What is the number that when divided by 50 gives a quotient of 111 and a remainder of 40?
Let’s read our problem again more slowly. And this time we’ll write it out as we read it as a missing number sentence. What is the number that when divided by 50 gives a quotient of 111? We can just remind ourselves that a quotient is the answer to a division. It’s the result we get when we divide one number by another. So, if we divide a number by 50, and it gives a quotient of 111, this means an answer of 111.
But there’s another part to our statement, doesn’t just give us a quotient of 111, it also gives us a remainder of 40. In other words, we have 40 left over that we can’t divide by 50 because it’s too small. To try to understand how we can find our missing number, we could sketch a bar model. Let’s ignore the remainder part for a moment. Imagine our calculation was just a number split into groups of 50 equals 111. We’d expect our bar model to be split into 111 groups and all of them being worth 50.
Obviously, we can’t sketch this. But what we can do is represent this using a multiplication, 111 lots of 50, or 111 multiplied by 50. So, this might be what our bar model might look like if we had no remainder. So, how would it change if we need to include a remainder of 40? Well, to start with, the number that we’re dividing by would be slightly larger. We’d need to extend the bar a little bit to show this. And the value of how much it’s extended by is the 40 that’s a remainder.
Now, if we look carefully at our bar model, we can see how we need to find our missing number. First, we need to find 111 lots of 50, and then we need to add 40. In this number sentence, we have a multiplication and an addition. When we get to calculation like this, we always work out the multiplication first. But just to remind ourselves and make sure we don’t make any mistakes, we could put parentheses around the part we want to do first.
To begin with then, let’s multiply 111 by 50. There are lots of ways we could do this. We could use long multiplication. We could multiply by 100, and then halve the answer. Or we could remember that 50 is the same as five lots of 10. So, we could multiply by five and then by 10. Let’s use this method because it’s a quick one.
If we multiply 111 by five, we’re going to replace all the ones for fives. 111 multiplied by five is 555. Now, what we need to do is to multiply this answer by 10. We know that when a number is multiplied by 10, the digits shift one place to the left. So, 555 becomes worth 5550. So, the answer to our multiplication is 5550. Now, all we need to do is to add the remainder of 40. We know 50 plus 40 equals 90. And so, 5550 plus 40 equals 5590.
To find the number that when divided by 50 gives a quotient of 111, we needed to multiply 111 by 50. And to find the number that gives a remainder of 40 too, we needed to multiply 111 by 50 and then add the remainder of 40 on the end. So, this is what we did to find our answer. The number which when divided by 50 gives a quotient of 111 and a remainder of 40 is 5590.