Video: Multiplying Two Mixed Numbers

Work out 1(1/4) × 1(2/3).

02:34

Video Transcript

Work out one and one-quarter multiplied by one and two-thirds.

Here, we have a pair of mixed numbers. Now, we know that, to multiply proper fractions, in other words, fractions between zero and one, we multiply the numerators together and then separately multiply the denominators. Now, in fact, this holds for improper fractions. And so to be able to find the product of a mixed number and any other fraction, we first begin by converting that mixed number into an improper fraction. So let’s begin by converting one and one-quarter into an improper fraction.

We begin by multiplying the integer part, that’s the whole number, by the denominator of the fraction. One times four is four. We then add this number to the numerator of our fraction. Four plus one is equal to five. This forms the numerator of the fraction; the denominator remains unchanged. So one and one-quarter is the same as five-quarters. Let’s do this again with one and two-thirds. Once again, we multiply the integer part by the denominator of the fraction; one times three is three. And then we take this number and we add it to the numerator of our fraction; three plus two is five.

Again, five forms the numerator of our improper fraction, and the denominator remains unchanged. So one and two-thirds is five-thirds. And so to multiply one and a quarter by one and two-thirds, we’re going to multiply five-quarters by five-thirds. We know, of course, that to multiply fractions, we simply multiply their numerators together and then multiply their denominators together. So here, that’s five times five over four times three, which gives us 25 over 12. Now, of course, we were given a question in mixed numbers, so we’re not quite finished.

We’re going to need to convert twenty-five twelfths back into a mixed number. And to do so, we essentially perform a reverse process to changing a number from a mixed number into an improper fraction. We divide our numerator by our denominator. We ask ourselves how many 12s make 25? And this is one of the very few times we use remainders. We say that 25 divided by 12 is two remainder one. Two forms the integer part of our answer; it’s the whole number. And one is the numerator of the fraction. The denominator remains unchanged, so it’s 12. And so we see that one and a quarter times one and two-thirds is two and one twelfth.

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