Common Customary Length Conversions Using Unit Fractions
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In this video, we’ll perform length conversions
using unit fractions. In the first example, we’re going to convert six feet to inches. We’ll begin by writing
six feet as a fraction with a denominator of one. And now looking at the conversions, notice one foot is equal to 12 inches, we can use this conversion
to form a unit fraction to convert feet to inches. Because we want feet to simplify out, and right now we have
feet in the numerator, when we form the unit fraction, in order for the units
of feet to simplify out, we need to have feet in the denominator and inches in the numerator. And since one foot equals 12 inches, the unit fraction is 12
inches over one foot. And again, we have feet divided by feet, and therefore the units
of feet simplify out leaving us with inches. And now we multiply. And notice how the denominator is one, and therefore we just have
six times 12 which is 72, giving us a product of 72 inches. We now know six feet equals 72 inches. Next, we’re going to
convert 126 inches to yards. We begin by writing 126
inches as a fraction with a denominator of one. And our goal is to convert to yards. Looking at the conversions,
there’s not a direct conversion from inches to yards, we
can use the conversion of one foot equals 12 inches
to convert inches to feet, and then use the conversion
one yard equals three feet to convert feet to yards. Because we have to use two conversions, we have to multiply by two unit fractions. Let’s first convert inches to feet. Because we have inches
in the numerator here, and we want inches to simplify out, we must have inches in the denominator and feet in the numerator. The conversion is one
foot equals 12 inches, which means the unit fraction
is one foot over 12 inches. Because we have inches divided by inches, the units of inches simplify out, and now we have feet, but our goal is to have yards not feet, so now we convert feet to yards using a second unit fraction. Because we want feet to simplify out, we have to have feet in the denominator. Because we have feet
in the numerator here, and we’re converting feet to yards, and therefore we have
yards in the numerator. The conversion is one
yard equals three feet, and therefore the second unit fraction is one yard over three feet. And notice the units of feet simplify out leaving us with yards. So now we multiply. In the numerator we have 126, in the denominator we have
12 times three which is 36, and now the units are yards. To finish, we need to find this quotient, let’s use the calculator. 126 divided by 36 is equal to 3.5. 126 inches is equal to 3.5 yards. Next, we want to convert
2,200 yards to miles. We begin by writing 2,200
yards as a fraction, with a denominator of one. There is not a direct conversion given from yards to miles. What we can do is convert yards to feet, that’s one yard equals three feet, and then convert feet to miles, since one mile equals 5,280 feet. So the first unit fraction, we
want to convert yards to feet. We want yards to simplify out, and therefore we have to
have yards in the denominator and feet in the numerator. Since one yard equals three feet, the first unit fraction is
three feet over one yard. Because we have yards divided yards, units of yards simplify out, leaving us with feet. And now we convert feet to miles. So we multiply by another unit fraction. We want feet to simplify out, and therefore we must have
feet in the denominator, and miles in the numerator. The conversion is one
mile equals 5,280 feet, and therefore the second unit fraction is one mile over 5,280 feet. Notice we have feet divided by feet, the units of feet simplify
out, leaving us with miles. Now we multiply. Notice how the units are miles. Multiplying in the numerator, we have 2,200 times three which is 6,600. In the denominator we have 5,280. And now we need to find this quotient to determine how many
miles in 2,200 yards. So going back to the calculator, 6,600 divided by 5,280 is equal to 1.25, giving us 1.25 miles. 2,200 yards equals 1.25 miles. And now for the last conversion, we want to convert 1.5 miles to inches. We begin by writing 1.5
miles as a fraction, with a denominator of one. Once again, there’s no direct conversion from miles to inches. We can use the conversion,
one mile equals 5,280 feet, convert miles to feet, and then use the conversion
one foot equals 12 inches to convert the feet into inches. Because we’re using two conversions, we need two unit fractions. Let’s first convert miles to feet, we want miles to simplify out, and therefore miles must
be in the denominator and feet in the numerator. One mile equals 5,280 feet, and therefore the first unit fraction is 5,280 over one mile. The units of miles simplify
out, leaving us with feet. And now we convert feet to inches. We want feet to simplify out, and therefore feet must
be in the denominator and inches in the numerator. The conversion of one
foot equals 12 inches, and therefore the unit fraction
is 12 inches over one foot. And notice the units of feet simplify out, leaving us with inches. So now we multiply, and again we now know the units are inches. Notice how the denominator is one, and therefore the product is
just 1.5 times 5,280 times 12, which gives us 95,040, and therefore there are
95,040 inches in 1.5 miles. I hope you found this helpful.

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