Sure, let's solve the problem step by step.
1. Convert the mixed numbers to improper fractions.
- For [tex]\( 12 \frac{3}{10} \)[/tex]:
- Whole number part: 12
- Fractional part: [tex]\(\frac{3}{10}\)[/tex]
- To convert this to an improper fraction, multiply the whole number part by the denominator and add the numerator:
[tex]\[
12 \times 10 + 3 = 120 + 3 = 123
\][/tex]
- Thus, [tex]\( 12 \frac{3}{10} \)[/tex] converts to [tex]\( \frac{123}{10} \)[/tex].
- For [tex]\( 1 \frac{9}{10} \)[/tex]:
- Whole number part: 1
- Fractional part: [tex]\(\frac{9}{10}\)[/tex]
- To convert this to an improper fraction, multiply the whole number part by the denominator and add the numerator:
[tex]\[
1 \times 10 + 9 = 10 + 9 = 19
\][/tex]
- Thus, [tex]\( 1 \frac{9}{10} \)[/tex] converts to [tex]\( \frac{19}{10} \)[/tex].
2. Subtract the fractions:
- We have:
[tex]\[
\frac{123}{10} - \frac{19}{10}
\][/tex]
- Since the denominators are the same, we directly subtract the numerators:
[tex]\[
\frac{123 - 19}{10} = \frac{104}{10}
\][/tex]
3. Simplify the resulting fraction if possible:
- The greatest common divisor of 104 and 10 is 2. So, divide both the numerator and the denominator by 2:
[tex]\[
\frac{104 \div 2}{10 \div 2} = \frac{52}{5}
\][/tex]
4. The fraction [tex]\(\frac{52}{5}\)[/tex] can be converted into a mixed number:
- Divide the numerator by the denominator:
[tex]\[
52 \div 5 = 10 \, \text{R} \, 2
\][/tex]
- This means:
[tex]\[
52 = 5 \times 10 + 2
\][/tex]
- Thus, [tex]\( \frac{52}{5} \)[/tex] can be written as:
[tex]\[
10 \frac{2}{5}
\][/tex]
Therefore, the result of [tex]\( 12 \frac{3}{10} - 1 \frac{9}{10} \)[/tex] is [tex]\( \boxed{10 \frac{2}{5}} \)[/tex].
