| There is another way that we can write division problems. Say we have: | ||
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21 ÷ 3 |
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| Another way to do this is: | ||
| Write down the 3 and the 21 next to each other, | ||
| like this: | ||
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| And draw a line that goes between the numbers and over the 21, | ||
| like this: | ||
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| Now we're ready to start. | ||
| Since what we're dividing by is a 3, | ||
| we need to think about dividing things into 3 piles. | ||
| Start with the first number under the lines (the 2). | ||
| Can we divide 2 into 3 piles evenly? | ||
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| What do you mean evenly? | ||
| I mean with whole numbers, not fractions. | ||
| No, we can't. | ||
| Can we divide it up so that there is at least 1 whole one in each pile? | ||
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No, we can't. |
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| OK, then we go on. | ||
| Look at the next number under the lines too. | ||
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| Can we divide 21 into 3 piles evenly? | ||
| I think so: | ||
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| So there are 7 in each pile. Write 7 above the 1 in 21. | ||
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| Now multiply the number on the top (the 7) | ||
| times the number on the left (the 3). | ||
| Write the answer under the 21, | ||
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7 x 3 = 21 |
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| Subtract the number you just wrote down from the number above it. | ||
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| Since we got zero as the answer when we subtracted, we're done. | ||
| 21 divided by 3 equals 7. | ||
| The answer is the number at the top. | ||
| OK, so the dividing up 21 into 3 piles way of doing things | ||
| is going to get old real fast. | ||
| Did you notice that 3 x 7 = 21? | ||
| That means when we're doing these instead of writing the piles, | ||
| we can just say "3 times WHAT is 21." | ||
| If you know the times tables up that far, it's easy. | ||
| Try Another One: | ||
| Example: | ||
| What is 224 divided by 8? | ||
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| Compare the 8 to the first number under the lines: | ||
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| 8 is bigger than 2. | ||
| There's no whole number that: | ||
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8 × (that number) = 2 |
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| That means we look at the next number under the lines too: | ||
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| Is 22 bigger than 8? Yes! we're in business! | ||
| Figure out how many 8's there are in 22. | ||
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1 × 8 = 8 |
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2 × 8 = 16 |
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3 × 8 = 24 |
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| OK, 2 x 8 is smaller than 22. 3 x 8 is bigger than 22. | ||
| What do we do now? | ||
| 2 is the biggest number that we can use and stay less than 22. | ||
| That means we use 2. | ||
| Write the 2 at the top. | ||
| Write it above the second 2 under the lines. | ||
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| It goes above THAT 2 | ||
| because we have used both of the 2's under the line to get it. | ||
| Now multiply the number at the top (the 2) times the number at the left (the 8). | ||
| Write the answer at the bottom. | ||
| 2 x 8 = 16 so: | ||
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| We wrote the 16 under the 22 because we used the 22 to get it. | ||
| Now subtract the 16 from the 22. | ||
| (22 - 16 = 6) | ||
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| We can't get any more 8's out of that 6. The 6 needs help. | ||
| It can get help from the last number in the 224. | ||
| The 4 that's still sitting up under the lines. | ||
| Bring it down next to the 6 at the bottom. | ||
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| Now the 6 is a 64. | ||
| How many 8's are there in 64? | ||
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1 × 8 = 8 |
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| 2 × 8 = 16 | ||
| 3 × 8 = 24 | ||
| 4 × 8 = 32 | ||
| 5 × 8 = 40 | ||
| 6 × 8 = 48 | ||
| 7 × 8 = 56 | ||
| 8 × 8 = 64 | ||
| We have a WINNER! | ||
| 8 x 8 = 64. Write the 8 at the top next to the 2 and above the 4. | ||
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| Multiply the new number at the top (the 8) times the number at the left (the 8) | ||
| and write that at the bottom. | ||
| (8 x 8 = 64, I think we've seen that somewhere before.) | ||
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| Now subtract that number from the number above it. | ||
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| We're all out of numbers, so we're done. | ||
| The answer is the number at the top. | ||
| 224 divided by 8 equals 28. | ||
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224 ÷ 8 = 28 |
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copyright 2005 Bruce Kirkpatrick |
