Multi-Step Unit Conversions  (US Standard – Unit Fractions)
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Welcome to a lesson on multi-step conversions. In the first example, we’re asked, how many minutes are in a week? To answer the question, we convert one week to minutes. So to begin with one week as a fraction, with a denominator of one. And now we multiply by unit fractions to convert
one week to minutes. Notice how there’s not one conversion relating weeks to minutes and therefore, we will have to use more than one unit fraction to convert weeks to minutes. To begin we use the conversion, one week equals seven days, to convert weeks to days. And this one is pretty obvious. We’ll go ahead and use a unit fraction. Because we want weeks to simplify out, we must have weeks in the denominator, because right now we have weeks in the numerator. Because we’re converting weeks to days we have days in the numerator and the conversion is, one week equals seven days and therefore, the unit fraction is seven days divided by one week. Notice how the units of weeks simplify to one. And now we have days, so we use the conversion, one day equals twenty-four hours, to convert days to hours. So we’d multiply it by another unit fraction. We want days to simplify out, so we must have days in the denominator, which means we’ll have hours in the numerator. Because one day equals twenty-four hours, the unit fraction is twenty-four hours divided by one day. The units of days simplify to one and now we have hours, so we’ll use the conversion, one hour equals sixty minutes to convert hours to minutes. We want hours to simplify out, so we must have hours in the denominator, the numerator will be minutes. The conversion is one hour equals sixty minutes and therefore, the unit fraction is sixty minutes divided by one hour. And again, notice how the units of hours simplify to one. And now we multiply. Notice how the denominator is one and therefore, the product is seven times twenty-four, times sixty, which is equal to ten thousand eighty minutes. So now we know there are ten thousand eighty minutes in a week. For b, Brian needs ten cups of fruit juice to make Sangria. How many quarts of juice should he buy at the grocery store? To answer this question, we must convert ten cups to quarts. We begin with ten cups as a fraction with a denominator of one. We need to multiply by unit fractions to convert cups to quarts. We are not given a conversion relating cups to quarts and therefore, we will have to use more than one unit fraction. Because one pint equal two cups, we’ll first convert cups to pints by multiplying by a unit fraction. Because we want cups to simplify out, we must have the units of cups in the denominator and therefore, we will have pints in the numerator. And because one pint equals two cups, the unit fraction will be one pint divided by two cups. And notice how the units of cups simplify to one. And now we have pints, so we convert pints to quarts using the conversion, one quart equals two pints. We multiply it by another unit fraction. We want pints to simplify out and therefore, pints must be in the denominator, and therefore we have quarts in the numerator. The conversion is one quart equals two pints and therefore, the unit fraction is one quart divided by two pints. The units of pints simplify to one. Now we multiply. The numerator is ten, the denominator is four. So we have ten-fourths quarts. Of course ten-fourths simplifies. Because ten and four share a common factor of two, this simplifies to five- halves, so we could say five-halves quarts. Let’s also convert this to a mixed number as well as a decimal. To do this we divide, so we’d have five divided by two. There are two twos in five. Two times two is four, we subtract, the remainder is one. So the quotient is two and one-half, which equals two point five. Let’s go ahead and say ten cups equals two and a half quarts. Which means Brian needs to buy two and a half quarts of juice. I hope you found this helpful.

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