Video Transcript
What number can replace the
question mark in this calculation? Complete the calculation to solve
it.
The calculation that’s mentioned in
the question is this one here. It looks like the column method has
been used to multiply a pair of two-digit numbers. 33 multiplied by 30. Oh! We’ve got a digit missing here. There’s a question mark. And the first part of this problem
asks us what number can replace this question mark. Now we could look at this
calculation and say to ourselves, “There are lots of possible answers. The missing digit could be anything
from zero up to nine.” But you know, this isn’t true
because we’re given one more piece of information. We can see that someone has already
started working out the answer to this multiplication, and they’ve already found the
partial product 132.
Now, when we’re using the column
method like this, usually the first thing that we do is multiply everything by the
ones in the second number. So to start with, we’d multiply the
three in 33 by the ones in the second number; then we’d multiply the 30 in 33 by
those ones in the second number. Then we do exactly the same, this
time multiplying by the tens in the second number, so that would be four
multiplications altogether. But can you see the way that this
calculation is being set out? There’s only space for two partial
products. In other words, the person that’s
working out the answer is going to multiply 33 all in one go. So that’s 33 multiplied by the
ones, which, of course, we don’t know at the moment, and then 33 multiplied by the
tens. So that’s 33 times 30.
Now that we know what’s happening
in this working out, we can use it to find out our missing number: 33 times what
gives us an answer of 132. Now, the important digit we need to
think about here is the digit two. What digit could we multiply our
three ones by that would give us an answer that ends in two? Well, obviously, two is less than
three. It’s not a multiple of three, so we
need to think about a two-digit number that ends in a two. And we know that three times four
is 12, and 12 ends in a two. Let’s see whether 33 times four is
correct. As we’ve said, three times four is
12. That’s the same as one 10 and two
ones. And because three times four is 12,
we know three 10s times four must be 12 10s. We’ve got one 10 as well underneath
we need to remember to include, so that’s 13 10s. And there’s our number 132.
The calculation is clearly 33 times
34, and our missing digit is four. Finally then, we’re just asked to
complete the calculation to solve it. What is 33 times 34? Well, we’ve worked out the first
partial product, so now we just need to work out the second. We need to multiply 33 by the tens
digit in 34. In other words, 33 times 30. Now we know this number we’re
multiplying by 30 is only 10 lots of three. So why don’t we multiply 33 by
three and then use this to help? Three times three is nine, and
three 10s times three is nine 10s or 90. So if 33 times three is 99, then 33
times three 10s will be the same as 99 10s, which is 990.
So we’ve multiplied 33 by four. Then we’ve multiplied 33 by 30. Now we just need to add these two
partial products together. Two ones plus zero ones is two
ones. Three 10s plus nine 10s equals 12
10s, which is the same as 100 and two ones. Then 100 plus nine 100s is 10 100s
plus the one that we’ve exchanged equals 11 100s, which is the same as 1,100. And we can just write that 1000
directly into the thousands place. This was an interesting question
because as well as using the column method, we had to use what we knew about it to
help find a missing digit. The number that replaces the
question mark in the calculation is four, and 33 times 34 is 1,122.
