- Sophia's calculation is incorrect because she failed to correctly subtract \(\frac{6}{10}\) from \(3 \frac{5}{10}\).
- Converting the numbers to improper fractions, we get \(\frac{35}{10} - \frac{6}{10} = \frac{29}{10}\).
- As a mixed number, \(\frac{29}{10}\) is equal to \(2 \frac{9}{10}\).
- Sophia's mistake was performing the subtraction as if the fractions were \(\frac{6}{10} - \frac{5}{10} = \frac{1}{10}\) and incorrectly keeping the 3.
- The correct result is \(\boxed{2 \frac{9}{10}}\).
Explanation
- Analyzing the expression and Sophia's work
The problem asks to evaluate whether Sophia correctly computed the subtraction \(3 \frac{1}{2} - \frac{3}{5}\).
Sophia's method:
- Convert \(3 \frac{1}{2}\) to \(3 \frac{5}{10}\).
- Convert \(\frac{3}{5}\) to \(\frac{6}{10}\).
- Perform the subtraction: \(3 \frac{5}{10} - \frac{6}{10} = 3 \frac{1}{10}\).
We need to verify if this result is correct by performing the calculation ourselves. First, observe that \(3 \frac{1}{2} = \frac{7}{2}\). To subtract \(\frac{3}{5}\) from \(\frac{7}{2}\), we find a common denominator, which is 10:
\(\frac{7}{2} = \frac{7 \times 5}{2 \times 5} = \frac{35}{10}\)
\(\frac{3}{5} = \frac{3 \times 2}{5 \times 2} = \frac{6}{10}\)
Now, perform the subtraction:
\(\frac{35}{10} - \frac{6}{10} = \frac{29}{10}\)
Converting the result \(\frac{29}{10}\) back to a mixed number gives \(2 \frac{9}{10}\). Sophia's result was \(3 \frac{1}{10}\). Comparing the two, we see that \(2 \frac{9}{10}
eq 3 \frac{1}{10}\). Therefore, Sophia's calculation is incorrect.
- Identifying and correcting the mistake
Sophia's mistake occurred in the final subtraction step. She correctly converted both terms to have a common denominator but failed to properly perform the subtraction.
Specifically, when subtracting \(\frac{6}{10}\) from \(3 \frac{5}{10}\), she seems to have calculated the difference between the fractions as \(\frac{6}{10} - \frac{5}{10} = \frac{1}{10}\) and incorrectly combined this with the whole number 3, resulting in \(3 \frac{1}{10}\).
To solve this correctly, we must recognize that \(\frac{6}{10}\) is greater than \(\frac{5}{10}\). Thus, we must borrow from the whole number part:
\(3 \frac{5}{10} = 2 + 1 + \frac{5}{10} = 2 + \frac{10}{10} + \frac{5}{10} = 2 \frac{15}{10}\)
Now we subtract \(\frac{6}{10}\) from this form:
\(2 \frac{15}{10} - \frac{6}{10} = 2 \frac{15 - 6}{10} = 2 \frac{9}{10}\)
This confirms the correct answer is \(2 \frac{9}{10}\).
Examples
Imagine you are a chef with 3 and a half cups of flour. If a recipe requires 3/5 of a cup to make a batch of cookies, understanding how to subtract fractions is essential for scaling recipes. If you incorrectly calculate the remaining flour by simply flipping the fractional difference, you might end up with too little or too much flour, potentially ruining your next batch. Accurate arithmetic ensures that your measurements are precise and your culinary creations come out perfectly every time!