To solve the expression [tex]\(10 \frac{3}{10} - 3 \cdot \frac{4}{6}\)[/tex], let's break it down into several steps for clarity.
1. Convert the mixed number to an improper fraction or a decimal:
[tex]\[
10 \frac{3}{10}
\][/tex]
This can be seen as:
[tex]\[
10 + \frac{3}{10}
\][/tex]
Converting the fractional part to a decimal:
[tex]\[
\frac{3}{10} = 0.3
\][/tex]
So:
[tex]\[
10 \frac{3}{10} = 10 + 0.3 = 10.3
\][/tex]
2. Simplify the expression [tex]\(3 \cdot \frac{4}{6}\)[/tex]:
First, simplify the fraction [tex]\(\frac{4}{6}\)[/tex]:
[tex]\[
\frac{4}{6} = \frac{2 \times 2}{2 \times 3} = \frac{2}{3}
\][/tex]
Now, multiply this fraction by 3:
[tex]\[
3 \cdot \frac{2}{3} = 3 \times \frac{2}{3} = \frac{3 \times 2}{3} = \frac{6}{3} = 2
\][/tex]
3. Subtract the result from the mixed number:
We need to find:
[tex]\[
10.3 - 2
\][/tex]
Perform the subtraction:
[tex]\[
10.3 - 2 = 8.3
\][/tex]
Thus, the result of the expression [tex]\(10 \frac{3}{10} - 3 \cdot \frac{4}{6}\)[/tex] is:
[tex]\[
8.3
\][/tex]
