In the last lesson, you learned how to complete subtraction equations like this:
894 - ? = 447
Now, what if we have subtraction on both sides of the equation, like below?
752 - ? = 586 - 213
Let's learn how to solve it.
Subtraction is taking away part of a number.
Every part of a subtraction equation has a name.
The minuend is the big number that we take away from.
Think of it as the whole, and you take away some part to get another part.
We call this the whole-part model, or way of thinking.
If you have a missing part, you subtract the part you know from the whole.
So to find the missing part above, we just solve:
5 - 3 = ?
Here's another example of finding a missing part, this time with 3-digit numbers:
We think about it the same.
We swap the subtrahend and difference (the two parts) to get the unknown part alone on the right side of the equals sign. Then we can see exactly what it equals.
Awesome!
Now, what if you're missing the minuend, or whole?
If you're missing the whole (minuend), you add the parts you know to find the whole.
So to solve:
? - 3 = 2
We just need to figure out:
? = 2 + 3
Here's another example with three-digit numbers:
To find the missing whole, or minuend, we add the two parts we know, the subtrahend and difference.
Your teachers may ask you to "balance the equation" below.
This just means to find the value of the missing part that will keep it balanced, or true.
Let's practice balancing an equation together:
698 - ? = 560 - 237
How are we going to solve it?
First, simplify any numbers that you can. Then, use the whole-part diagram to figure out what's missing.
Let's try it.
The right-side of this equation is complete. It can be simplified. It has no missing parts.
Let's simplify and rewrite the right side:
Now, let's use the whole-part model.
Ask yourself, "Are we missing the whole or one of its parts?"
Very good. We're missing one of the parts.
To find the missing part, we subtract the part we know from the whole.
698 - 323 = ?
You can use column form to find the answer.
Nice job. The missing number is 375. ✅
Let's see if we got the right answer by plugging it back in to the original equation.
698 - 375 = 560 - 237
Great work. This equation is balanced, as both sides have the same value, 323.
Let's balance this equation:
341 - 174 = ? - 425
First, simplify.
Perfect!
Now, once again, we have a simple subtraction equation.
The minuend is missing.
? - 425 = 167
Ask yourself, "is the whole or a part missing?"
The whole is missing.
To find the missing minuend (whole), we need to add the two parts.
425 + 167 = ?
We use column form to find the sum:
Great work. The missing number is 592.
Let's plug that back in to our equation and see if it's balanced.
341 - 174 = 592 - 425
Awesome! 👏 This equation is balanced since both sides have the same value, 167.
Think you got it? Try the practice.
A bit confused? See our 4th grade lesson on balancing subtraction equations. It teaches how to solve equations without the whole-part model.