Elijah has five ropes of different length and color. He needs to know the length of
each rope in feet and inches. Complete the table below. In the first row, we have a red rope with a length of four feet. We want to convert four feet to inches. We’ll perform the
conversion by multiplying by a unit fraction which is a fraction that’s equal to one but
will convert feet to inches. We begin with the given
length of four feet. Let’s write four feet as a fraction with a denominator of one and now we multiply by a unit fraction that will convert feet to
the desired unit of inches. Because a conversion is one foot equals 12 inches and we want feet to simplify out of this product, we write the unit of
feet in the denominator and inches in the numerator. Because the conversion is
one foot equals 12 inches, the unit fraction is 12
inches over one foot. The units of feet simplify out and we are left with four times 12 inches which equals 48 inches, the
number of inches in four feet. Looking at this product again, we should be able to recognize a shortcut for converting from feet to inches is to multiply by 12 so when converting from feet to inches, again we multiply by 12, because each foot is equal to 12 inches. Next, the white rope has
a length of 36 inches which you want to convert to feet. We begin with 36 inches as a fraction with a denominator of one. We multiply it by a
unit fraction to convert the units from inches to feet. This time we want inches to simplify out which means for the unit fraction the units of inches are on the bottom and feet are on the top. Using the conversion one
foot equals 12 inches now the unit fraction is
one foot over 12 inches. The units of inches simplify out. Now we multiply and we
have 36 over 12 feet. Remember, a fraction bar means division. 36 divided by 12 is three. 36 inches equals three feet. Notice how to convert inches to feet we ended up dividing by 12. So again, 36 inches equals three feet. The shortcut is when
converting from inches to feet in this direction we divide by 12 again because 12 inches equals one foot. We will use these two shortcuts for the remaining conversions. In the next row, the blue
rope has a length of 11 feet. We want to convert 11 feet to inches. Because each foot is equal to 12 inches to perform this conversion
we’ll multiply 11 by 12. 11 times 12 equals 132. 11 feet equals 132 inches. The red rope has a length of 180 inches. We want to convert 180 inches to feet. Because we are converting inches to feet or because 12 inches is equal to one foot, to perform the conversion
we divide 180 by 12. There’s one 12 in 18, subtract. The difference is six. Bring down the zero. There are five 12’s in 60. Five times 12 is 60 and
the difference is zero showing 180 inches equals 15 feet. And then finally we have the green rope that has a length of
three and a half feet. We want to convert three
and a half feet to inches. Because each foot is equal to 12 inches, we multiply three and
a half by 12 to convert three and a half feet to inches. So we begin with three
and a half times 12. Let’s write three and a half
as an improper fraction. The denominator remains two. The numerator is two times
three plus one which is seven. Let’s write 12 as a fraction
with a denominator of one. Simplifying before multiplying, there is one two in two and six twos in 12 giving us seven times
six which is equal to 42. Three and a half feet equals 42 inches. For the next question, write an expression that can be used to
convert feet to inches. Use the expression to convert
14 3/4 feet to inches. Looking at the table above, we recognized to convert
from feet to inches we multiply by 12 so if
we define the variable F to be equal to the given length in feet, we can write an expression
to convert feet to inches so let’s let F equal the length in feet which means the expression
to convert feet to inches is F times 12 but F times 12 is normally written as 12F. These two expressions are equivalent but 12F is much more common. So now if we’re given
that F equals 14 3/4, we substitute 14 3/4 for F and evaluate the expression. So we would have 12 times 14 3/4. Let’s write 12 as a fraction
with a denominator of one and now we’ll convert 14
3/4 to an improper fraction. The denominator remains four. The numerator is 14 times
four which is 56 plus three which is 59. Simplifying before multiplying. There’s one four in four
and three fours in 12. For three times 59, because
three times 60 is 180, three times 159 is going to
be three less which is 177. Which means 14 3/4 feet equals 177 inches. I hope you found this helpful.