| Most people like multiplying more than they like dividing. | ||
| It would be great if we could change division into multiplication. | ||
| WE CAN! | ||
| Say we have 21 and we want to divide it by 7: | ||
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21 ÷ 7 |
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| Instead of dividing by 7 | ||
| we need to find something to multiply by instead. | ||
| What? | ||
| Here's the deal, instead of dividing by 7 we multiply by 1/7. | ||
| We multiply by the thing that times 7 equals 1. | ||
| It is called the Multiplicative Inverse of 7. | ||
| Step 1: | ||
| Give the number a denominator of 1 ... | ||
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| Now we multiply this by 1/7. | ||
| Multiplying fractions together is pretty easy. | ||
| To multiply them, | ||
| you just multiply the numerators (numbers on top) | ||
| and the denominators (numbers on the bottom). | ||
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Now simplify if possible. |
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| 21 is equal to 7 x 3 so: | ||
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| Example: | ||
| Divide 28 by 4. | ||
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28 ÷ 4 = ? |
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| The take the 4 and flip it over to get 1/4 and multiply: | ||
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| Now simplify if possible. | ||
| 28 = 4 x 7 so: | ||
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| We could have broken those 4's into 2 x 2 | ||
| to get all the way to prime factors before simplifying if we wanted to. | ||
| OK, so far this is pretty easy. | ||
| In fact, we have seen it all on earlier pages in a slightly different way. | ||
| But here's where we really need this stuff: | ||
| Divide 3 by 2/3 . | ||
| Icky! Icky! Nasty! Nasty! | ||
| What do we do? | ||
| Don't sweat it. | ||
| Just flip over the thing you are dividing by and multiply: | ||
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| We can write the 3 as 3/1 to make things look nice if we want. | ||
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| Always look to see if you can simplify these. | ||
| This time, the number on top breaks into prime factors as 9 = 3 x 3 | ||
| (hmm, I think we saw those 3's a second ago). | ||
| There are no 3's that are in that denominator of 2. | ||
| That means we can't simplify this one. | ||
| Here's another one ... | ||
| Example: | ||
| Divide 3/5 by 2/3 : | ||
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| and | ||
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| The prime factors in the top part are 3 x 3. | ||
| The prime factors in the bottom part are 5 x 2. | ||
| No numbers show up in both places so there's nothing to cancel. | ||
| OK, One More ... | ||
| Example: | ||
| Divide - 3 by 3/4 : | ||
| OH NO! NOT A NEGATIVE NUMBER! | ||
| Yeah a negative number. No big deal. | ||
| The negative number doesn't change a thing. | ||
| Do the problem the same way. | ||
| Put a 1 under the -3 as a denominator and we're off: | ||
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| Now multiply: | ||
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| Try to simplify by breaking both parts into prime factors. | ||
| The prime factors of - 12 are -1 x 2 x 2 x 3 | ||
| The prime factors of 3 are, hmm, 3. | ||
| So | ||
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copyright 2005 Bruce Kirkpatrick |
