To solve the multiplication of a mixed number and an integer, we can follow a detailed step-by-step process.
### Step 1: Convert the Mixed Number to an Improper Fraction
First, convert the mixed number [tex]\( 2 \frac{1}{10} \)[/tex] into an improper fraction.
A mixed number [tex]\( a \frac{b}{c} \)[/tex] can be converted into an improper fraction by using the formula:
[tex]\[
\text{Improper Fraction} = a \cdot c + b \frac{1}{c} = \frac{a \cdot c + b}{c}
\][/tex]
So for [tex]\( 2 \frac{1}{10} \)[/tex]:
[tex]\[
2 \frac{1}{10} = \frac{(2 \times 10) + 1}{10} = \frac{20 + 1}{10} = \frac{21}{10}
\][/tex]
### Step 2: Multiply the Improper Fraction by the Integer
Now, multiply the improper fraction [tex]\( \frac{21}{10} \)[/tex] by the integer [tex]\( 15 \)[/tex].
Multiplication of a fraction by an integer can be done by multiplying the numerator of the fraction by the integer:
[tex]\[
\frac{21}{10} \times 15 = \frac{21 \times 15}{10}
\][/tex]
### Step 3: Perform the Multiplication
Calculate the multiplication:
[tex]\[
21 \times 15 = 315
\][/tex]
So,
[tex]\[
\frac{21 \times 15}{10} = \frac{315}{10}
\][/tex]
### Step 4: Simplify the Fraction
Simplify the fraction [tex]\( \frac{315}{10} \)[/tex]:
[tex]\[
\frac{315}{10} = 31.5
\][/tex]
So, the result of multiplying [tex]\( 2 \frac{1}{10} \)[/tex] by [tex]\( 15 \)[/tex] is:
[tex]\[
31.5
\][/tex]
### Final Answer
[tex]\[
2 \frac{1}{10} \times 15 = 31.5
\][/tex]
