James spilled ink on his multiplication homework. Write the numbers that are covered in ink.
Here, we see that James has been trying to work out three different multiplications as part of his homework. 61 multiplied by nine, 53 multiplied by five, and then 32 multiplied by six. And in each calculation, there’s a great splotch of ink where he’s spilled some ink on his work. Our job is to work out the numbers that have been covered by the ink. And the way we can do this is to understand the method that James has used. Let’s look at the first calculation to try to see how James has worked out the answer.
We can see that James has used short multiplication to find the answer. And what he’s done is he’s written out each step as he’s gone along. We know that, to use short multiplication, we need to multiply the tens and the ones digit by the number we’re multiplying by. So we need to multiply 60 by nine and then one by nine. And we can do it in another order.
In this case, we can see that James has started with the tens digit. 60 multiplied by nine equals 540. Then he’s gone on to multiply the ones. One times nine is nine. His final step is to add to find the total. And this is the part that has been covered with ink. So let’s have both numbers now to find a total. Zero ones plus nine ones equal nine ones. And then there’s nothing else in the tens or the hundreds places for the last number. So we know the digits must be five and four. Our first missing number is 549.
In the next calculation, the number that James has covered in ink is the first multiplication, the first step that he’s done. And we know that this is multiplying the tens digit by the number we’re multiplying by, in other words, 50 multiplied by five. We know five multiplied by five is 25. So 50 lots of five must equal 250. And just to check our missing number’s correct, we can add the two together and see if they make 265. Zero ones plus five ones equal five ones. Five tens plus one ten equals six tens. And then we’ve got nothing to add to our two hundreds. Our missing number in the second multiplication is 250.
Now, let’s look at the final multiplication where we working out 32 multiplied by six. Again, James starts off by multiplying the tens digit by six. We know that 30 sixes is 180. But it’s now the second part of the multiplication where James has spilled his ink. This is where he multiplies the ones digit by six., in other words, two times six. Well, we know two sixes are 12. Let’s check whether the missing number’s correct by adding our two numbers together and this time seeing if they make the total 192.
Zero plus two equals two. Eight tens plus one ten equals nine tens. And finally, we’ve got nothing to add to the hundreds. So the answer is 192. And so although James has had an accident with his ink, we managed to find out the different numbers that were covered over by the ink by thinking about the method that he was using. The three missing numbers are 549, 250, and 12.