Upstudy AI Solution
Answer
Solution

Sign in to Unlock Answers for Free!
A Learning Platform Trusted by Millions of Real Students and Teachers.

Answered by UpStudy AI and reviewed by a Professional Tutor
Mind Expander
To solve \( 3 \frac{3}{4}-1 \frac{2}{5} \), we start by converting the mixed numbers into improper fractions. For \( 3 \frac{3}{4} \): \[ 3 \frac{3}{4} = 3 \times 4 + 3 = 12 + 3 = \frac{15}{4} \] For \( 1 \frac{2}{5} \): \[ 1 \frac{2}{5} = 1 \times 5 + 2 = 5 + 2 = \frac{7}{5} \] Now we need to subtract \( \frac{15}{4} \) and \( \frac{7}{5} \). To do this, we need a common denominator, which for 4 and 5 is 20. Next, we convert both fractions: \(\frac{15}{4}\) to a fraction with a denominator of 20: \[ \frac{15}{4} = \frac{15 \times 5}{4 \times 5} = \frac{75}{20} \] \(\frac{7}{5}\) to a fraction with a denominator of 20: \[ \frac{7}{5} = \frac{7 \times 4}{5 \times 4} = \frac{28}{20} \] Now we can perform the subtraction: \[ \frac{75}{20} - \frac{28}{20} = \frac{75 - 28}{20} = \frac{47}{20} \] Finally, we can convert \( \frac{47}{20} \) back into a mixed number: \[ \frac{47}{20} = 2 \frac{7}{20} \] Therefore, the simplified result is: \[ \boxed{2 \frac{7}{20}} \]