Answer :
To solve the problem
[tex]$$
193\frac{2}{3} - 1\frac{3}{4},
$$[/tex]
we follow these steps:
1. Convert the mixed numbers to improper fractions.
For [tex]\(193\frac{2}{3}\)[/tex]:
[tex]\[
193\frac{2}{3} = \frac{193 \times 3 + 2}{3} = \frac{579 + 2}{3} = \frac{581}{3}.
\][/tex]
For [tex]\(1\frac{3}{4}\)[/tex]:
[tex]\[
1\frac{3}{4} = \frac{1 \times 4 + 3}{4} = \frac{4 + 3}{4} = \frac{7}{4}.
\][/tex]
2. Subtract the improper fractions.
We need a common denominator to subtract [tex]\(\frac{581}{3}\)[/tex] and [tex]\(\frac{7}{4}\)[/tex]. The least common denominator for [tex]\(3\)[/tex] and [tex]\(4\)[/tex] is [tex]\(12\)[/tex].
Convert each fraction:
[tex]\[
\frac{581}{3} = \frac{581 \times 4}{3 \times 4} = \frac{2324}{12},
\][/tex]
[tex]\[
\frac{7}{4} = \frac{7 \times 3}{4 \times 3} = \frac{21}{12}.
\][/tex]
Now subtract:
[tex]\[
\frac{2324}{12} - \frac{21}{12} = \frac{2324 - 21}{12} = \frac{2303}{12}.
\][/tex]
3. Convert the result to a mixed number.
Divide [tex]\(2303\)[/tex] by [tex]\(12\)[/tex]:
[tex]\[
2303 \div 12 = 191 \text{ with a remainder of } 11,
\][/tex]
since [tex]\(12 \times 191 = 2292\)[/tex] and [tex]\(2303 - 2292 = 11\)[/tex].
Therefore, the mixed number is:
[tex]\[
191\frac{11}{12}.
\][/tex]
The final answer is:
[tex]$$
\boxed{191\frac{11}{12}}.
$$[/tex]
[tex]$$
193\frac{2}{3} - 1\frac{3}{4},
$$[/tex]
we follow these steps:
1. Convert the mixed numbers to improper fractions.
For [tex]\(193\frac{2}{3}\)[/tex]:
[tex]\[
193\frac{2}{3} = \frac{193 \times 3 + 2}{3} = \frac{579 + 2}{3} = \frac{581}{3}.
\][/tex]
For [tex]\(1\frac{3}{4}\)[/tex]:
[tex]\[
1\frac{3}{4} = \frac{1 \times 4 + 3}{4} = \frac{4 + 3}{4} = \frac{7}{4}.
\][/tex]
2. Subtract the improper fractions.
We need a common denominator to subtract [tex]\(\frac{581}{3}\)[/tex] and [tex]\(\frac{7}{4}\)[/tex]. The least common denominator for [tex]\(3\)[/tex] and [tex]\(4\)[/tex] is [tex]\(12\)[/tex].
Convert each fraction:
[tex]\[
\frac{581}{3} = \frac{581 \times 4}{3 \times 4} = \frac{2324}{12},
\][/tex]
[tex]\[
\frac{7}{4} = \frac{7 \times 3}{4 \times 3} = \frac{21}{12}.
\][/tex]
Now subtract:
[tex]\[
\frac{2324}{12} - \frac{21}{12} = \frac{2324 - 21}{12} = \frac{2303}{12}.
\][/tex]
3. Convert the result to a mixed number.
Divide [tex]\(2303\)[/tex] by [tex]\(12\)[/tex]:
[tex]\[
2303 \div 12 = 191 \text{ with a remainder of } 11,
\][/tex]
since [tex]\(12 \times 191 = 2292\)[/tex] and [tex]\(2303 - 2292 = 11\)[/tex].
Therefore, the mixed number is:
[tex]\[
191\frac{11}{12}.
\][/tex]
The final answer is:
[tex]$$
\boxed{191\frac{11}{12}}.
$$[/tex]
