier, you learned about related division equations. Here are two related division equations:
72 ÷ ___ = 12
72 ÷ 12 = ___
If we figure out the answer to the bottom equation, then we'll have our answer to the top equation too!
So, we divide 72 by 12 to find the missing part.
72 ÷ 12 = 6
The missing number is 6. ✅
Let's plug our answer 6 back into the equation to see if it's correct:
Simplify the expression on the left.
72 ÷ 6 = 12
Then, simplify the expression on the right.
36 ÷ 3 = 12
Both expressions equal 12. So, yes, the equation is balanced. 👏
Let's balance one more equation together:
First, we simplify the equation.
Let's divide the numbers on the left side.
This means that the value of the right side should also be 16.
Now, to find the missing part, you've learned a few tricks you can use already.
This time, let's think about the whole-part model.
80 is the whole, and we're dividing it by an unknown part to get another part, 16.
So to find the unknown part, we divide the part we do know, 16, from the total, 80.
80 ÷ 16 = 5
The missing number is 5. ✅
Let's put that 5 back into our equation to see if we got the right answer:
Let's simplify both sides to see if it's balanced.
96 ÷ 6 = 16
80 ÷ 5 = 16
Yes, it's balanced! Both sides have the same value.
Now, try the practice to help you learn more and remember for longer.