Video: Determining Whether the Sum of Given Decimals Belongs to the Set of Natural Numbers

Is (255.5 + 168.8) ∈ or ∉ ℕ?

03:30

Video Transcript

Is 255.5 plus 168.8 an element of or not an element of the set of natural numbers?

This problem only contains two words. All the rest are either symbols or digits. And so, we have to understand what each of the symbols means to understand what the problem’s asking. The calculation is straightforward enough, 255.5 plus 168.8. But what about the three symbols that follow it? Let’s remind ourselves what they mean.

Our first symbol means is an element of. The number, or the value, that we’re talking about belongs to a certain set. So, you can probably guess that the same symbol with a line through it means is not an element of, where a value does not belong to a certain set. So, if we imagine a sorting circle and inside that circle we put a set of numbers, we’d use the first symbol to describe any value that is an element of that set and a second symbol to describe any value that is not an element of that set. It doesn’t belong in the sorting circle.

Our third symbol is a symbol that we use to describe natural numbers. What is a natural number? Well, if we imagine a number line, a natural number is any number to the right of zero that’s a whole number, a positive integer. Natural numbers are the numbers we use to count, one, two, three, and so on. If it’s positive, and if it’s a whole number, it’s a natural number.

Let’s add that symbol to our sorting circle. Now our sorting circle contains numbers, or values, that are elements of the set of natural numbers. We can write some in to remind ourselves what this means. We can write some numbers that are not in the set of natural numbers to remind ourselves what that means too. Our problem wants us to think about the value in brackets, 255.5 plus 168.8. Will that make a natural number, a positive integer, or a number that is not a natural number?

If we write the numbers vertically, we only need to look at the digits in the tenths column to find our answer. We don’t have to work out the entire calculation. Five tenths plus eight tenths is 13 tenths, which is the same as 1.3. So, we know that our answer is going to end in 0.3. It’s not going to be a whole number. And it’s not going to belong to the set of natural numbers. We don’t need to work out the rest of the calculation. And so, 255.5 plus 168.8 is not an element of the set of natural numbers.

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