To solve the expression [tex]\(3 \frac{1}{3} - 1 \frac{3}{4}\)[/tex], follow these steps:
1. Convert the mixed fractions to improper fractions:
- For [tex]\(3 \frac{1}{3}\)[/tex]:
[tex]\[
3 \frac{1}{3} = 3 + \frac{1}{3}
\][/tex]
To convert to an improper fraction, multiply the whole number (3) by the denominator (3) and add the numerator (1):
[tex]\[
3 + \frac{1}{3} = \frac{3 \times 3 + 1}{3} = \frac{9 + 1}{3} = \frac{10}{3}
\][/tex]
- For [tex]\(1 \frac{3}{4}\)[/tex]:
[tex]\[
1 \frac{3}{4} = 1 + \frac{3}{4}
\][/tex]
Similarly, convert this to an improper fraction by multiplying the whole number (1) by the denominator (4) and adding the numerator (3):
[tex]\[
1 + \frac{3}{4} = \frac{1 \times 4 + 3}{4} = \frac{4 + 3}{4} = \frac{7}{4}
\][/tex]
2. Perform the subtraction:
- Convert [tex]\(\frac{10}{3}\)[/tex] and [tex]\(\frac{7}{4}\)[/tex] to a common denominator to subtract them. The least common multiple of 3 and 4 is 12.
- Convert [tex]\(\frac{10}{3}\)[/tex] to a fraction with a denominator of 12:
[tex]\[
\frac{10}{3} = \frac{10 \times 4}{3 \times 4} = \frac{40}{12}
\][/tex]
- Convert [tex]\(\frac{7}{4}\)[/tex] to a fraction with a denominator of 12:
[tex]\[
\frac{7}{4} = \frac{7 \times 3}{4 \times 3} = \frac{21}{12}
\][/tex]
- Now subtract the two fractions with the common denominator:
[tex]\[
\frac{40}{12} - \frac{21}{12} = \frac{40 - 21}{12} = \frac{19}{12}
\][/tex]
3. Simplify the result if necessary:
The fraction [tex]\(\frac{19}{12}\)[/tex] is already in its simplest form, but it can also be expressed as a mixed number:
[tex]\[
\frac{19}{12} = 1 \frac{7}{12}
\][/tex]
Thus, the result of [tex]\(3 \frac{1}{3} - 1 \frac{3}{4}\)[/tex] is:
[tex]\[
3 \frac{1}{3} - 1 \frac{3}{4} = 1 \frac{7}{12} \approx 1.5833
\][/tex]
