Question

How do you multiply mixed numbers?

Answer 1

Hint: To solve the given question, we should know the meaning of mixed numbers. Mixed numbers are also called improper fractions. A mixed number is a combination of a whole number and a fraction. We can not directly perform any operation on mixed numbers, to perform any algebraic operation like addition, multiplication, subtraction or division, we have to first convert the mixed fraction in proper fraction form.

Complete step by step solution:
We are asked to multiply mixed numbers. We know that the mixed number is a combination of a whole number and a fraction. For example, \[1\dfrac{2}{5}\And 2\dfrac{3}{8}\] etc.
We will multiply these two mixed numbers, as we cannot directly perform any operation on mixed numbers, to perform any algebraic operation like multiplication, we have to first convert the mixed fraction in proper fraction form.
We can write \[1\dfrac{2}{5}\] in proper fraction form as \[1\dfrac{2}{5}=\dfrac{5\times 1+2}{5}=\dfrac{7}{5}\], similarly we can write \[2\dfrac{3}{8}\]in proper form as \[2\dfrac{3}{8}=\dfrac{8\times 2+3}{8}=\dfrac{19}{8}\]. Now, that we have the proper form for these two numbers, we can multiply them. By doing this, we get \[\dfrac{7}{5}\times \dfrac{19}{8}\]. Simplifying this multiplication \[\dfrac{7}{5}\times \dfrac{19}{8}=\dfrac{133}{40}\].
Thus, we get the multiplication for two improper fractions.

Note: Same as multiplication, to perform other mathematical operations like addition, subtraction, division we have to first write the mixed numbers in their proper fraction form. Calculation mistakes while converting to proper fraction form should be avoided. One should also know how to convert proper fraction to improper form, as it can also be needed to solve a question.