The temperature in Antarctica at noon is 14°F. By 9:00PM, the temperature had dropped by 16.2 degrees. What was the temperature at 9:00PM?
The temperature at 9:00PM would be 14°F - 16.2°F = <<14-16.2=-2.2>>-2.2°F. Answer: \boxed{-2.2°F}.
We're gonna talk about how to model an expression in one variable. Here, I have a situation. The price of diapers has risen $3.25, then was reduced by $1.25 and then rose again by $0.75 or 75 cents. Write an expression to represent the price of diapers. Now, in order to write this expression, I need to know how much diapers were initially and that is my unknown amount. I'm going to have to use a variable to indicate that unknown amount and I always have to make sure that I identify what that variable stands for. In this case, I'm gonna use d because we're talking about diapers, so d equals the price of diapers originally, so how much they cost originally. Now, what do I know? That they cost that amount d and then the price rose by $3.25, so "rose" means addition. I took that original price and I'm going to add 3.25. 01:10: While we're writing this expression, we do not use the dollar sign in it. Then the price was reduced by $1.25, so "reduced" means take away, so I'm gonna subtract 1.25 and then it rose again by 75 cents or three quarters of a dollar, so I'm gonna add 0.75. This is my expression to represent the price. Now, I could combine my like terms if I wanted to or I could just leave it this way, it really doesn't matter. Let's see, d plus 3.25 plus 0.75 is $4 and I wanna subtract $1.25, so that's gonna be 2.75. That would be my final expression. Let's try it again. 01:54: You need to determine the amount of water in your aquarium. You notice that two gallons have evaporated so you add three more gallons. Then a little while later, another half a gallon has evaporated. Write an expression for the amount of water in your tank. Again, I have to identify my unknown variable, so w equals the amount of water in tank [02:20] ____. Okay. I've identified this variable and now I'm going to write my expression. So w, two gallons have evaporated, so that's minus two, I add three more gallons, so that's plus three and then another half gallon has evaporated, so that's minus 0.5. Let's see, this would be w plus 0.5.
After reading this transcript answer these questions below.
1. What does d represent in the first example?
the new price
the discounted price
the original price
2. What expression represents the first example
d + 3.25 + 1.25 + 0.75
d - 3.25 - 1.25 - 0.75
d + 3.25 - 1.25 + 0.75
3. What expression represents the second example
w - 2 + 3 - 0.5
w + 2 + 3 + 0.5
w - 2 - 3 - 0.5
1. The answer is: "the original price"
2. The answer is: "d + 3.25 - 1.25 + 0.75"
3. The answer is: "w - 2 + 3 - 0.5"
Let's review how to convert between percents, decimals, and fractions. Let's start off with an expression like 42%. Recall that "percent" means per or out of 100. So 42% can be written as 42/100. Of course, we can reduce that fraction a little bit further. Divide the numerator and denominator by 2 and that gets us 21/50th. On the other hand, since we're taking 42 and dividing it by 100, that's the same thing as dividing it by 10 and then dividing it by 10 again. When you divide the number 42 by 10, the decimal point which is at the end moves one place to the left. Divided by 10 again, it moves another place. So you end up with 0.42 as a third way to write the same expression: 42%, 21/50th, 0.42. 01:02: If we take a number that's larger than 100%, say 110%, and we convert it the same way, we'll see that it still works out. We get 110 over or out of 100. That's our fraction form. Of course, that can be reduced by dividing numerator and denominator by 10 so that we end up with 11/10ths. On the other hand, if we start with 110 and move the decimal point two places to the left, we end up with 1.10. Of course, we could just write that as 1.1. That would be the decimal form. So 1.1, 11/10th, 110%. They're all saying the same thing.
answer the questions
What is 42% expressed as a fraction
42/10
21/50
To convert a percentage to a decimal. move the decimal to the
left
right
What is 110% expressed as a fraction
55/5
11/10
1. What is 42% expressed as a fraction?
The answer is: 21/50
2. To convert a percentage to a decimal, you move the decimal to the:
The answer is: left
3. What is 110% expressed as a fraction?
The answer is: 11/10
To find the temperature at 9:00 PM, we need to subtract the temperature drop of 16.2 degrees from the noon temperature of 14°F.
14°F - 16.2°F = -2.2°F
Therefore, the temperature at 9:00 PM was -2.2°F in Antarctica.
To find the temperature at 9:00 PM, we need to subtract the temperature drop of 16.2 degrees from the noon temperature of 14°F.
To solve this, you can subtract 16.2 from 14:
14°F - 16.2°F = -2.2°F
Therefore, the temperature at 9:00 PM in Antarctica was -2.2°F.