﻿ How to Divide using Distributive Property. Step by step Examples and practice problems

# Dividing using Distribution

### A Starting Example

As the above example of long division shows, we can "split up" the dividend (693) into a sum and distribute our division, one by one over each part. In this case, we split up the dividend 964 into 900 + 60 + 4, and we divide each part by 3, then at, the end we sum them all up. In this case, we split up the dividend 401 into 400 + 0 + 1, and we divide each part by 4, then at, the end we sum them all up. In this case, we split up the dividend 6,937 into 6000 + 900 + 30 + 7, and we divide each part by 3, then at, the end we sum them all up.

### What about carrying ?

All of the problems that we have done so far have not involved carrying remainders from one part to the next.

For instance, in the prior problem $$6837 \div 3$$ , our divisor 3 evenly divided into the following parts.
• $$6,000 \div 3$$ gives us the nice even quotient of 2,000
• $$900 \div 3$$ yields 300
• $$30 \div 3$$ yields 10

It's not till the very last part of 7 that a remainder comes into play. The same thing occurs with the first problem that we did.

Or look at the first problem we did, our divisor 3 evenly divided into each part. $$900 \div 3$$ gives us the nice even quotient of 300 and $$600 \div 3$$ yields 200 exactly etc..

### What if we change one digit?

We are going to change the first digit , from our first problem, by one.
##### Problem 4 (with carrying)

Let's take our old question 1 and change the first digit. How should we approach this now? 