A marathon is 26.2 miles. How many kilometers is a marathon when one mile is 1.6 kilometers?

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Quizplus · Accepted Answer

In order to convert between different units of measurement, we use what is called a conversion factor. A conversion factor is a ratio (written as a fraction) where one of the units is the numerator and one is the denominator. In order to convert one type of unit to another, you will cross-multiply the starting value by the conversion factor. *We decide which unit goes on the top based on what we are trying to convert. Basically, the units have to match - the units of one numerator should be the same as the numerator of the second fraction. In this case, we know the conversion factor to be the number of kilometers in one mile. This can be written as either of the following: ^{1 mile} / _{1.6 kilometers} OR ^{1.6 kilometers} / _{1 mile} These can both be used as conversion factors because the ratio of miles to kilometers is the SAME in both. In order to decide which version to use, we come to our problem. We are told that we have 26.2 miles, and we're trying to convert the miles to kilometers. Since the number of kilometers is unknown, we're going to represent it as x. In order to solve using ratios, we need to write the first ratio as a fraction. We know that we have 26.2 miles, so that will be the numerator in our fraction (ratio) to start. We have decided to use x to represent the unknown number of kilometers, so our fraction (ratio) will look like this: ^{26.2 miles}/_x Now, we know which version of the conversion factor to use. Miles is the unit used in the numerator, so we will use the conversion factor that also has miles in the numerator: ^{1 mile}/_{1.6 kilometers} Now we can set the ratios equal to one another in preparation to solve. ^{26.2 miles}/_x = ^{1 mile}/_{1.6 kilometers} Now, we can move forward and solve. Cross multiply across the equal sign to eliminate the ratios. This means you multiply the first numerator by the second denominator, and the first denominator by the second numerator. 26.2 mi • 1.6 km = x • 1 mi 41.92 mi • km = x • 1 mi Now, we can see that we have the 1 mi multiplying the x, so we have to divide both sides by 1 mi . Note that when you divide, you also divide by the units. This cancels out the ft on the left hand side as well. 41.92mi • km ÷ 1 mi = x • 1 mi ÷ 1 mi 41.92km = x Looking at our answer choices, we can see that they are all given as whole numbers. Simply round your answer to the nearest whole number. 41.92 → 42

A Marathon Is 26