What is the difference between proportions and rates

Simply put all in ratios, and then look at proportions. Proportions and ratios worksheets Proportions - Integers The Magic Square Learn about the History of pi The number Pi has Most downloaded worksheets Vectors measurement of angles What is Mathemania?

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It is mandatory to procure user consent prior to running these cookies on your website. Many proportion problems can also be solved using dimensional analysis , the process of multiplying a quantity by rates to change the units. However, we earlier found that miles on 15 gallons gives a rate of 20 miles per gallon. Notice that with the miles per gallon example, if we double the miles driven, we double the gas used. Likewise, with the map distance example, if the map distance doubles, the real-life distance doubles.

This is a key feature of proportional relationships, and one we must confirm before assuming two things are related proportionally. You have likely encountered distance, rate, and time problems in the past. This is likely because they are easy to visualize and most of us have experienced them first hand. In our next example, we will solve distance, rate and time problems that will require us to change the units that the distance or time is measured in.

To answer this question, we need to convert 20 seconds into feet. If we know the speed of the bicycle in feet per second, this question would be simpler. We might start by converting the 20 seconds into hours:. A foot spool of bare gauge copper wire weighs How much will 18 inches of the wire weigh, in ounces?

How many tiles will be needed to tile the floor of a 20 ft by 20 ft room? In this case, while the width the room has doubled, the area has quadrupled. Since the number of tiles needed corresponds with the area of the floor, not the width, tiles will be needed. We could find this using a proportion based on the areas of the rooms:. Sometimes when working with rates, proportions, and percents, the process can be made more challenging by the magnitude of the numbers involved.

Sometimes, large numbers are just difficult to comprehend. The U. To gain perspective on how much money this is, answer the following questions.

Of course, imagining a billion dollars is very difficult, so it can help to compare it to other quantities. To address this question, we will first need data. To find the rate per capita per person , we will also need the population of the two countries. From the World Bank, [2] we can find the population of China is 1,,,, or 1. While China uses more than 5 times the electricity of Japan overall, because the population of Japan is so much smaller, it turns out Japan uses almost twice the electricity per person compared to China.

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