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In this video I will show how to multiply and divide fractions with each other.
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I will also do a few examples on
how this works.
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We begin by reviewing the calculation rules, that will be useful in this video.
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When you multiply two fractions a / c and c / d, you multiply
to the numerators separately with each other. The result of this calculation is placed in the numerator.
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You also multiply the denominators separately. The result of this calculation is then placed in the denominator.
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When two fractions are divided by each other, we should first note that you can write this division with either a horizontally or diagonally line.
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Here we divide (a / b) / (c / d). The result is ad/bc
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We multiply the numerator in the first fraction by the denominator in the second fraction, and we multiply the denominator in the first fraction by the numerator in the second fraction.
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Think of it as if we multiply zigzag, almost like a snake
that winds through the fraction.
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So a · d, or ad, which is the same thing, will thereby be placed in the numerator and b · c, or bc, will be placed in
the denominator.
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We will do four examples.
We will start by calculating (4/5) · (3/8)
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Here we multiply 4 by 3 and 5 to 8 and the outcome will be 12/40.
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We can simplify this fraction by dividing both the numerator and denominator by 4. That will give us 3/10
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In the next example we will divide (4/5) by (3/7)
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First we will switch over from a horizontal fraction line
a diagonal fraction line.
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Then we use the rule for the division and get (4·7) / (5·3).
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This is equal to 28/15 or 1 and 13/15
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In the next example we will calculate (3/7) · 5
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We can re-write 5 as a fraction and get 5/1 instead. Then the calculation looks like this: (3/7) · (5/1)
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This is equal to 15/7. We could also express it as 2 and 1/7
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We will do one last example and here we will calculate
(1/2 + 1/3) / (4)
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First, we calculate the parentheses in the numerator.
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To do this we have to have the same denominator in both fractions. We must then multiply the first fraction by 3 and the second fraction by 2
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The expression now looks like this: (3/6 + 2/6) / 4. We can now simplify the two fractions in the numerator and write it as one, since they have the same denominator. The expression will then look like this: (5/6) / 4
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The next step is to write the division with a diagonal fraction line and re-write the 4 as the fraction 4/1
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We now use the rule for the division and multiply 5 by 1, and 6 by 4. The final result will then be 5/24