Certainly! Let's solve the multiplication [tex]\( 6 \times 5 \frac{1}{5} \)[/tex] step-by-step.
1. Convert the Mixed Number to an Improper Fraction:
To start, we need to convert the mixed number [tex]\( 5 \frac{1}{5} \)[/tex] into an improper fraction.
- The whole number part is 5.
- The fractional part is [tex]\( \frac{1}{5} \)[/tex].
To convert [tex]\( 5 \frac{1}{5} \)[/tex] to an improper fraction:
[tex]\[
5 \frac{1}{5} = \left( 5 + \frac{1}{5} \right) = \frac{5 \times 5 + 1}{5} = \frac{25 + 1}{5} = \frac{26}{5}
\][/tex]
2. Multiply by 6:
Now, multiply the integer 6 by the improper fraction [tex]\( \frac{26}{5} \)[/tex]:
[tex]\[
6 \times \frac{26}{5}
\][/tex]
Multiply the numerator by 6:
[tex]\[
6 \times 26 = 156
\][/tex]
The denominator remains the same (5), so we have:
[tex]\[
\frac{156}{5}
\][/tex]
3. Convert the Resulting Improper Fraction to a Mixed Number:
Next, we convert the improper fraction [tex]\( \frac{156}{5} \)[/tex] back to a mixed number.
- Divide 156 by 5 to get the whole number part and the remainder.
[tex]\[
156 \div 5 = 31 \quad \text{with a remainder of} \quad 1
\][/tex]
- The whole number part is 31.
- The fractional part is the remainder over the original denominator, which is [tex]\( \frac{1}{5} \)[/tex].
Therefore, [tex]\( \frac{156}{5} \)[/tex] as a mixed number is:
[tex]\[
31 \frac{1}{5}
\][/tex]
4. Final Answer:
Combine the whole part and the fractional part to get the final result:
[tex]\[
6 \times 5 \frac{1}{5} = 31 \frac{1}{5}
\][/tex]
Thus, the result of [tex]\( 6 \times 5 \frac{1}{5} \)[/tex] is [tex]\( 31 \frac{1}{5} \)[/tex].
