Question Video: Evaluating Functions at Specific Values given Its Function Rule Mathematics • 6th Grade

Given that 𝑦 = 40 ÷ 𝑥, complete the table.

03:21

Video Transcript

Given that 𝑦 equals 40 divided by 𝑥, complete the following table.

We can see that in the table that we’re given, there are two rows. The first row contains values for 𝑥. 𝑥 is just a letter that we’re using to represent numbers. And the second row contains values for another letter, 𝑦. And we’re told in the question that these values for 𝑦 are the same as 40 divided by 𝑥. We can see in the table that there are three sections that haven’t been completed yet. We need to complete them. And we’re going to use the equation 𝑦 equals 40 divided by 𝑥 to help us.

In the first column, we can see that 𝑥 has a value of eight. But we need to find the value of 𝑦. That’s where the blank space is. We know that 𝑦 equals 40 divided by 𝑥. And in this column, we know what 𝑥 is worth. It’s worth eight. And so, 𝑦 is worth 40 divided by eight. How many eights are in 40? 8, 16, 24, 32, 40. There are five eights in 40. Five times eight equals 40. So 𝑦 must be worth five.

Now, let’s look at the second column. This time the value for 𝑥 is missing. But we know that 𝑦 is worth two. We know that 𝑦 is worth 40 divided by 𝑥. And so, because we know what 𝑦 is worth, we can say that two is equal to 40 divided by 𝑥. In other words, 40 divided by something gives us an answer of two.

Another way we could find the answers to look at the relationship between the top number and the bottom number in each column. If 40 divided by the top number equals the bottom number, then what do we notice? Eight times five equals 40. So another way of thinking about our second missing number is what do we multiply by two to make 40. Well, 40 divided by two equals 20. And we can say 20 times two equals 40. Our missing value is 20.

Let’s look at our final column. We’ll write out the equation one more time to help us: 𝑦 equals 40 divided by 𝑥. In this column, we can see that 𝑥 is worth 40. So 𝑦 is going to be worth 40 divided by 40. How many 40s are there in 40? There’s only one. And once again, we can check our answer by multiplying both numbers in the column to see if they make 40. 40 multiplied by one? Yes, it makes 40.

So given that 𝑦 equals 40 divided by 𝑥, the missing numbers in the table from left to right are five, 20, and one.

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