Raldo measured a room at nine feet long by ten feet wide to get an area measurement of ninety square feet. He wants to carpet the room with new carpet, which is measured in square yards. Raldo knows that one yard is equivalent to three feet, so he ordered thirty square yards of carpet. Did he order the correct amount? Notice to get thirty square yards, Raldo took the area of ninety square feet and divided by three, because there are three feet in one yard. However, this does not work because the area is in square units, or two-dimensional units, and the conversion is in one-dimensional units. And therefore, Raldo did not order the correct amount. Let’s convert ninety square feet to square yards to see how much carpet Raldo should have ordered. Before we do this though, we need to understand the units of square feet. NInety square feet, or ninety feet squared is equal to ninety feet times feet. Again, feet times feet gives us square units, which is how we measure area. And now to convert ninety square feet to square yards, we’ll write ninety square feet as a fraction with the denominator of one and then multiply by the unit fraction to convert square feet to square yards.
Well we are going to write ninety square feet in this form here. So we have ninety feet times feet, or ninety square feet all over one, times a unit fraction, which will give us the area in square yards. Now we use the conversion, one yard equals three feet to form a unit fraction, so that both units of feet will simplify to one. We know we have to have the units of feet in the denominator. So let’s go ahead and put feet in the denominator and yards in the numerator. The conversion is one yard equals three feet and therefore, part of the unit fraction is one yard divided by three feet. But notice how this unit fraction alone is not enough to simplify out both factors of the feet. And therefore, we have to multiply by another fraction of one yard divided by three feet.
Notice how by using two unit fractions of one yard divided by three feet, both factors of feet simplify to one, leaving us with the correct units of yards squared. So now we multiply like we normally do. The numerator is ninety. The denominator is three times three, which equals nine and the units are square yards. And ninety divided by nine is equal to ten and therefore, ninety square feet equals ten square yards. Raldo should have ordered ten square yards of carpet, not thirty square yards of carpet.
To better understand why we divided by nine here, let’s assume this square here is one square yard. Well we know one yard equals three feet, so let’s cut this square yard into square feet and count the number of square feet. To do this we cut the square vertically into three equal parts and horizontally into three equal parts. Now we can see there are nine square feet in one square yard, which is the reason why we divided ninety square feet by nine – to convert to square yards. Let’s go ahead and write a sentence and say Raldo should have ordered ten square yards of carpet not thirty square yards of carpet. I hope you found this helpful..
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