Calculate 173 multiplied by 87.
So now, what I’m gonna do to actually solve this problem is I’m actually gonna show you three methods. So I’m gonna start with the column method. And then, I’m gonna show you the grid method. And then, I’m gonna show you another method that has various names, but can be known as the Chinese or lattice method. Just say that you have three different strategies that you can use to solve a problem like this.
So as I said, what I’m gonna start with is the column method. So I’ve actually set it up like this: we’ve got 173 multiplied by 87. And to actually utilize this method, what we’re gonna do first is multiply the seven from the 87 by each of the numbers in our 173. Then, I’m gonna multiply the eight or the 80 from our 87 by again each of the numbers in our 173.
So I’m gonna start with three multiplied by seven. Well, three multiplied by seven is 21. So then, what I’m gonna do is I’ll put the one in the units column. And then, we’ll carry the two. And I have actually written this down here in the tens column.
Next, I’ll multiply seven by seven, which is gonna give us 49. Then, I add on the two that we carried. That makes it 51. So then, I have one in the tens column and carry five into the hundreds column. It’s actually worth mentioning at this point that I said seven multiplied by seven is 49. Well, actually, in reality, what it is is seven multiplied by 70 which give us 490. But actually, we’re already dealing with that when we’re moving along the place columns.
Okay, so now, we’ve got seven multiplied by one, which gives us seven. And then, we add on the five that we carried from earlier, which then gives us 12. So therefore, we have 1211. Okay, great, so we now we finished multiplying the seven, let’s move on to the eight.
Well, now, because actually our eight is in the tens columns. So it’s actually really eighty. What we’re gonna start with is by putting a zero in the units column. So now, we’ve got our eight multiplied by three. So this gives us 24. So I put four in the tens column and then carry two into the hundreds column.
And now, we do eight multiplied by seven. Well, eight multiplied by seven is gonna be 56. And then, we add the two that we carried which gives us 58. So then, the eight goes into the hundreds column and we carry the five into the thousands column.
So then, we have eight multiplied by one, which is gonna give us eight. Then, we add the five that we carried. So we’re gonna get 13. So we put three in the thousands column and one in the ten thousands column. So we get 13840. Okay, great, so now, we move on to the final stage.
Well, the final stage is actually to add our 1211 and our 13840. And we’re actually gonna do that using column addition. So we have one add zero. So we’re gonna put one in our units column. Then, we have one add four which is five. Then, we have two add eight which gives us 10. So therefore, as it’s 10, we’re gonna put a zero into the hundreds column and carry our one into the thousands column.
Then, we have one add three, which is four then add the one that we’ve carried from earlier gives us five. And then, finally, we’ve just got a one in the ten thousands column. This gives us 15051.
So therefore, we can say that 173 multiplied by 87 is equal to 15051. So right, what we’re gonna do now is move on to the other method that we’ve talked about. So first, we’re gonna start with the grid method.
So now, when I set up the grid, I’ve actually set it up as a two-by-three grid or it could be a three-by-two. With the numbers we’ve got, it doesn’t matter which way around it goes. And I’ve actually split our numbers up. So we have 100 then 70 then three across the top for our 173 and then 80 and seven along the left-hand side for our 87.
So the first multiplication we’re gonna do is actually 80 multiplied by 100, so our top left box. And in order to do this, the easiest way is first of all to actually multiply eight by one, which will give us eight. And then, we look at how many zeros there are in the multiplication we started with. Well, we’ve got one from our 80 and two from our 100. So therefore, we add in three zeros. So we know that 80 multiplied by 100 gives us 8000. Okay, that’s our first box filled.
So now, we’re gonna do 80 multiplied by 70. So eight multiplied by seven is 56. And in this time, we have two zeros. So we’re gonna add them on. So we’ve got 5600. And then, finally, in the top row, we’ve got three multiplied by 80. So we’ve got eight threes a 24. And then, we’ve got one zero from our 80. So we get 240.
Now, we’re actually gonna use the same method to work out the bottom row. So we have seven multiplied by 100 is 700. And then, we have seven multiplied by 70 is 490. And we got that because seven multiplied by seven is 49. And then, we had one zero from our 70. And then, finally, seven multiplied by three is 21.
Okay, great, so that’s all the multiplying we’ve actually finished with. So now, what we need to do is actually add these values up. So now, what I’ve done is actually set up a column addition. So it doesn’t matter which order you put the numbers in. I’ve actually put them in descending order. But what is important is to make sure that actually all the place values are lined up correctly.
So the only value we’ve actually got in our units columns is a one. So I’ve got one in our units column. Then, we have nine add four which is 13 add another two which is 15. So we put a five into the tens column and carry a one into the hundreds column. Then, we have six add seven which is 13 add four which is 17 add two which is 19 then add the one that we carried from earlier which is 20. So therefore, we put a zero into our hundreds columns and carry a two into our thousands column. Then, finally, we have eight add five, which is gonna give us 13, add the two that we carried. So we get 15. So we have a five in our thousands column and a one in our ten thousands column.
So the grid method has also given us the value 15051, so the same as we got with the column method. So we know yeah, definitely, it’s the correct value for this question.
So now, what we’re gonna do is move on to our final method — so the method that we’re gonna show you — and that is the Chinese or lattice. I’ve also heard it called the Italian, so various types or names this method is called. So we’re gonna have a look at that now.
Okay, so now, for the Chinese method or lattice method, we actually set up a grid again. However, as you can see, there’s actually these diagonal lines actually divide it up. Also what we’ve done is written our 173 and our 87. But this time we just include the set of digits, so the integers. So we’ve got one seven three for 173 and then we’ve got 87 as eight seven. And it’s on the right-hand side instead of the left-hand side.
So the great thing about this method is actually we only have to multiply single digits by each other. So we’re gonna start with the first multiplication, which is our top left square. So we’ve got one multiplied by eight and this is eight. So what we do here is we put a zero because it’s zero tens in the top left section of the square. And we put an eight in the bottom right.
Then, we move on to seven multiplied by eight which is 56. So we put a five in the top left and a six in the bottom right and then eight multiplied by three which is 24. So we put a two in the top left and a four on the bottom right.
Then, we move on to the next row. So we have seven multiplied by one which is seven. So we put a zero and a seven. Then, we have seven multiplied by seven which is 49. So we’ve a four in top left and a nine in the bottom right. And then, finally, we’ve got seven multiplied by three which is 21. So now, it’s actually all of our multiplying finished.
So what we can do is actually look down the set of slants. So what we’ve got first of all is one because that’s what’s down the first diagonal. So then, in this method, what we actually do is we actually add down our diagonals. So here, we have nine add two which is 11 add four which is 15. So we actually put a five down that diagonal and carry a one into the next diagonal, which is gonna be our hundreds diagonal.
So we’re gonna add up again within this diagonal. So we have seven add four which is 11 add six which is 17 add two which is 19 and then the one that we carried makes it 20. So we’re gonna have a zero in the hundreds diagonal and then carry the two into the thousands diagonal. So then we’ve got eight add five which gives us 13 add the two that we carried — it was 15. So we write a five in this diagonal and then carry the one.
And then in order to actually read the answer, so the final answer of this type of method, we actually read in the direction shown here by the arrow. And when we do that, again we get 15051. So now, what I have done is actually shown you three different strategies for attempting this kind of question. You can use any of these so that it will get you the marks that you require.
So we can definitely say that 173 multiplied by 87 is equal to 15051.