About this video
Shadytown's population fell by 159 residents over 3 years, the same each year, so the change per year is -159 ÷ 3 = -53 residents per year. A TV show lost 20,000 viewers over 5 months, so the change per month is -20,000 ÷ 5 = -4,000 viewers per month. A negative divided by a positive is negative.
You'll be able to
- write a decrease as a negative total change.
- divide a negative total by a positive time to find the change per year or month.
- explain why dividing numbers with different signs gives a negative.
Key words
- population
- The number of people living in a place.
- residents per year
- A rate: how many residents the population changes by each year.
- decrease
- A drop or loss; recorded here with a negative number.
Transcript
- [Instructor] We're told the population in Shadytown has decreased by 159 residents over the past three years. The same number of residents left each year. What was the change in the town's population each year? Pause this video and see if you can figure that out.
All right, now let's work through this together. So first, we decreased by 159 residents. So the total change is negative 159 residents. Now how much time did that happen over? Well, it tells us this happened over the past three years. So we could divide this, we could divide that by three years.
And what is that going to give us? Well, if you take 159 divided by three, actually let me do that over here. If I take three, I might need more space than that. Let me do it over here. If I take three, goes into 159, three doesn't go into one, it goes into 15 five times.
Five times three is 15. Subtract, we have 15 minus 15 is zero. Bring down that nine. Three goes into nine three times. Three times three is nine, and we have no remainder. So it goes exactly 53 times. So this is going to be equal to 53. And the units, if we wanna look at it, we have residents per year, alright, res for short, residents per year.
But what they told us is that we use positive numbers to track increases in population and negative numbers to track decreases in population. This is clearly a decrease every year. If we're losing the same amount every year, then in total we've lost 159. So this is a decrease every year.
Now you might also recognize that when you're dividing integers, if you have different signs, a positive and a negative, or a negative and a positive, then you're also going to get a negative in after you have divided them. But the reasoning is, well, I have lost 53 residents per year and so after three years, I would've lost a total of 159 residents.
But this right over here is our answer. Let's do another example. A certain reality TV show lost a total of 20,000 viewers. So this looks like it's going to be negative as well. Lost a total of 20,000 viewers. Lemme just write that down. So negative 20,000 over the past five months.
Same idea. What was the change in viewers each month? I already started it, but you could still pause this video and have a go at it. Well, they tell us this is over the past five months. So we are going to want to divide this. Actually, lemme put the units here.
So this is 20,000 viewers, and we're going to want to divide this over five months. And so what is this equal to? Well, first of all, we know it's going to be a decrease. So it's a negative right over there. And then 20,000 divided by five, 20 divided by five is four.
So 20,000 divided by five is 4,000. So it's 4,000 viewers. Viewers, I can write that a little bit neater. Viewers per month, or I should say actually negative 4,000 viewers per month. We're losing 4,000 viewers every month.
Video © Khan Academy, used under CC BY-NC-SA. Watch on Khan Academy. Puzzicle is not affiliated with Khan Academy.