Solving Division Patterns Over Increasing Place Values

Instructor: T.J. Hoogsteen

T.J. is currently a grade 5 teacher and Vice-Principal. He has a master's degree in Educational Administration and is working toward an Ed.D. in Educational Leadership.

In this lesson, you will learn how to identify division patterns over increasing place values by using basic division facts. A quiz will follow the lesson.

A Horrible Nightmare

It can be a nightmare to walk into class in the morning and find a quiz question on the board that you haven't studied for. Let's say you've only been learning to do division problems with single digits, but today you see this question on the board: 60 ÷ 3 =

The panic might really start to set in. We never learned how to divide numbers that big - how can we be expected to answer this question?

The truth is, in all that panic you may have answered your own question already! When presented with a problem like the one above, basic division steps you already know can be used to help solve division equations when one of the digits increases in place value. These steps can help even if both numbers in the equation increase in place value. Keep reading to find out how.

Solving Division Patterns Over Increasing Place Values

First of all, what exactly does increasing place value mean? The easy answer is when you add a zero to the end of a number (such as adding a 0 to 6 to make 60) the place value is being increased because the number '6' is being moved from the ones place to the tens place. Now, to solve an equation like the one pictured above, the first step is to look at the dividend (the number being divided) and the divisor (the number of groups the dividend is being divided into). In this situation, look at the digits that are not zeroes - that leaves 6 and 3. This is an equation that can be easily solved: 6 ÷ 3 = 2

If we go back to the first equation, in really simple terms, 60 is really just 6 with a zero added at the end, so when dividing 60 by 3, think of 6 divided by 3. Then add a zero to the quotient (the solution to a division equation), like this:


Now imagine the teacher changed the equation to 600 divided by 3. Again, forget about the zeroes and focus on 6 divided by 3. Since 600 has two zeroes, two zeroes go in the answer, like this:


To answer equations where the dividend has a large place value, focus on dividing the dividend's first digit by the divisor and then make sure the quotient has the same amount of zeroes as the dividend.

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