Most of us grew up learning the basic method for long division. (Forget what that means? Watch the “Dividing by a Single Digit video for a review“)! Today, our kids are learning many new methods of long division. Here we explain the box method for long division. Let Homework Unlocked teach you these new methods so that you can help your kids with their math homework!
If you only have time to listen to the lesson, feel free to click on our audio file below.
New Methods for Long Division: Box Method Division
The box method of long division breaks up the dividend into smaller pieces by subtracting multiples of the divisor. To use this method:
First, set up your box. To set up your box, draw a box and place your divisor on the outside of the box and your dividend on the inside.
Next, break up your dividend by multiples of the divisor until you reach zero or you have a remainder.
This sounds more complicated in the abstract, so let’s go through an example together.
Example: Divide 423 by 3 using the box method.
Step 1. Set up your box. Draw a box and place your divisor,3, on the outside of the box and your dividend, 423, inside the box nearly touching the top.
Step 2. We need to find a large multiple of our divisor to subtract from our dividend. Since our dividend is a 3 digit number let’s start with 100. Place 100 above the box and then subtract 3 x 100 from the quotient. 423 – 300 = 123. (please note, if we started with 200, then our product of 3 times 200 would be greater than our dividend and wouldn’t work).
Next, Add an additional box to the right and move what’s left of our quotient, 123, to the new box.
Step 3. We need to find a multiple of our divisor to subtract from what is left of the dividend. 300 is too large so let’s try a 2- digit multiple. 40 is our next greatest multiple of 10 that fits evenly within what is left of the dividend 3 x 40 = 120,. (you could choose a smaller multiple of 10, but then you would need to add additional steps before you reached the final quotient).
Place a 40 above the box and subtract 3 x 40 from the quotient.
3 x 40 = 120, 123 – 120 = 3.
Since we still have a remainder (3), add an additional box to the right of your original box, and move what is left of the quotient, 3, to the new box.
Step 4. Now we only have 3 left of our quotient. The only multiple of the divisor that fits is 1. Place a 1 above the box and subtract 3 from the quotient. 3 – 3 = 0 we’re all done!
The Box method is computationally very similar to the Division by Multiples of 10, so it may be helpful to review this video as well! (see our video, New Methods for Long Division: Division by Multiples of 10). When comparing the two methods, just remember that the notation is very different.
For a more complicated example of the box method, please see our video “the box method of long division when there is a remainder”
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