Content

• To step
• Tips

A mixed number consists of an integer next to a fraction, such as 3 ½. Multiplying two mixed numbers can be tricky because you have to convert them to improper fractions first. If you want to know how to multiply mixed numbers just follow these simple steps.

To step

1. Suppose you want 4 /₂ with 6 /₅ multiply.
2. Converts the first mixed number to an improper fraction. An improper fraction is a number with a numerator greater than the denominator. You can convert a mixed number to improper fraction with the following simple steps:
   • Multiply the whole number by the denominator of the fraction. If you get the number 4 /₂ To convert to an improper fraction, you first multiply the integer 4 by the denominator of the fraction, 2. So: 4 x 2 = 8
   • Add this number to the numerator of the fraction. So we add 8 to the numerator, 1. So: 8 + 1 = 9.
   • Place this new number above the original denominator of the fraction.The new number is 9, so you can place this above 2, the original denominator. The mixed number 4/₂ can be converted to the improper fraction /₂.
3. Convert the second mixed number to improper fraction. Follow exactly the same steps as described above:
   • Multiply the whole number by the denominator of the fraction . If you are 6 /₅ converting to an improper fraction, you first multiply the whole number 6 by the denominator of the fraction, 5. So: 6 x 5 = 30.
   • Add this number to the numerator of the fraction. So we add 30 to the numerator 2, and we get 30 + 2 = 32.
   • Place this number above the original denominator of the fraction. The new number is 32, so you can place it above 5 (the original denominator). The mixed number 6/₅ is convertible to the improper fraction /₅.
4. Multiply the two improper fractions. Once you have converted each of the mixed numbers to improper fractions, you can start multiplying them. To be able to multiply the numbers, you first multiply the numerators and then the denominators of the fractions.
   • To /₂ and /₅ multiplying by each other, you multiply the numerators, 9 and 32. So: 9 x 32 = 288.
   • Now multiply the denominators, 2 and 5. So: 2 x 5 = 10.
   • Place the new numerator above the new denominator and get /₁₀.
5. Simplify your answer to the smallest terms. To simplify the fraction to the smallest terms, find the Greatest Common Divisor (GCD), the largest number that is divisible by both numerator and denominator. Then divide the numerator and denominator by this number.
   • 2 is the greatest common divisor of both 288 and 10. Divide 288 by 2 to get 144 and divide 10 by 2 to get 5. /₁₀ is reduced to /₅.
6. Convert your answer to a mixed number. Because the question is in mixed number form, the answer should also be in mixed number form. To convert it to a mixed number, you will have to work backwards to calculate your answer. You do this as follows:
   • First divide the top number by the bottom number. Do long division and divide 144 by 5. 5 goes into 144 28 times. This means that the quotient is 28. The remainder (the number that remains) is 4.
   • Make the quotient the new integer. Take the remainder and place it above the original denominator to finish converting the improper fraction to mixed number. The quotient is 28, the remainder is 4, and the original denominator was 5, so /₅ expressed as a mixed number is 28 /₅.
7. Ready!4/₂ x 6 /₅=28/₅

Tips

• When multiplying mixed numbers, you cannot multiply the whole numbers first and then the fractions. This produces an incorrect answer.
• When you cross-multiply mixed numbers, you multiply the numerator of the first fraction by the denominator of the second, and the denominator of the first fraction by the numerator of the second.