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Solve and reduce the answer to simplest form: [tex]2 \frac{3}{8} - \frac{7}{8}[/tex]

Sagot :

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].
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