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Find the result of one fifteenth plus one half plus four fifth giving the answer in its simplest form.
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We need to add these three fractions together, but we notice that they all three have different denominators.
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And we know that in order to add fractions together, they must have a common denominator.
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So before we move any further, we have to find a common denominator for all three of these fractions.
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To find the common denominator, we’ll first need to find the least common multiple between 15, two, and five.
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Before we can find the least common multiple, we’ll just need to list out multiples of 15, two, and five.
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Starting with 15, it’s of course 15 as a multiple.
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The next multiple for 15 would be 15 times two or a 30.
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After that comes 45 and then 60.
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Next, we’ll find the multiples of two, but remember we’re trying to find a common multiple between 15, two, and five.
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Two of course has a multiple of two, then four, six, eight, 10, 12, 14, 16, 18, 20.
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The thing is we still haven’t found a common multiple between two and 15.
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When I look at the list of multiples of 15 though, I see 30 and I know that 30 is an even number, which means 30 is divisible by two.
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30 is in fact a multiple of two.
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So we can go ahead and put 30 in the list of multiples of two.
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Now, we need to make sure that 30 is also a common multiple of five.
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The first multiple of five is five, then 10, 15, 20, 25, and finally 30.
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So we found a common denominator.
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What’s next?
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We need to convert each of these fractions into a fraction with a denominator of 30.
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To move from 15 in the denominator to 30 in the denominator, we multiply by two.
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But if we multiply by two on the bottom, we have to multiply by two on the top.
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We need to multiply our numerator of one by two as well.
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One fifteenths then becomes two thirtieths.
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We need to do the same thing with one-half.
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How would we get from two to 30?
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We multiplied by 15.
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And if we multiply our denominator by 15, we must multiply our numerator by 15.
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One times 15 is 15.
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We do this process one more time with the four-fifths.
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How do we get from five to 30?
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Multiply by six.
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Then we need to multiply our numerator by six; four times six is 24.
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So now, we have two thirtieths plus fifteen thirtieths plus twenty-four thirtieths.
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I’ll just bring that down, so it’s a little bit easier to see.
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And we found our common denominator.
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Now that we have our common denominator, our next step is just to add: two plus 15 plus 24 equals 41.
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The denominator doesn’t change, so we have forty-one thirtieths.
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And now we’re finished adding.
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We need to do one more thing though; we need to write this in its simplest form.
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41 over 30 is an improper fraction; its numerator is larger than its denominator.
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To simplify here, we’ll want to take out any whole parts.
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I know that 30 out of 30 equals one whole.
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If I take one whole or 30 over 30 away from this forty-one thirtieths, in other words if I subtract 30 from 41, I have two pieces: 30 over 30 plus eleven thirtieths.
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What I wanna do now is rewrite 30 over 30 as one.
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We can then write our improper fraction 41 over 30 as a mixed number of one and eleven thirtieths.