Answer :
Sure, let's solve this step by step!
1. Convert the Mixed Number:
- You have the mixed number [tex]\(3 \frac{1}{10}\)[/tex]. This can be converted to an improper fraction.
- [tex]\(3 \frac{1}{10} = 3 + \frac{1}{10} = \frac{30}{10} + \frac{1}{10} = \frac{31}{10}\)[/tex].
2. Common Denominator:
- The goal is to perform the subtraction of fractions, so we need a common denominator. The denominators involved are 10, 5, and 2.
- The least common multiple of these numbers is 30.
- Convert each fraction to this common denominator:
- [tex]\(\frac{31}{10} = \frac{93}{30}\)[/tex]
- [tex]\(\frac{4}{5} = \frac{24}{30}\)[/tex]
- [tex]\(\frac{1}{2} = \frac{15}{30}\)[/tex]
3. Multiply and Subtract:
- The original expression is [tex]\(2 \times 3 \frac{1}{10} - \frac{4}{5} - \frac{1}{2}\)[/tex].
- Substitute the converted improper fraction:
[tex]\[2 \times \frac{31}{10} - \frac{4}{5} - \frac{1}{2} \][/tex]
- This becomes:
[tex]\[2 \times \frac{93}{30} - \frac{24}{30} - \frac{15}{30}\][/tex]
- Perform the multiplication:
[tex]\(\frac{93 \times 2}{30} = \frac{186}{30}\)[/tex]
4. Final Calculation:
- Now, subtract the fractions:
[tex]\(\frac{186}{30} - \frac{24}{30} - \frac{15}{30}\)[/tex]
- Combine:
[tex]\(\frac{186 - 24 - 15}{30} = \frac{147}{30}\)[/tex]
5. Simplify:
- Convert [tex]\(\frac{147}{30}\)[/tex] to a decimal to find the final result.
- The decimal form is approximately 4.9.
So the result of the expression [tex]\(2 \times 3 \frac{1}{10} - \frac{4}{5} - \frac{1}{2}\)[/tex] is 4.9.
1. Convert the Mixed Number:
- You have the mixed number [tex]\(3 \frac{1}{10}\)[/tex]. This can be converted to an improper fraction.
- [tex]\(3 \frac{1}{10} = 3 + \frac{1}{10} = \frac{30}{10} + \frac{1}{10} = \frac{31}{10}\)[/tex].
2. Common Denominator:
- The goal is to perform the subtraction of fractions, so we need a common denominator. The denominators involved are 10, 5, and 2.
- The least common multiple of these numbers is 30.
- Convert each fraction to this common denominator:
- [tex]\(\frac{31}{10} = \frac{93}{30}\)[/tex]
- [tex]\(\frac{4}{5} = \frac{24}{30}\)[/tex]
- [tex]\(\frac{1}{2} = \frac{15}{30}\)[/tex]
3. Multiply and Subtract:
- The original expression is [tex]\(2 \times 3 \frac{1}{10} - \frac{4}{5} - \frac{1}{2}\)[/tex].
- Substitute the converted improper fraction:
[tex]\[2 \times \frac{31}{10} - \frac{4}{5} - \frac{1}{2} \][/tex]
- This becomes:
[tex]\[2 \times \frac{93}{30} - \frac{24}{30} - \frac{15}{30}\][/tex]
- Perform the multiplication:
[tex]\(\frac{93 \times 2}{30} = \frac{186}{30}\)[/tex]
4. Final Calculation:
- Now, subtract the fractions:
[tex]\(\frac{186}{30} - \frac{24}{30} - \frac{15}{30}\)[/tex]
- Combine:
[tex]\(\frac{186 - 24 - 15}{30} = \frac{147}{30}\)[/tex]
5. Simplify:
- Convert [tex]\(\frac{147}{30}\)[/tex] to a decimal to find the final result.
- The decimal form is approximately 4.9.
So the result of the expression [tex]\(2 \times 3 \frac{1}{10} - \frac{4}{5} - \frac{1}{2}\)[/tex] is 4.9.
