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Sarah needs one point five cups of ketchup to make her famous meatloaf recipe. She has a brand new twenty ounce bottle of ketchup in her cupboard. How much of this will she need for her meat loaf? To answer this question we will convert one point five cups to ounces by multiplying by a unit fraction. So we begin with one point five cups, which we write as a fraction with the denominator of one. Multiply it by a unit fraction that will convert cups to ounces. To form the unit fraction we use the conversion one cup equals eight ounces. Because we want cups to simplify out, and right now we have cups in the numerator, the unit of cups must be in
the denominator and therefore, the units in the numerator will be ounces. Because the conversion is one cup equals eight ounces, the unit fraction is eight ounces divided by one cup. Notice I’m multiplying by this fraction, which is equal to one. We don’t change the value, we change the
units. The units of cups simplifies out, or simplifies to one, we’re left with one point five times eight ounces, which equals twelve ounces. So now we know Sarah needs twelve ounces of ketchup. Part b, write twenty-six inches in feet and inches. There are several ways to go about doing this. But let’s be consistent and use a unit fraction. We’ll convert twenty-six inches to feet and interpret the results. We begin with twenty-six inches as a fraction, with a denominator of one. We multiply it by a unit fraction that will convert inches to feet. To form the unit fraction, we use a conversion one foot equals twelve inches. We want inches to simplify out, so we must have inches in the denominator and feet in the numerator. One foot equals twelve inches and therefore, the unit fraction is one foot divided by twelve inches. The inches simplify out, or simplify to one. Multiplying we have twenty-six twelfths feet. Normally we would simplify, but this time we won’t because if we determine this quotient, we can determine how many feet are in twenty-six inches and the remainder will tell us how many inches are left over. Let’s find this quotient on the side. We have twenty-six divided by twelve. Again because twelve inches is equal to one foot, this quotient will tell us how many feet are in twenty-six inches and the remainder will be how many inches are left over. Well there are two twelves in twenty-six. Two times twelve is twenty-four, we subtract. The difference is two, which means twenty-six inches is equal to two feet, two inches. Just to make sure this makes sense, twenty-six inches is equal to twelve inches, plus twelve inches, plus two inches. And twelve inches is equal to one foot, so we have one foot plus one foot, plus two inches, which does give us two feet two inches. And now for the last example, we’re asked to write five pounds six ounces in ounces. To do this, we’ll first convert five pounds to ounces and then add those ounces to six ounces to determine the total number of ounces. So we’ll convert five pounds to ounces first. So it will not be the final answer though, we still have to add six ounces. We multiply by a unit fraction to convert pounds to ounces. The conversion we need is one pound equal sixteen ounces. We want pounds to simplify out and therefore, we have pounds in the denominator and ounces in the numerator. The conversion is sixteen ounces equals one pound and therefore, the unit fraction is sixteen ounces divided by one pound. The pounds simplify to one and we’re
left with five times sixteen ounces, which equals eighty ounces. So now we know five pounds equals eighty ounces. So now we can write five pounds six ounces in ounces. Five pounds plus six ounces, which is what we’re given, is equal to eighty ounces plus six ounces, which equals eighty-six ounces. I hope you found this helpful.