Video: Comparing Numerical Expressions Without Evaluating Them

Complete: 278 − 12 − 39 is _ less than 278 − 39. Top Tip: Draw a model to help you.


Video Transcript

Complete: 278 take away 12 take away 39 is what less than 278 take away 39. Top tip: draw a model to help you.

In this question, we’re given two subtractions. 278 take away 12 take away 39. Notice that this subtraction has got two numbers we’re taking away. And then the second subtraction is 278 take away 39. We’re not being asked to calculate the answers to these calculations. We just need to complete the missing number and say how many less the first expression is than the second one. Now, we could think to ourselves, right, what we’ve got to do is first find the answer to 278 take away 12 take away 39, then after we’ve done that, find the answer to 278 take away 39, and then when we’ve done that, find the difference and subtract two answers from each other. Then we’ll find out how much less the first expression is from the second.

Now, of course, this is a method that we could be using, but it’s nowhere near the most efficient method. It’s not very quick. It involves three different subtractions. And we can actually find the answer without doing any subtractions at all. How do we know this? Well, if we look at the two subtractions that we’re comparing, we can see some similarities. They both start with 278. Here’s where we can start using the advice to draw a model to help us. Let’s draw a bar model. This length bar can represent the starting number in both calculations; that’s 278.

Are there any other similarities between the subtractions? Yes, we can see that in both calculations one of the numbers we’re taking away is 39. So let’s include 39 on our bar model, too. There we go. These pink bars represent 39 that we’re taking away. Our second bar model is actually complete now. It shows 278 take away 39. And the answer to this, the difference between these two numbers, is this bar here. Now, with our first subtraction, there’s one more number we need to take away. We need to subtract another 12. Let’s use this green bar here to represent the extra 12 that were subtracting. There’s actually a clue to the answer in the sentence that we’ve just said. It’s an extra 12 that we’re subtracting.

So the answer to our subtraction, which is this by here just like the one below, is going to be 12 less. We’ve subtracted another 12 on top of the 39 that we’ve subtracted in both bar models. Now, if we draw a dotted line to show the difference between our two answers for the two subtractions, we can see that the difference is this gap here. And we can see that it’s worth 12. In the calculation 278 take away 12 take away 39, we’re subtracting an extra 12 than if we just subtracted 278 and 39. And so we can say 278 take away 12 take away 39 is 12 less than 278 take away 39. The missing number is 12.

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