3.3.8 More Division Strategies

Admittedly, division is usually more difficult than multiplication, but you can help yourself by having a good knowledge of the multiplication tables. In addition to this there are some other approaches we might use when dividing to help.

1. Using Groups of the Divisor

One way of looking at division problems is to see the problem as a question about the number of groups. For example, if the problem is 159 division 13, you may think, “How many groups of 13 are in 159?”

This approach uses multiplication to create groups of the divisor, keeping track of what part of the dividend remains. You may think about ten groups of 13, or 10 multiplication 13 equals 130. Next, you would subtract 130 from 159 mentally, leaving 29. Recognize that two more groups of 13 can “fit” into what remains, accounting for 26 more with only three left over. So 13 goes into 159 a total of 10 plus two equals 12 times, with three left over. To check that, multiply 12 multiplication 13 equals 156, and 156 plus three equals 159. Bravo!

2. Breaking the Dividend into Parts

In this strategy, think about the dividend first, and how it can be broken up into numbers that are easier to divide by the divisor. For example, for the problem 159 division 13, you could think: “How can I break 159 apart to make this an easier problem to solve?”

You might think of this as:

multiline equation line 1 equation left hand side 159 division 13 equals right hand side open 130 division 13 close plus open 29 division 13 close line 2 equation left hand side equals right hand side open 10 close plus open 29 division 13 close line 3 equation left hand side equals right hand side sum with, 3 , summands 10 plus two plus open three division 13 close line 4 equation left hand side equals right hand side 12 r times e times m times a times i times n times d times e times r 13 line 5 equals 12 cap r times three

Of course, there are many other strategies. Let’s look at two more that you might find useful in different situations.

3.3.7 Commutative Property

3.3.9 Equivalent Problems (Division Strategies)