Beginning Division Simplified

Simplified AMAP (As Much As Possible), That Is

This is a follow-on post to the one on multiplication here.

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Division can, like multiplication, sometimes seem a little daunting, so let’s run through a couple of simple examples.

First, though, let’s get the division symbol down:

You might see the division symbol like this: ÷, such as: 42 ÷ 6

…but it’s easier to work out division challenges using this funky little dude: ⟌ , such as: 6 ⟌ 42

The number under the symbol is called the dividend (in this example 42); the number to the left is the divisor (in this case 6); the answer, which is called the quotient, is written (by you) above the symbol.

To figure out how many times six “goes into” 42 (either exactly or without exceeding 42), you can either count up: 6 (once), 12 (twice), 18 (thrice), 24 (four times), 30 (five times), 36 (six times), 42 (seven times—voila! an exact match!), or you can use the handy multiplication table:

NOTE: Multiplication and Division are mathematical cousins; in fact, if you eventually learn some algebra, you could restate the challenge “42 ÷ 6” as “6 x n = 42”, where “n” will be replaced with the answer or quotient

Find the number 42 in the 6’s row (since 6 is the divisor, that’s the row you want to horizontally follow). The 42 is rectangled in a beautiful amber hue in the table above. Then see which column the 6’s 42 is in. If you follow the column vertically to the top, you’ll see that the 42 is in the 7’s column, which is the answer/quotient to the division challenge. Your work should look like this:

Now let’s try a division challenge that’s a little more complicated (which doesn’t have an exact match on the multiplication table to provide you with the quotient). Let’s figure out the quotient for 71 ÷ 8, or:

8 ⟌ 71

Consulting the multiplication table, you won’t find a “71” in the 8’s row. You will see a 72, which is close to 71, but is too big a number. So, go with the next closest but lower number in the row (64). What’s the initial part of the answer? Look up the column to discover an 8. Here’s how your work should look so far:

But 64 is obviously not 71. You have “leftovers” or, in math-speak, a remainder. To get the exact value of the remainder, multiply the divisor (8) by the quotient (also 8). You should come up with 64. Now subtract that from the dividend. Doing so leaves you with 7, which is the remainder. Write it like so:

…and then append (add) the remainder to the quotient, with the letter “r” signifying that what follows is the remainder:

And voila! That’s how to do simple division.

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To learn how to do more advanced division, see the following videos (part of the “Math Antics” series of videos):

Math Antics Long Division

Math Antics Long Division with 2-Digit Divisors

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÷

⟌

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