Sure, let's find the difference between the two mixed fractions [tex]\( 6 \frac{3}{4} \)[/tex] and [tex]\( 4 \frac{4}{5} \)[/tex] and express the result as a mixed fraction.
1. Convert the mixed fractions to improper fractions:
- For [tex]\( 6 \frac{3}{4} \)[/tex]:
[tex]\[
6 \frac{3}{4} = 6 + \frac{3}{4} = \frac{6 \times 4 + 3}{4} = \frac{24 + 3}{4} = \frac{27}{4}
\][/tex]
- For [tex]\( 4 \frac{4}{5} \)[/tex]:
[tex]\[
4 \frac{4}{5} = 4 + \frac{4}{5} = \frac{4 \times 5 + 4}{5} = \frac{20 + 4}{5} = \frac{24}{5}
\][/tex]
2. Find a common denominator to subtract these fractions:
The denominators are 4 and 5, so the common denominator would be [tex]\( 4 \times 5 = 20 \)[/tex].
- Convert [tex]\( \frac{27}{4} \)[/tex] to an equivalent fraction with a denominator of 20:
[tex]\[
\frac{27}{4} = \frac{27 \times 5}{4 \times 5} = \frac{135}{20}
\][/tex]
- Convert [tex]\( \frac{24}{5} \)[/tex] to an equivalent fraction with a denominator of 20:
[tex]\[
\frac{24}{5} = \frac{24 \times 4}{5 \times 4} = \frac{96}{20}
\][/tex]
3. Subtract the fractions:
[tex]\[
\frac{135}{20} - \frac{96}{20} = \frac{135 - 96}{20} = \frac{39}{20}
\][/tex]
4. Convert the result back to a mixed fraction:
- Divide 39 by 20 to get the whole number part and the remainder:
[tex]\[
39 \div 20 = 1 \text{ R } 19
\][/tex]
- Thus, [tex]\( \frac{39}{20} = 1 \frac{19}{20} \)[/tex]
So, the answer is:
[tex]\[
\boxed{1 \frac{19}{20}}
\][/tex]
