Multiplying Mixed Numbers
A mixed number has a whole number and a fractional part. The fractional part consists of a numerator and a denominator.
Pictorially this can be shown as:
Here, we divide each whole into 2 equal parts. So, the denominator of the fraction is 2. There are 7 shaded parts and the fraction represented is 7 2 .
There are 3 whole parts and onehalf part. Thus, the fraction represented is 312.
Multiplying a mixed number by a whole number:
Step 1: Convert the mixed number into an improper fraction.
Step 2: Rewrite the whole number as a fraction with denominator 1.
Step 3: Multiply two fractions by multiplying the numerators and denominators separately.
Example 1: 212 x 2
First, convert 212 into an improper fraction.
212=(2x2) + 12 = 52
Now, the whole number 2 can be written as a fraction with denominator 1.
212 x 2= 52 x 21 = 5 x 1 1 x 1 = 51= 5
Example 2: 435 x 6
First, convert 435into an improper fraction.
435=(4 x 5)+ 35 = 235
Now, the whole number 6 can be written as a fraction with denominator 1.
435x 6 = 235 x 61= 23 x 65 x 1 = 1381
Now, convert the improper fraction into a mixed number.
138÷5 = Q27 R3
1385 = 2735
Thus, 4 3 5 x 6= 2735.
Multiplying two mixed numbers:
Step 1: Convert the mixed numbers into improper fractions.
Step 2: Multiply the two fractions by multiplying the numerators and denominators separately.
Example 3: 112 x213.
First, convert 112 and213into improper fractions.
112 = (1 x 2) + 12 = 32
213 = (2 x 3) + 13 =73
Now, multiply the two improper fractions.
112 = 213 =32x 73
Cancel the common factors and multiply the numerators and denominators separately.
3 2 x 7 3 = 1x7 2x1 = 7 2
Now, convert the improper fraction into a mixed number.
7 ÷ 2 = Q3 R1
72 = 312
Thus, 112 = 213= 312
Example 4: 323= 525
First, convert 323and 525into improper fractions.
323=(3 x 3) + 23 = 113
525=(5 x 5) + 25 = 275
Now, multiply the two improper fractions.
323 = 5 25 = 11 3 x 27
5
Cancel the common factors and multiply the numerators and denominators separately.
11 3 x 27 5 = 11
1 x 9 5 = 11x 9 5 = 995
Now, convert the improper fraction into a mixed number.
99 ÷ 5 = Q19 R4
995 = 1945
Thus,
3 23 x 5 25 = 194 5
Fun facts:

112x 3 =112 + 112 + 112 = 1 + 1 + 1 +1 2 + 1 2 + 1 2 = 3 + 3 2 = 62 + 32 = 92= 412