Get the answer to "What is the simplified value of 17+314+23+25+56?"

Dalia Morales

Answered question

2022-02-07

What is the simplified value of

\frac{1}{7} + \frac{3}{14} + \frac{2}{3} + \frac{2}{5} + \frac{5}{6}

Answer & Explanation

Vaughn Bradley

Beginner2022-02-08Added 16 answers

To add $\frac{1}{7} + \frac{3}{14} + \frac{2}{3} + \frac{2}{5} + \frac{5}{6}$ , firs convert all denominators to Lease Common Denominator (LCD), which is nothing but Least common multiple of 7, 14, 3, 5 and 6.
LCD of 7, 14, 3, 5 and 6 is
$14 \times 6 \times 5 = 420$ (as 7 is a factor of 14 and 3 is a factor of 5).
Hence, converting each denominator of $\frac{1}{7} + \frac{3}{14} + \frac{2}{3} + \frac{2}{5} + \frac{5}{6}$ to 420,
$\frac{1}{7} + \frac{3}{14} + \frac{2}{3} + \frac{2}{5} + \frac{5}{6}$
$= \frac{1 \times 60}{7 \times 60} + \frac{3 \times 30}{14 \times 30} + \frac{2 \times 140}{3 \times 140} + \frac{2 \times 84}{5 \times 84} + \frac{5 \times 70}{6 \times 70}$
$= \frac{60}{420} + \frac{90}{420} + \frac{280}{420} + \frac{168}{420} + \frac{350}{420}$
$= \frac{60 + 90 + 280 + 168 + 350}{420}$
$= \frac{948}{420} = \frac{237 ⧸ 948}{105 ⧸ 420} = \frac{237}{105} = 2 \frac{27}{105}$
(We have divided 948 and 420 by 4 here to simplify.)

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