Subtracting fractions with unlike denominatorsYouTube↗  IA↗(long shot)
Education  870.5K views 3.2K likes 392 dislikes   04 Sep 2015
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- [VOICEOVER] Let's see if we can figure out what 4/3 minus 1/5 is, and
3 分の 4 ひく 5 分の 1 が 何か考えてみましょう。
if you think you know how to do it,
もし，あなたにはもうわかっていたら，
I encourage you to pause the video and give it a go.
ここでぜひビデオをポーズして， 自分自身で解いてみてください。
So, when you first look at this, the thing that
では，これをみると まずは，
might jump out at you is we have different denominators here.
分母が違っているということが わかると思います。
So, it's not obvious how to subtract 1/5 from 4/3 when
分母が違っているので， 3 分の 4 から 5 分の 1 をひくのは
you have these different denominators and
そんなに簡単ではないですね。
the key is, is to rewrite each of these fractions so that
鍵となるのは，これらの分数のそれぞれを
they have the same denominator.
同じ分母になるように 書き直すということです。
And how do we figure out what that same denominator is?
そして，その同じ分母が何かを どうやって求めればいいでしょうか?
Well, it's going to be a common multiple of three and five,
それは，3 と 5 の公倍数を 考えることになります。
and, ideally, it's going to be the least common multiple of
理想としては，3 と 5 の 最小公倍数だといいです。
three and five.
では，それをどうやって計算 すればいいでしょうか?
So, how can we calculate that? Well, we can start with the larger of the two numbers,
そうですね，2 つの数の 大きいほうをとって，
say five, and let's go through it's multiples and
ここは 5 ですが，その倍数を見ていき，
see when we get to one that's divisible perfectly by three.
それが 3 で割り切れる時が公倍数です。
So, five is not divisible by three,
さて，5 は 3 で割り切れません。
10 is not divisible by three, 15 is divisible by three.
10 は 3 で割り切れません。 15 は 3 で割り切れます。
In fact, 15 is three times five.
実は，15 は 3 かける 5 です。
So, I can rewrite both of these fractions as
すると，これらの両方の分数を
something over 15.
15 分の何かに書き直すことができます。
So, what's 4/3 if I were to rewrite it as something over 15?
3 分の 4 を 15 分の何かに 書き直すと何になりますか?
Well, to get from three to 15 in the denominator,
そうですね。分母が 3 から 15 に行くには，
we have to multiply by five.
5 をかけなくてはいけません。
So, if you multiply the denominator by five,
すると，分母に 5 をかけた時，
if you don't want to change the value of the fraction,
分数の値は変えたくないので，
you have to multiply the numerator by five as well.
分子も 5 をかけなくてはいけません。
So, you have to multiply the numerator by five as well,
ですから，分子にも 5 をかけます。
four times five is going to be 20.
4 かける 5 は 20 になります。
So, 4/3 is the same thing as 20/15.
3 分の 4 は 15 分の 20 と同じです。
Alright.
よし。
Now, how would we rewrite 1/5 and something over 15?
さて，5 分の 1 を 15 分の何かに 書き直すにはどうすればいいでしょうか?
So, we're going to have 15 in the denominator.
15 を分母にするようにしたいのです。
Well, to go from five to 15, we had to multiply by three.
5 から 15 に行くには， 3 をかけなくてはいけませんでした。
So, if we multiply the denominator by three,
分母に 3 をかけたので，
we have to multiply the numerator by three as well.
分子にも 3 をかけなくてはいけません。
So, times three.
かける 3。
One times three is just three.
1 かける 3 は単に 3 ですね。
So, 4/3 minus 1/5, we can rewrite that as
3 分の 4 ひく 5 分の 1 は，
20/15 minus 3/15.
15 分の 20 ひく 15 分の 3 と書き直せます。
Now, this becomes a lot more straight forward.
これでずっと簡単になりました。
What is this going to be?
これは何になるでしょうか?
Well, this is going to be a certain number of fifteenths.
これは，15 分の 1 がいくつかです。
We have 20/15 and we're
20 個の 15 分の 1 があって，
taking away three of those fifteenths.
ここから，15 分の 1 を 3 個とります。
So, we are going to have,
すると何が残るかというと，…
if you have 20 of something and you take away three of them,
もし，何かが 20 個あって， そこから 3 個をとると，
you're going to have 17 of those things.
何かは 17 個残ります。
In this case, we're talking about fifteenths.
この場合，15 分の 1 に ついて考えています。
So, this is going to be 17/15.
ですから 17 個の 15 分の 1 になります。
And if we wanted to write it as a mixed number,
もし，これを帯分数で書きたいとしたら，
we could say 15 goes into 17 one time with
15 は 17 に 1 つあり，余りが 2 です
a remainder of two.
余りは 2 です。
So, it's one and 2/15. Let's do another example.
すると 1 か 15 分の 2 です。 もう1つ問題を解いてみましょう。
Let's see if we can figure out what 7/10 minus 5/8 is.
10 分の 7 ひく 8 分の 5 が 何になるか考えてみましょう。
Five over eight. And I encourage you to pause this video and
ここでぜひビデオをポーズして，
see if you can calculate it yourself.
自分自身でできるか考えてみてください。
Well, just like we saw before,
では，前の問題でやったように，
we have different denominators but
ここには異なる分母の分数があります。
we need to rewrite them so they have a common denominator,
これらを共通の分母の ものに書き直せば，
that way, we can subtract.
ひき算ができます。
And so, what's a common multiple of 10 and eight and,
では，10 と 8 の公倍数は何でしょうか?
ideally, the least common multiple.
できれば最小公倍数がいいです。
It doesn't have to be but
実は別に最小公倍数で なくてもいいのですが，
it keeps things a little bit simpler.
（最小公倍数の方が） 少し問題が簡単になります。
Well, let's start with the larger of the two numbers and
では，2 つの数の大きい方 10 をとって，
then keep finding in their multiples and
その倍数を求めて，
find one that is perfectly divisible by the other one,
もう 1 つの数 8 で割り 切れる数を探しましょう。
by eight. So, ten isn't perfectly divisible by eight, 20 isn't,
10 は 8 で割り切れません。
30 isn't, 40 is.
20 もだめです。 30 もだめ，でも 40 は割り切れます。
40 is a multiple of 10 and it's a multiple of eight.
40 は 10 と 8 の公倍数です。
In fact, it's the least common multiple of 10 and eight.
実は，これが 10 と 8 の最小公倍数です。
So, we can rewrite both of these fractions as
すると，これらの分数の両方を，
something over 40.
40 分の何かに書き直すことができます。
So, that's going to be something over 40 minus
では，40 分の何かひく，
something over 40.
40 分の何かになります。
Minus something over 40 is equal to something.
ひく 40 分の何かです。
So, 7/10 is what over 40?
10 分の 7 は 40 分の何でしょうか?
Well, to go from 10 to 40 in the denominator,
分母を 10 から 40 にするために，
we multiplied by four.
4 をかけました。
So, we have to do the same thing in the numerator,
すると，分子にも同じことを しなくてはいけません。
multiply the numerator by four. Seven times four is 28.
つまり，分子に 4 をかけなくてはいけません。 7 かける 4 は 28 です。
So, 7/10 is the same thing as 28/40.
10 分の 7 は 40 分の 28 と同じです。
Now, let's do the same thing with the other fraction.
では，もう1つの分数にも 同じことをしましょう。
To go from eight to 40 in the denominator,
分母を 8 から 40 にするためには，
we had to multiply the denominator by five.
分母に 5 をかけなくては いけませんでした。
Eight times five is 40.
8 かける 5 は 40 です。
So, if we multiply the denominator by five,
すると，分母に 5 をかけたので，
we have to multiply the numerator by five as well.
分子にも同じく 5 をかけます。
Five times five is 25.
5 かける 5 は 25 です。
So, 7/10 minus 5/8 is the exact same things as
すると，10 分の 7 ひく 8 分の 5 は，
28/40 minus 25/40 and now this makes a lot of sense.
40 分の 28 ひく 40 分の 25 です。 これでわかりやすくなりました。
It's going to be a certain number of fortieths.
これは 40 分の 1 が何個かということになりました。
If I have 28/40 and I take away 25 of those fortieths,
もし，28 個の 40 分の 1 があって， 25 個の 40 分の 1 をとります。
how many fortieths am I going to have left?
40 分の 1 は何個残るでしょうか?
Well, I'm going to 3/40 left.
40 分の 3 です。
28/40 minus 25/40. So, I'm going to have 3/40.
28 個の 40 分の 1 ひく 25個の 40 分の 1 です。
28 minus 25 is three and we are done.
すると，3 個の 40 分の 1 になります。 28 ひく 25 は 3 です。 これでできました。
7/10 minus 5/8 is 3/40.
10 分の 7 ひく 8 分の 5 は 40 分の 3 です。
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