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