Question Video: Comparing Expressions Involving Addition and Subtraction Mathematics

Use <, >, or = to fill in the gap: (93423 − 45111) _ (59249 + 23114).


Video Transcript

Use the symbol for is less than, is greater than, or is equal to to fill in the gap, 93423 take away 45111 what 59249 plus 23114.

Here we have two expressions. One is a subtraction, and the other is an addition. And in between them, we have a gap. And we need to choose the correct symbol to use in between them. Is the first expression less than the second expression? Is it greater than the second expression? Or are the two expressions equal?

Now, both expressions involve numbers that have five digits. So, we might think to ourselves that we need to calculate each answer before we can actually answer the question. But the question doesn’t actually ask us to calculate each value. We just need to complete the gap. And if we look carefully at the numbers we’re dealing with, we can actually answer the question without calculating anything.

Let’s start by looking at our subtraction. Now, the first number in our subtraction, 93423, we could think of as being the same really as 90000. We’re just using this to give us an estimate. And we can think of our second number, which is 45111, as really being the same as 45000. Now, it’s quite helpful that this number is about the same as 45000 because 45000 is actually half of 90000. So, the answer to the subtraction is going to be approximately, and this is the symbol for approximately, 45000.

Now, if we look across at the addition, you can see why we don’t actually have to work out anything. The addition begins with a number much greater than 45000. It’s 59249 and then we’re adding some more onto it, another 23114. We can see straightaway that this value is going to be greater than the first value. And so, without working out any of the values exactly, we can confidently say that the symbol we need to put in between both expressions is is less than. The first expression is less than the second expression.

Now, although we don’t have to do this next step because we’re confident we’ve got the right answer. Let’s just prove it. Three take away one equals two. Two tens take away one 10 equals one 10. Four hundreds take away 100 leaves us with three hundreds. We can’t subtract five thousands from three thousands, so we can exchange one lot of 10000, which takes us now down to eight lots of 10000, and put it next to the three to give us 13 thousands.

13 thousands take away five thousands equals eight thousands. And then eight tens of thousands take away four tens of thousands leaves us with four tens of thousands. The value of the first expression is 48312. So, we can see straightaway this is less than the number that we start the addition with in the second expression. Our estimation was correct. 93423 take away 45111 is less than 59249 plus 23114.

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