Video: Multiplying Mixed Numbers by Proper Fractions

Calculate 7 1/4 × 1/2.

02:31

Video Transcript

Calculate seven and one-fourth times one-half.

Before multiplying these numbers together, let’s change this mixed number to an improper fraction. So seven and one-fourth, we have the whole number seven and then the fraction portion of one-fourth. So we’ll add them together.

However, in order to add fractions, they have to have a common denominator. So one-fourth has a denominator of four. But seven has a denominator of one. So to make the denominator be a four, we will have to multiply it by four.

However, we can’t just multiply a piece of a fraction. If we multiply the denominator by four, we need to multiply the numerator by four. So seven over one is equal to 28 over four.

So now we add them together. And when adding fractions, we add our numerators — the numbers on the top — so 28 plus one, which is 29. And then we keep our common denominator a four. So we get twenty-nine fourths. So originally, it said to multiply seven and one-fourth times one-half. So instead of seven and one-fourth, we will replace it with twenty-nine fourths.

So now, we need to multiply these fractions together. So we will multiply the numerators together, which are the 29 and the one. So we have 29 times one on the numerator. And then for the denominator, which are the numbers on the bottom, we multiply four and two together. So on the numerator, we have 29 times one, which is 29, and then on the denominator, four times two, which is eight.

So here, we have an improper fraction of twenty-nine eighths. However, the question originated using mixed numbers. So let’s go ahead and put our improper fraction of twenty-nine eighths as a mixed number. So the way that we will get our whole number is to think how many times does eight go into 29.

In our calculators, we can simply put 29 divided by eight. And we get three. So eight goes into 29 three times because eight times eight times eight is 24. So how many more do we need to get to 29? That would be five. So our answer in mixed number form will be three and five-eighths. And this will be our final answer.

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