I don't understand how to write the formulas for unit analysis. I can do the problems, but the explanation of the formulas in my book doesn't make sense with the problems I am doing. For instance, this one: Find the unit rate: $2 for 5 cans of vegetables. I know it is $0.40 per can but I don't know what kind of formula to write down to begin the problem and now my teacher says she wants us to show the 'unit analysis'. (my mom usually helps me but she has strep throat and isn't able to help much today.)

Question

I don't understand how to write the formulas for unit analysis. I can do the problems, but the explanation of the formulas in my book doesn't make sense with the problems I am doing. For instance, this one: Find the unit rate: $2 for 5 cans of vegetables. I know it is $0.40 per can but I don't know what kind of formula to write down to begin the problem and now my teacher says she wants us to show the 'unit analysis'. (my mom usually helps me but she has strep throat and isn't able to help much today.)

Answer 1

The unit rate is the price per unit. You can get it by dividing the price by the number of units that cost that amount. For example,

($2.00)/(5 cans) = $0.40/can

Answer 2

I'm sorry to hear that your mom is sick and unable to help you. I'll do my best to explain how to write the formulas for unit analysis.

Unit analysis, also known as dimensional analysis, is a method used to convert units of measurement and solve problems involving different units. It can be helpful to set up a formula or equation to guide your calculations. In this case, we want to find the unit rate for the price of the cans of vegetables.

To begin, let's define some variables:

Let's denote the price of the cans as "P" (in dollars).
Let's denote the number of cans as "N" (in units).

Now, we can set up our formula for unit analysis using these variables. The formula should represent the relationship between the price and the number of cans.

In this case, we are given that the price is $2 for 5 cans. So we can write:

P = $2
N = 5

Our formula would look like this:

P/N = $2/5

In unit analysis, we want to find the unit rate, which is the price per can. To get the unit rate, we divide the price by the number of cans:

P/N = $2/5 = $0.40 per can

Now, let's break down the steps to solve this problem:

1. Identify the given information: $2 for 5 cans.
2. Define the variables: P for price (in dollars) and N for the number of cans (in units).
3. Write the formula: P/N = $2/5.
4. Simplify the formula to find the unit rate: $2/5 = $0.40 per can.

By using this formula, we were able to determine that the unit rate for the cans of vegetables is $0.40 per can.

I hope this explanation helps! Let me know if you have any further questions.