Question

(1/122-2):(1/5-1/40)-(2+6 2/3):(1 5/6-1 2/3) по действиям

Answer 1

Ответ:

$-63\frac{163}{427}$

Пошаговое объяснение:

$(\frac{1}{122} - 2) / (\frac{1}{5} - \frac{1}{40}) - (2 + 6\frac{2}{3}) / (1\frac{5}{6} - 1\frac{2}{3})$

1) $\frac{1}{122} - 2 = \frac{1}{122} - \frac{2}{1} = \frac{1}{122} - \frac{244}{122} = - \frac{243}{122}$

2) $\frac{1}{5} - \frac{1}{40} = \frac{8}{40} - \frac{1}{40} = \frac{7}{40}$

3) $2+ 6\frac{2}{3} = 8\frac{2}{3} = \frac{26}{3}$

4) $1\frac{5}{6} - 1\frac{2}{3} = \frac{11}{6} - \frac{5}{3} = \frac{11}{6} - \frac{10}{6} = \frac{1}{6}$

5) $-\frac{243}{122} / \frac{7}{40} = -\frac{243}{122} * \frac{40}{7} = - \frac{243 * 40}{122* 7} = - \frac{9720}{854} = - 11\frac{326}{854} = - 11\frac{163}{427}$

6) $\frac{26}{3} / \frac{1}{6} = \frac{26}{3} * \frac{6}{1} = \frac{26 * 6}{3 * 1} = 52$

7) $-11\frac{163}{427} - 52 = -63\frac{163}{427}$

Answer 2

To simplify the expression (1/122-2):(1/5-1/40)-(2+6 2/3):(1 5/6-1 2/3), we can follow the order of operations (PEMDAS/BODMAS) to evaluate the expression step by step:

Step 1: Simplify the fractions: 1/122-2 becomes (1-2*122)/122 = (-243)/122 = -2

1/5-1/40 becomes (8/40-1/40) = 7/40

Step 2: Simplify the mixed numbers: 2+6 2/3 becomes 2+(6+2/3) = 2+(18/3+2/3) = 2+(20/3) = (6/3+20/3) = 26/3

1 5/6-1 2/3 becomes (6+5/6)-(3+2/3) = (66+5)/6 - (33+2)/3 = (36+5)/6 - (9+2)/3 = 41/6 - 11/3

Step 3: Convert the mixed number to a fraction: 41/6 - 11/3 becomes (413-116)/6 = (123-66)/6 = 57/6 = 19/2

Step 4: Perform the division: -2 / 7/40 = -2 * 40/7 = -80/7

26/3 / 19/2 = 26/3 * 2/19 = 52/57

Step 5: Subtract the results: (-80/7) - (52/57) = (-8057)/(757) - (527)/(577) = -4560/399 - 364/399 = (-4560 - 364)/399 = -4924/399

Therefore, the final result is -4924/399.