Question Video: Multiplying Two Mixed Numbers Mathematics • 5th Grade

Calculate (3 2/3) × (1 2/3).


Video Transcript

Calculate three and two-thirds multiplied by one and two-thirds.

In order to answer this question, we will begin by converting both of our mixed numbers into improper fractions. We know that one whole one is equal to three-thirds. This means that three whole ones is equal to nine-thirds. From the diagram, we can see that three and two-thirds can be written as the improper fraction eleven-thirds. A quick way of calculating the 11 is to multiply the whole number by the denominator and then adding the numerator. Three multiplied by three is nine, and adding two gives us 11. In the same way, we can see that the mixed number one and two-thirds is equal to the improper fraction five-thirds. We need to multiply eleven-thirds by five-thirds.

In order to multiply two fractions, we simply multiply the numerators and separately the denominators. 11 multiplied by five is 55, and three multiplied by three is nine. Eleven-thirds multiplied by five-thirds is equal to fifty-five ninths or 55 over nine. As the line in a fraction means divide, we can now convert this back to a mixed number by dividing 55 by nine. Nine multiplied by six is equal to 54. Therefore, 55 divided by nine is equal to six remainder one. The improper fraction fifty-five ninths is the same as the mixed number six and one-ninth. Therefore, three and two-thirds multiplied by one and two-thirds is also equal to six and one-ninth.

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