Fill in the blank. 257, what, and 159 are three odd numbers. Their sum is 589.
We can represent this problem using a bar model. We’ll use the first bar to represent the first number, which is 257. Then we have a missing number. This is the blank that we need to fill in. And then our final number is 159. So how could we find our missing number? What can we use to help us?
Well, we’re told two more pieces of information. Firstly, we’re told that all three numbers are odd. So we know we’re looking for an odd number. And then, secondly, we’re told that the sum of all three numbers is 589. So how can we use this information to help? What if we start with 589 then subtract 257 and then, secondly, subtract 159? Then we’ll be left with our missing number.
So as we say, for step one, we’re going to start with 589 and subtract 257. Nine take away seven equals two. 80 take away 50 leaves us with 30. And 500 take away 200 leaves us with 300. We have an answer of 332. What does this represent?
Well, we’ve subtracted the part worth 257. So this part here must be worth 332. So to find our missing number, we need to complete this second step. We need to start with the whole amount, which is 332, and take away 159. We can’t subtract nine from two. So we need to exchange. We’ll take one 10 from the tens place and exchange it for 10 ones. 12 take away nine equals three. This is looking good because we know we’re looking for an odd number. And because it ends in a three, we know that this is now going to be an odd number.
Unfortunately, we can’t subtract five tens from two tens, so we’re going to need to exchange again. We’ll take 100. So we now have two hundreds instead of three hundreds. And we’ll exchange it for 10 tens. 12 tens takeaway five tens equals seven tens. And finally, 200 take away 100 leaves us with 100. And so by subtracting 159, we found our missing number. It’s 173.
We know 173 looks like it might be correct because it’s an odd number. But one way we could find out for sure is to add all three numbers together and check that their sum is 589. Let’s do that quickly.
To begin with, let’s add the ones. We can combine seven and three quickly cause we know that makes 10. And if we add the nine on the end, we get a total of 19 ones, which is the same as one ten and nine ones. There’s a quick way to add the tens too. Can you see we’ve got two fives, which we can combine quickly to make 10? 10 and the remaining seven is 17. And then we’ve got one 10 underneath, which makes 18. 18 tens is the same as 180.
So far, so good. We’ve got our 89. And we just hope that our hundreds column adds up to five. 200 plus 100 plus 100 plus the 100 we’ve exchanged does equal 500. So we know our missing number was correct.
We found our missing number by starting with the sum of the three numbers, which was 589, and then subtracting the two numbers that we knew. This left us with the one missing number that we didn’t know. 257, 173, and 159 are three odd numbers. Their sum is 589. The missing number was 173.