Multiplying Mixed Numbers

Multiplying mixed numbers. Suppose we want to multiply two fractions and one of them was a mixed number. For example, two and one third times three fourths. We know that if we have two regular fractions like one sixth times two thirds, we simply multiply across. We multiply the numerators together and put the result in the answers numerator. Then we multiply the denominators and put the result in the answers denominator. This gives us 2/18, which simplifies to one ninth. Now, let's look at our original problem, the one with the mixed number. If we change the mixed number into an improper fraction, that should solve our problem. Let's start that process. We start by separating the whole number two from the fraction and adding it to the fractional part. Then we change the whole number into a fractional equivalent. Any whole number can be made into a fraction by putting it over one. In this case, two becomes 21 or 2/1. Now we can multiply to finish converting the mixed number to an improper fraction. Two times three is six, one times one is one and one times three is three. Now, since both fractions have like denominators, the bottom numbers, we can simply add the top numbers, the numerators, which gives us seven thirds put this back into our original problem and it becomes seven thirds times three fourths. Seven times three is 21 and three times four is 12. Our answer is 21/12. If both of the numbers we want to multiply are mixed numbers, then we just convert both sides of the multiplication to improper fractions. Here, three and a third times four and two fifths, 3/1 plus one third times 4/1 plus two fifths. We multiply to get and get fractions with denominators and add them together to get ten thirds times 22 tenths, which gives us 220/30. Because we can, we can simplify that to 22 thirds. So to multiply mixed numbers, you first convert them to improper fractions. Then you can simply multiply across the numerators and denominators.