Resolved: "Simplifying long fractions (8+34)+(323)(4+25}−(178) The correct answer is..."

aspifsGak5u

Answered question

2022-01-06

Simplifying long fractions

\frac{(8 + \frac{3}{4}) + (3 \frac{2}{3})}{(4 + \frac{2}{5}} - (1 \frac{7}{8})}

The correct answer is

(4 + \frac{278}{303})

Answer & Explanation

peterpan7117i

Beginner2022-01-07Added 39 answers

Combine the numerator into an improper fraction:

8 \frac{3}{4} + 3 \frac{2}{3} = 8 + 3 + \frac{3}{4} + \frac{2}{3}

= \frac{132}{12} + \frac{9}{12} + \frac{8}{12}

= \frac{149}{12}

Do the same for the denominator:

4 + \frac{2}{5} - 1 \frac{7}{8} = 4 - 1 + \frac{2}{5} - \frac{7}{8}

= \frac{120}{30} + \frac{16}{40} - \frac{35}{40}

= \frac{101}{40}

Then divide both:

\frac{\frac{149}{12}}{\frac{101}{40}} = \frac{149}{101} \cdot \frac{40}{12}

= \frac{149}{101} \cdot \frac{10}{3}

\frac{1490}{303}

= 4 + \frac{278}{303}

Beverly Smith

Beginner2022-01-08Added 42 answers

Just simplify it piece by piece.
First, you have

8 + \frac{3}{4} + 3 \frac{2}{3}

You can simplify this into one fraction.
Then, you simplify

4 \frac{2}{5} - 1 \frac{7}{8}

into one fraction.
Then use the rule

\frac{\frac{a}{b}}{\frac{c}{d}} = \frac{a d}{b c}

and you have just one fraction.

Vasquez

Expert2022-01-11Added 669 answers

Expand
$\frac{8 + \frac{3}{4} + 3 + \frac{2}{3}}{4 + \frac{2}{5} - 1 - \frac{7}{8}}$
by 120 to get
$\frac{11 \cdot 120 + 3 \cdot 30 + 2 \cdot 40}{3 \cdot 120 + 2 \cdot 24 - 7 \cdot 15} = \frac{1490}{303}$

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