This is kind of a "dumb" question, but why carry out we main point the numerators and denominators when multiplying fractions? because that example: 1/5 x 2/3 = 2/15Intuitively, I understand why we require a usual denominator when adding and individually fractions. We need to add apples to apples and also oranges to oranges because that it come logically make sense. But why carry out we all of sudden not need a common denominator when multiplying fractions??? Wouldn"t the same analogy apply here? Don"t we have to do an apples to apples sort of operation?
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This is type of a "dumb" question, however why do we multiply the numerators and denominators when multiplying fractions? because that example: 1/5 x 2/3 = 2/15Intuitively, I know why we require a typical denominator when including and subtracting fractions. We need to include apples to apples and also oranges to oranges for it come logically make sense. Yet why execute we all of sudden not need a typical denominator as soon as multiplying fractions??? Wouldn"t the very same analogy use here? Don"t we have to do an apples to apples kind of operation?
Let"s do a slightly much easier problem, namely 1/5 X 1/3. Your trouble is just a little bit harder.Imagine a pie cut into three big pieces, two of i m sorry have currently been eaten, so the we have 1/3 of the pie. If we desire to divide this piece of pie among five civilization equally, what fraction of the pie will each get? I"m utilizing the idea that dividing by 5 is the exact same as multiply by 1/5.There are numerous different forms for the portion 1/3, such as 2/6, 3/9, and so on. A form with a 5 in the numerator would be beneficial - 5/15 would be a great choice. So one-fifth of 5/15 would be 1/15. After doing numerous such problems, you might get the idea the the answer could have to be calculated much more quickly merely by multiplying the numerators (getting 1) and the platform (getting 15).
It"s addressed now. I initially wrote 3/12, and also neglected to remove the 2 when I adjusted the fraction to 3/9. Many thanks for the correction!
This is type of a "dumb" question, however why do we main point the numerators and denominators as soon as multiplying fractions?
The most persuasive factor for law it that way: so that you acquire the appropriate answer! execute it any other way, and also the prize won"t agree v physical reality. No, I"m not kidding!
One method to look at it is the the denominator that a portion is a "unit". Simply as saying the size of a heat segment is "3 meters" method that ns am making use of "meter" as my unit the length and the heat segment is three of them, for this reason the portion "3/4" means that us are handling units the "one fourth" and also we have actually three that them.So just as a rectangle with sides "3 meters" and also "5 meters" has actually area "15 square meters" or "15 m^2" so the portion "3/4= 3 fourths" multiplied by the fraction "3/5= 3 fifths" is 9 (fourths x fifths)= 9/20.
This is kind of a "dumb" question, however why do we multiply the numerators and denominators when multiplying fractions? because that example: 1/5 x 2/3 = 2/15Intuitively, I know why we require a usual denominator when including and individually fractions. We require to add apples to apples and also oranges come oranges because that it to logically do sense. However why carry out we suddenly not require a typical denominator as soon as multiplying fractions??? Wouldn"t the exact same analogy use here? Don"t we should do one apples come apples sort of operation?
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It"s not a dumb question at all. This is one means of looking at it: 1/5 is by an interpretation the real number x such the 5x=1. 1/3 is characterized similarly. 2/3 need to be interpreted as ##2cdotfrac13##. To multiply the fractions 1/5 and also 2/3 is to settle the equation ##frac 1 5 cdot frac 2 3 =x##. If you main point both political parties by 5, you obtain ##frac23=5x##. If you main point both political parties of that by 3, you obtain 2=3·5·x. If you main point both political parties of that by ##frac13cdot 5##, you obtain ##frac2cdot 13cdot 5=x##.You likewise asked about the usual denominator when we"re law addition. I would say the the factor is that we would like to use the distributive law: a(b+c)=ab+ac. If we see a amount ab+ac through a common factor (in this situation a) in both terms, the distributive law tells united state that we can rewrite the amount as a(b+c). The allude of rewriting ##frac 2 3+frac 4 5## v a usual denominator is that it enables us to recognize a typical factor in every term:eginalign&frac 2 3+frac 4 5 =frac 2 3cdot 1+frac 4 5cdot 1 =frac 2 3cdot frac 5 5 +frac 4 5cdotfrac 3 3 =frac2cdot 53cdot 5+frac4cdot 35cdot 3\& =frac115cdot 10+frac115cdot 12 =frac115(10+12)=frac11524=frac2415.endalign The very first calculation i did reflects that we don"t need a common denominator as soon as we main point fractions. The 2nd calculation should explain why: The distributive regulation is used only once both enhancement and multiplication are involved.