Solve the following problem. Reduce your answer to its simplest form.

[tex]\[ 7 \frac{1}{6} - 3 \frac{4}{9} \][/tex]

Select one of the following:

A. [tex]\[ 4 \frac{2}{3} \][/tex]

B. [tex]\[ 3 \frac{13}{18} \][/tex]

C. [tex]\[ 4 \frac{7}{18} \][/tex]

D. [tex]\[ 2 \frac{15}{18} \][/tex]



Answer :

To solve the problem [tex]\( 7 \frac{1}{6} - 3 \frac{4}{9} \)[/tex], we will go through the steps to subtract these two mixed numbers and express the result in its simplest form.

1. Convert the mixed fractions to improper fractions:

[tex]\[ 7 \frac{1}{6} \rightarrow 7 + \frac{1}{6} = 7 + 0.166\overline{6} = 7.166\overline{6} \][/tex]

[tex]\[ 3 \frac{4}{9} \rightarrow 3 + \frac{4}{9} = 3 + 0.4\overline{4} = 3.4\overline{4} \][/tex]

2. Perform the subtraction:

[tex]\[ 7.166\overline{6} - 3.4\overline{4} = 3.7222222\overline{2} \][/tex]

3. Convert the result back to a mixed fraction:

The result we obtained is [tex]\( 3.7222222\overline{2} \)[/tex]. Breaking it down into a mixed number, we get:

[tex]\[ \text{Whole number part} = 3 \][/tex]

[tex]\[ \text{Fractional part} = 0.7222222\overline{2} \][/tex]

4. Convert the decimal part to a fraction:

[tex]\[ 0.7222222\overline{2} \][/tex]

First, recognize it as:

[tex]\[ 0.7222222\overline{2} = \frac{13}{18} \][/tex]

5. Combine the whole number with the fraction:

Thus, [tex]\( 3.7222222\overline{2} \)[/tex] can be written as:

[tex]\[ 3 \frac{13}{18} \][/tex]

Selecting the simplified and correct answer from the options:

[tex]\[ \boxed{3 \frac{13}{18}} \][/tex]