Get detailed and reliable answers to your questions on IDNLearn.com. Get comprehensive and trustworthy answers to all your questions from our knowledgeable community members.
Sagot :
Alright, let's break down each part of the question and solve them step-by-step:
### 1. First Expression:
[tex]\[ \frac{5}{3} - \left(\frac{2}{5} \times \frac{7}{2}\right) - \frac{1}{3} \][/tex]
1.1 Calculate [tex]\(\frac{2}{5} \times \frac{7}{2}\)[/tex]:
[tex]\[ \frac{2}{5} \times \frac{7}{2} = \frac{2 \times 7}{5 \times 2} = \frac{14}{10} = \frac{7}{5} \][/tex]
1.2 Substitute back into the expression:
[tex]\[ \frac{5}{3} - \frac{7}{5} - \frac{1}{3} \][/tex]
1.3 Find a common denominator for the fractions, which is 15:
[tex]\[ \frac{5}{3} = \frac{5 \times 5}{3 \times 5} = \frac{25}{15} \][/tex]
[tex]\[ \frac{7}{5} = \frac{7 \times 3}{5 \times 3} = \frac{21}{15} \][/tex]
[tex]\[ \frac{1}{3} = \frac{1 \times 5}{3 \times 5} = \frac{5}{15} \][/tex]
1.4 Substitute these fractions into the expression:
[tex]\[ \frac{25}{15} - \frac{21}{15} - \frac{5}{15} = \frac{25 - 21 - 5}{15} = \frac{-1}{15} \][/tex]
### Final answer for the first expression:
[tex]\[ -0.0667 \, (\text{approximately}) \][/tex]
### 2. Second Expression:
[tex]\[ \left(\frac{2}{3} \times 5 - \frac{3}{4}\right) \times \frac{7}{2} \][/tex]
2.1 Calculate [tex]\(\frac{2}{3} \times 5\)[/tex]:
[tex]\[ \frac{2}{3} \times 5 = \frac{2 \times 5}{3} = \frac{10}{3} \][/tex]
2.2 Substitute back into the expression:
[tex]\[ \left(\frac{10}{3} - \frac{3}{4}\right) \times \frac{7}{2} \][/tex]
2.3 Find a common denominator for the fractions, which is 12:
[tex]\[ \frac{10}{3} = \frac{10 \times 4}{3 \times 4} = \frac{40}{12} \][/tex]
[tex]\[ \frac{3}{4} = \frac{3 \times 3}{4 \times 3} = \frac{9}{12} \][/tex]
2.4 Substitute these fractions into the expression:
[tex]\[ \left(\frac{40}{12} - \frac{9}{12}\right) = \frac{31}{12} \][/tex]
2.5 Multiply by [tex]\(\frac{7}{2}\)[/tex]:
[tex]\[ \frac{31}{12} \times \frac{7}{2} = \frac{31 \times 7}{12 \times 2} = \frac{217}{24} = 9.0417 \, (\text{approximately}) \][/tex]
### Final answer for the second expression:
[tex]\[ 9.0417 \, (\text{approximately}) \][/tex]
### 3. Third Expression:
[tex]\[ \left[\left(\frac{-7}{3} \times \frac{4}{5}\right) - 2\right] \times \frac{5}{3} \][/tex]
3.1 Calculate [tex]\(\frac{-7}{3} \times \frac{4}{5}\)[/tex]:
[tex]\[ \frac{-7}{3} \times \frac{4}{5} = \frac{-7 \times 4}{3 \times 5} = \frac{-28}{15} \][/tex]
3.2 Substitute back into the expression:
[tex]\[ \left(\frac{-28}{15} - 2\right) \][/tex]
3.3 Convert the integer to a fraction with a common denominator:
[tex]\[ 2 = \frac{30}{15} \][/tex]
3.4 Substitute back into the expression:
[tex]\[ \left(\frac{-28}{15} - \frac{30}{15}\right) = \frac{-28 - 30}{15} = \frac{-58}{15} \][/tex]
3.5 Multiply by [tex]\(\frac{5}{3}\)[/tex]:
[tex]\[ \frac{-58}{15} \times \frac{5}{3} = \frac{-58 \times 5}{15 \times 3} = \frac{-290}{45} = -6.4444 \, (\text{approximately}) \][/tex]
### Final answer for the third expression:
[tex]\[ -6.4444 \, (\text{approximately}) \][/tex]
### Summary of Results:
1. [tex]\(\frac{5}{3} - \left(\frac{2}{5} \times \frac{7}{2}\right) - \frac{1}{3} \approx -0.0667\)[/tex]
2. [tex]\(\left(\frac{2}{3} \times 5 - \frac{3}{4}\right) \times \frac{7}{2} \approx 9.0417\)[/tex]
3. [tex]\(\left[\left(\frac{-7}{3} \times \frac{4}{5}\right) - 2\right] \times \frac{5}{3} \approx -6.4444\)[/tex]
So the final results are:
[tex]\[ (-0.0667, 9.0417, -6.4444) \][/tex]
### 1. First Expression:
[tex]\[ \frac{5}{3} - \left(\frac{2}{5} \times \frac{7}{2}\right) - \frac{1}{3} \][/tex]
1.1 Calculate [tex]\(\frac{2}{5} \times \frac{7}{2}\)[/tex]:
[tex]\[ \frac{2}{5} \times \frac{7}{2} = \frac{2 \times 7}{5 \times 2} = \frac{14}{10} = \frac{7}{5} \][/tex]
1.2 Substitute back into the expression:
[tex]\[ \frac{5}{3} - \frac{7}{5} - \frac{1}{3} \][/tex]
1.3 Find a common denominator for the fractions, which is 15:
[tex]\[ \frac{5}{3} = \frac{5 \times 5}{3 \times 5} = \frac{25}{15} \][/tex]
[tex]\[ \frac{7}{5} = \frac{7 \times 3}{5 \times 3} = \frac{21}{15} \][/tex]
[tex]\[ \frac{1}{3} = \frac{1 \times 5}{3 \times 5} = \frac{5}{15} \][/tex]
1.4 Substitute these fractions into the expression:
[tex]\[ \frac{25}{15} - \frac{21}{15} - \frac{5}{15} = \frac{25 - 21 - 5}{15} = \frac{-1}{15} \][/tex]
### Final answer for the first expression:
[tex]\[ -0.0667 \, (\text{approximately}) \][/tex]
### 2. Second Expression:
[tex]\[ \left(\frac{2}{3} \times 5 - \frac{3}{4}\right) \times \frac{7}{2} \][/tex]
2.1 Calculate [tex]\(\frac{2}{3} \times 5\)[/tex]:
[tex]\[ \frac{2}{3} \times 5 = \frac{2 \times 5}{3} = \frac{10}{3} \][/tex]
2.2 Substitute back into the expression:
[tex]\[ \left(\frac{10}{3} - \frac{3}{4}\right) \times \frac{7}{2} \][/tex]
2.3 Find a common denominator for the fractions, which is 12:
[tex]\[ \frac{10}{3} = \frac{10 \times 4}{3 \times 4} = \frac{40}{12} \][/tex]
[tex]\[ \frac{3}{4} = \frac{3 \times 3}{4 \times 3} = \frac{9}{12} \][/tex]
2.4 Substitute these fractions into the expression:
[tex]\[ \left(\frac{40}{12} - \frac{9}{12}\right) = \frac{31}{12} \][/tex]
2.5 Multiply by [tex]\(\frac{7}{2}\)[/tex]:
[tex]\[ \frac{31}{12} \times \frac{7}{2} = \frac{31 \times 7}{12 \times 2} = \frac{217}{24} = 9.0417 \, (\text{approximately}) \][/tex]
### Final answer for the second expression:
[tex]\[ 9.0417 \, (\text{approximately}) \][/tex]
### 3. Third Expression:
[tex]\[ \left[\left(\frac{-7}{3} \times \frac{4}{5}\right) - 2\right] \times \frac{5}{3} \][/tex]
3.1 Calculate [tex]\(\frac{-7}{3} \times \frac{4}{5}\)[/tex]:
[tex]\[ \frac{-7}{3} \times \frac{4}{5} = \frac{-7 \times 4}{3 \times 5} = \frac{-28}{15} \][/tex]
3.2 Substitute back into the expression:
[tex]\[ \left(\frac{-28}{15} - 2\right) \][/tex]
3.3 Convert the integer to a fraction with a common denominator:
[tex]\[ 2 = \frac{30}{15} \][/tex]
3.4 Substitute back into the expression:
[tex]\[ \left(\frac{-28}{15} - \frac{30}{15}\right) = \frac{-28 - 30}{15} = \frac{-58}{15} \][/tex]
3.5 Multiply by [tex]\(\frac{5}{3}\)[/tex]:
[tex]\[ \frac{-58}{15} \times \frac{5}{3} = \frac{-58 \times 5}{15 \times 3} = \frac{-290}{45} = -6.4444 \, (\text{approximately}) \][/tex]
### Final answer for the third expression:
[tex]\[ -6.4444 \, (\text{approximately}) \][/tex]
### Summary of Results:
1. [tex]\(\frac{5}{3} - \left(\frac{2}{5} \times \frac{7}{2}\right) - \frac{1}{3} \approx -0.0667\)[/tex]
2. [tex]\(\left(\frac{2}{3} \times 5 - \frac{3}{4}\right) \times \frac{7}{2} \approx 9.0417\)[/tex]
3. [tex]\(\left[\left(\frac{-7}{3} \times \frac{4}{5}\right) - 2\right] \times \frac{5}{3} \approx -6.4444\)[/tex]
So the final results are:
[tex]\[ (-0.0667, 9.0417, -6.4444) \][/tex]
We appreciate every question and answer you provide. Keep engaging and finding the best solutions. This community is the perfect place to learn and grow together. For dependable answers, trust IDNLearn.com. Thank you for visiting, and we look forward to assisting you again.
