To multiply the mixed numbers [tex]\(1 \frac{3}{8}\)[/tex] and [tex]\(5 \frac{1}{3}\)[/tex], we will follow a systematic approach.
### Step 1: Convert Mixed Numbers to Improper Fractions
First, we need to convert each mixed number to an improper fraction.
For [tex]\(1 \frac{3}{8}\)[/tex]:
[tex]\[ 1 \frac{3}{8} = \frac{8 \times 1 + 3}{8} = \frac{11}{8} \][/tex]
For [tex]\(5 \frac{1}{3}\)[/tex]:
[tex]\[ 5 \frac{1}{3} = \frac{3 \times 5 + 1}{3} = \frac{16}{3} \][/tex]
### Step 2: Multiply the Improper Fractions
Next, we multiply these improper fractions.
[tex]\[
\frac{11}{8} \times \frac{16}{3} = \frac{11 \times 16}{8 \times 3} = \frac{176}{24}
\][/tex]
### Step 3: Simplify the Fraction
The fraction [tex]\(\frac{176}{24}\)[/tex] can be simplified by finding the greatest common divisor (GCD) of the numerator and the denominator. However, we see it directly to be simplified:
[tex]\[
\frac{176}{24} = 7 \frac{8}{24}
\][/tex]
### Step 4: Convert Improper Fraction to Mixed Number
Finally, we convert the simplified improper fraction back to a mixed number.
Divide 176 by 24 to get the whole number part:
[tex]\[ 176 \div 24 = 7 \text{ remainder } 8 \][/tex]
Thus,
[tex]\[ \frac{176}{24} = 7 \frac{8}{24} \][/tex]
Since [tex]\( \frac{8}{24} \)[/tex] simplifies to [tex]\( \frac{1}{3} \)[/tex], the final mixed number will be:
[tex]\[
7 \frac{8}{24} = 7 \frac{1}{3}
\][/tex]
### Conclusion
The product of [tex]\(1 \frac{3}{8}\)[/tex] and [tex]\(5 \frac{1}{3}\)[/tex] simplifies to the mixed number [tex]\( \boxed{7 \frac{1}{3}} \)[/tex].
