Let's say you want to subtract from three and one fifths, one and one third. The first step here is to get our mixed numbers back into the form of improper fractions. We know that three here means that we have three wholes, and we also have one fifth. The equivalent way of writing this is to write sixteen divided by five, or sixteen fifths. Because three multiplied by five is fifteen, and we have one here. Sixteen. To get this number in its improper fractional form, we do three multiplied by one is three, and we add the one here, to get four divided by three. We now need to get this subtraction in a form where we can subtract the numbers from each other. We notice that these two numbers do not have the same denominator, which means that we need to multiply this numerator and this denominator by three, and this numerator and this denominator by five. So let's do that. Sixteen multiplied by three is forty-eight. Five multiplied by three is fifteen. Four multiplied by five is twenty. And three multiplied by five is fifteen. Add a subtraction sign, and we have one more step. The final step is to subtract only the numerators to give us twenty-eight fifteenths. Let's just recap. Our first step is to get these mixed numbers back in the form of improper fractions. We did this by multiplying the denominator by the number in front and adding the existing numerator, in this case, three times five plus one is sixteen. We do this for both numbers and realize now that we have to get these numbers with the same denominator. The way we do that is we cross-multiply three to this numerator and denominator, and we cross-multiply five to this numerator and denominator, giving us this subtraction. We finally subtract this numerator from this numerator, and leave the denominators unchanged, to give us twenty-eight divided by fifteen, or twenty-eight fifteenths. And this is how to subtract mixed numbers.

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