Certainly! Let's solve the problem [tex]\(2 \frac{3}{8} - \frac{7}{8}\)[/tex] step-by-step:
1. Convert the mixed number to an improper fraction:
We have the mixed number [tex]\(2 \frac{3}{8}\)[/tex]. This can be converted to an improper fraction.
[tex]\[
2 \frac{3}{8} = 2 + \frac{3}{8}
\][/tex]
Convert the whole number 2 to a fraction with the same denominator as [tex]\(\frac{3}{8}\)[/tex]:
[tex]\[
2 = \frac{16}{8}
\][/tex]
Now add the fractions:
[tex]\[
2 + \frac{3}{8} = \frac{16}{8} + \frac{3}{8} = \frac{19}{8}
\][/tex]
2. Perform the subtraction [tex]\( \frac{19}{8} - \frac{7}{8}\)[/tex]:
Since both fractions have the same denominator, we can subtract the numerators:
[tex]\[
\frac{19}{8} - \frac{7}{8} = \frac{19 - 7}{8} = \frac{12}{8}
\][/tex]
3. Reduce the fraction [tex]\(\frac{12}{8}\)[/tex] to its simplest form:
Find the greatest common divisor (GCD) of 12 and 8, which is 4. Then divide both the numerator and the denominator by their GCD:
[tex]\[
\frac{12}{8} = \frac{12 \div 4}{8 \div 4} = \frac{3}{2}
\][/tex]
4. Convert the improper fraction [tex]\(\frac{3}{2}\)[/tex] to a mixed number:
Divide the numerator by the denominator to separate the whole number part from the fraction:
[tex]\[
\frac{3}{2} = 1 \frac{1}{2}
\][/tex]
So, after performing the subtraction [tex]\(2 \frac{3}{8} - \frac{7}{8}\)[/tex] and reducing the result to its simplest form, we get [tex]\(1 \frac{1}{2}\)[/tex].
