simplify 1/5+2/7-6/11 — step-by-step solution

Let's reduce:

\frac{1}{5} + \frac{2}{7} - \frac{6}{11}

ⓘ To add fractions, put them over the same denominator, then add the numerators. We choose

35

, the least common multiple of

5

and

7

. Multiplying the numerator and the denominator by the same number does not change the fraction:

\frac{1}{5} + \frac{2}{7}

\frac{1 \times 7}{5 \times 7} + \frac{2 \times 5}{7 \times 5}

\frac{1 \times 7 + 2 \times 5}{5 \times 7}

\frac{7 + 2 \times 5}{5 \times 7}

\frac{7 + 2 \times 5}{5 \times 7} - \frac{6}{11}

ⓘ Multiplications are done before additions and subtractions:

2 \times 5

10

ⅰ

5 \times 7

35

\frac{7 + 10}{35} - \frac{6}{11}

ⓘ The numerator and the denominator are computed before the division:

7 + 10

17

\frac{17}{35} - \frac{6}{11}

ⓘ To add fractions, put them over the same denominator, then add the numerators. We choose

385

, the least common multiple of

35

and

11

. Multiplying the numerator and the denominator by the same number does not change the fraction:

\frac{17}{35} - \frac{6}{11}

\frac{17 \times 11}{35 \times 11} + \frac{-6 \times 35}{11 \times 35}

\frac{17 \times 11 - 6 \times 35}{35 \times 11}

\frac{17 \times 11 - 6 \times 35}{35 \times 11}

ⓘ Multiplications are done before additions and subtractions:

17 \times 11

17 \times (10 + 1)

17 \times 10 + 17

170 + 17

187

6 \times 35

6 \times (30 + 5)

6 \times 30 + 6 \times 5

180 + 30

210

ⅰ

35 \times 11

35 \times (10 + 1)

35 \times 10 + 35

350 + 35

385

\frac{187 - 210}{385}

ⓘ The numerator and the denominator are computed before the division:

187 - 210

-23

▶Simplified form:

- \frac{23}{385}

The numeric value of:

- \frac{23}{385}

equals:

▷

\approx -5.974 \times 10^{- 2}