Question

-1+2 1/9 -4+3 1/2-5/7+4/7-5/8+7/8-1/6+15/12-1/127/15-11/155/16-1/16-5/6+2/3-3/4+4/5-1/2+1/8​

Answer 1

1)

$- 1 + 2 \frac{1}{9} = - 1 + 2 + \frac{1}{9} = ( - 1 + 2) + \frac{1}{9} = 1 + \frac{1}{9} = 1 \frac{1}{9}$

2)

$- 4 + 3 \frac{1}{2} = - 4 + \frac{7}{2} = \frac{ - 8 + 7}{2} = - \frac{1}{2}$

3)

$- \frac{5}{7} + \frac{4}{7} = \frac{ - 5 + 4}{7} = \frac{ - 1}{7} = - \frac{1}{7}$

4)

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

5)

$- \frac{1}{6} + 1 = \frac{ - 1 + 6}{6} = \frac{5}{6}$

6)

$\frac{5}{12} - \frac{1}{12} = \frac{5 - 1}{12} = \frac{4}{12} = \frac{1}{3}$

7)

$\frac{7}{15} - \frac{11}{15} = \frac{7 - 11}{15} = \frac{ - 4}{15} = - \frac{4}{15}$

8)

$\frac{5}{16 } - \frac{1}{16} = \frac{5 - 1}{16} = \frac{4}{16} = \frac{1 }{4}$

9)

$- \frac{3}{4} + \frac{4}{5} = \frac{ - 15 + 16}{20} = \frac{1}{20}$

10)

$- \frac{1}{2} + \frac{1}{8} = \frac{ - 4 + 1}{8} = \frac{ - 3}{8} = - \frac{3}{8}$

Answer 2

To evaluate the given expression, let's break it down step by step:

-1 + 2 + 1/9 - 4 + 3 + 1/2 - 5/7 + 4/7 - 5/8 + 7/8 - 1/6 + 15/12 - 1/12 - 5/6 + 2/3 - 3/4 + 4/5 - 1/2 + 1/8

Addition and Subtraction:

We can start by performing the addition and subtraction operations from left to right:

-1 + 2 = 1

1 + 1/9 = 10/9

10/9 - 4 = -26/9

-26/9 + 3 = 7/9

7/9 + 1/2 = 23/18

23/18 - 5/7 = 61/126

61/126 + 4/7 = 109/126

109/126 - 5/8 = 17/504

17/504 + 7/8 = 71/504

71/504 - 1/6 = 59/504

59/504 + 15/12 = 77/72

77/72 - 1/12 = 191/144

191/144 - 5/6 = 41/144

41/144 + 2/3 = 197/144

197/144 - 3/4 = 41/144

41/144 + 4/5 = 209/144

209/144 - 1/2 = 161/144

161/144 + 1/8 = 1309/1152

Simplification:

To simplify the fraction 1309/1152, we can find the greatest common divisor (GCD) of the numerator and denominator, and then divide both by the GCD:

GCD