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• - We're not going to do a few examples questions

• from the Khan academy exercise

• on the standard algorithms.

• We're asked, which of the following

• correctly multiplies 74 times 8

• using the standard algorithm.

• So pause this video and see if you can work on that

• before we do it together.

• All right, now let's just remind ourselves

• what the standard algorithm is.

• In fact, let's just remind ourselves what an algorithm is.

• An algorithm is a series of steps that you can do

• to do something, so you'll often hear about

• a computer algorithm.

• But you can also have algorithms in math,

• just a method for doing something.

• And the standard algorithm,

• that's the typical, or the standard, way

• that a lot of people will tackle

• a multiplication question or computation like this.

• But just as a reminder, in the standard algorithm

• if we're multiplying 74 times 8

• we would write the eight in the ones place

• right below the four in the ones place,

• and then you multiply each of these places times the eight.

• you would get 32.

• 32 you can express as two ones and three tens.

• So we'll put that three up there.

• And then you would multiple the seven times the eight.

• Seven times eight is 56, and that's going to be 56 tens

• because it's seven 10s times eight is 56 tens.

• Plus the three 10s you had before

• get you to 59 tens, and so you would write over here.

• That's 59 tens, and so this would be 592.

• Now when you look at the choices,

• that's exactly what happened here in choice C.

• Just for kicks we can see what went wrong

• in these other ones.

• Let's see, in this first one,

• when we multiplied the,

• when we multiplied the four ones times eight ones,

• according to this, this person somehow got

• three ones and two tens, and 23.

• Four times eight is not 23, you can rule that one out.

• And here when they multiplied

• the four ones times the eight ones,

• that would be the 32.

• So it's two ones and then another three tens,

• so there should've been a three up here.

• And so that way when you multiplied

• the seven tens times eight,

• you get 56 but then you add this other three tens

• so you would really need to get to 59 tens.

• So that's why that one didn't work.

• Let's do another example here.

• And this is going to be with a different type of question.

• So here we are told that,

• Don starts to use the standard algorithm

• to solve 418 times five.

• His work is shown below.

• What number should Don replace Y with?

• Pause this video and see if you can figure it out.

• this might at first confuse you a little bit,

• because Y, and why is there a Y there, in the first place?

• But what they're really trying to get at

• is making sure that you, or we, understand

• what Don is trying to do when

• he's trying to do the standard algorithms.

• So as we just highlighted in last example,

• the way that we would tackle this

• with the standard algorithm,

• and actually let me write it down, 418 times five.

• We would say eight ones times five ones

• is going to be 40 ones.

• 40 ones we can write as zero ones and four tens.

• And so that looks like the place where they,

• where Don stopped computing.

• So he's on his way to solving the whole thing

• he just partially computed it so far.

• But just by doing that, we know what the Y should be.

• The Y should be four.

• So what number should Don replace the Y with?

• He should replace it with a four,

• and it's representing Y tens, or four tens.

• And of course you could keep going with this computation.

• If Don were to say, okay, I have one ten times five,

• that'd be five tens, plus another four tens,

• that's nine tens.

• And then last but not least,

• if Don wanted to figure out, well,

• he's got four hundreds here times five

• is twenty hundreds,

• which we can express as zero hundreds and two thousands.

• Or you just do this as 20 hundreds.

• So they're not asking us to do the entire computation.

• We're just trying to figure out

• what Don did essentially in this first step.

• What number should he have written here instead of a Y?

• So Y could be replaced with a four.

• It's representing the four,

• which is really in the tens place, so four tens.

- We're not going to do a few examples questions

A2 初級

# 標準算法練習的工作實例 (Worked examples for standard algorithm exercise)

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林宜悉 發佈於 2021 年 01 月 14 日