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Multiplying Mixed Numbers

The mixed numbers have summation of whole number and proper fraction. Proper fraction is nothing but the numerator of the fraction is less that that the denominator of the fraction. By multiplying the mixed numbers, we must follow certain procedure as follow.

How to Multiply Mixed Numbers

Let us see the procedure:
Step 1: Convert the given mixed numbers to improper fraction.

Step 2: Multiply the numerator and denominator of the improper fraction separately.

Step 3: Again convert the solution into mixed fraction.

To make the mixed numbers to improper fraction, we multiply the whole number and denominator of the fraction and add the result to the numerator of the fraction.

Example: 2 ¼

Multiply 2 and 4 we get 8

Add the number 8 to the numerator of the fraction 1, we get 8 + 1 = 9.

Now get the improper fraction of the mixed number 2 ¼ = $\frac{9}{4}$

Here are the examples on Multiplying Mixed Numbers

Example 1:

Multiplying the mixed numbers 3 ½ and 6 ¼.

Solution:

Step 1: Convert the mixed numbers 3 ½ to improper fraction, we get

3 ½ = $\frac{7}{2}$

Step 2: Convert the mixed numbers 6 ¼ to improper fraction, we get

6 ¼ = $\frac{25}{4}$

Step 3: Multiplying the improper fractions $\frac{7}{2}$ and $\frac{25}{4}$, we get

$\frac{7}{2}$ * $\frac{25}{4}$ = $\frac{175}{8}$

Step 4: Convert the improper fraction $\frac{175}{8}$ to mixed number.

Mixed number $\frac{175}{8}$ = 21$\frac{7}{8}$

Answer: 21$\frac{7}{8}$

Example 2:

Multiplying the mixed numbers 4 ½ and 2 ¾.

Solution:

Step 1: Convert the mixed numbers 4 ½ to improper fraction, we get

4 ½ = $\frac{9}{2}$

Step 2: Convert the mixed numbers 2 ¾ to improper fraction, we get

2 ¾ = $\frac{11}{4}$

Step 3: Multiplying the improper fractions $\frac{9}{2}$ and $\frac{11}{4}$, we get

$\frac{9}{2}$ * $\frac{11}{4}$ = $\frac{99}{8}$

Step 4: Convert the improper fraction $\frac{99}{8}$ to mixed number.

Mixed number $\frac{99}{8}$ = 12$\frac{3}{8}$

Answer: 12$\frac{3}{8}$

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