To subtract the mixed numbers [tex]\(5 \frac{1}{10} - 2 \frac{1}{4}\)[/tex], follow these steps:
1. Convert each mixed number to an improper fraction.
- For [tex]\(5 \frac{1}{10}\)[/tex]:
[tex]\[
5 \frac{1}{10} = \frac{5 \cdot 10 + 1}{10} = \frac{50 + 1}{10} = \frac{51}{10}
\][/tex]
- For [tex]\(2 \frac{1}{4}\)[/tex]:
[tex]\[
2 \frac{1}{4} = \frac{2 \cdot 4 + 1}{4} = \frac{8 + 1}{4} = \frac{9}{4}
\][/tex]
2. Find a common denominator to perform the subtraction.
The least common multiple (LCM) of 10 and 4 is 20.
- Convert [tex]\(\frac{51}{10}\)[/tex] to have the common denominator 20:
[tex]\[
\frac{51}{10} = \frac{51 \cdot 2}{10 \cdot 2} = \frac{102}{20}
\][/tex]
- Convert [tex]\(\frac{9}{4}\)[/tex] to have the common denominator 20:
[tex]\[
\frac{9}{4} = \frac{9 \cdot 5}{4 \cdot 5} = \frac{45}{20}
\][/tex]
3. Subtract the numerators.
[tex]\[
\frac{102}{20} - \frac{45}{20} = \frac{102 - 45}{20} = \frac{57}{20}
\][/tex]
4. Convert the result back to a mixed number.
- Divide the numerator by the denominator:
[tex]\[
57 \div 20 = 2 \quad \text{with a remainder of} \quad 17
\][/tex]
- This means:
[tex]\[
\frac{57}{20} = 2 \frac{17}{20}
\][/tex]
So, the result of subtracting [tex]\(5 \frac{1}{10} - 2 \frac{1}{4}\)[/tex] is [tex]\(2 \frac{17}{20}\)[/tex].
