Question

(-2 1/8)*(-1 29/51)+(-1 23/42)*3 1/13-(-4 2/3)

Answer 1

$1) - 2 \frac{1}{8} \times ( - 1 \frac{29}{51} ) = \\ \frac{17}{8} \times \frac{80}{51} = \frac{10}{3} = 3 \frac{1}{3}$

$2) - 1 \frac{23}{42} \times 3 \frac{1}{13} = - \frac{65}{42} \times \frac{40}{13} = \\ - \frac{5 \times 20}{21} = - \frac{100}{21} = - 4 \frac{16}{21}$

$3)3 \frac{1}{3} - 4 \frac{16}{21} = 3 \frac{7}{21} - 4 \frac{16}{21} = \\ - 1 \frac{9}{21} = - 1 \frac{3}{7}$

$4) - 1 \frac{3}{7} - ( - 4 \frac{2}{3} ) = \\ - 1 \frac{9}{21} + 4 \frac{14}{21} = 3 \frac{5}{21}$

Answer 2

To solve this expression, we'll need to follow the order of operations (PEMDAS) and simplify each term separately:

First, we'll simplify (-2 1/8)*(-1 29/51):

-2 1/8 can be written as -17/8 -1 29/51 can be written as -80/51

So, (-2 1/8)(-1 29/51) = (-17/8)(-80/51) = 34/17

Next, we'll simplify (-1 23/42)*3 1/13:

-1 23/42 can be written as -65/42 3 1/13 can be written as 40/13

So, (-1 23/42)3 1/13 = (-65/42)(40/13) = -100/21

Finally, we'll simplify (-4 2/3):

-4 2/3 can be written as -14/3

Now, we can substitute all of these simplified terms into the original expression:

34/17 - 100/21 - (-14/3)

Simplifying the double negative:

34/17 - 100/21 + 14/3

Getting a common denominator of 51*3 = 153:

(334)/(317) - (7100)/(721) + (1714)/(317)

Simplifying:

6/17 - 20/3 + 14/3

Getting a common denominator of 3*17 = 51:

(36)/(317) - (1720)/(317) + (1714)/(317)

Simplifying:

18/51 - 340/51 + 238/51

Combining like terms:

(18 - 340 + 238)/51

Simplifying:

-84/51 or -28/17

Therefore, (-2 1/8)*(-1 29/51)+(-1 23/42)*3 1/13-(-4 2/3) = -28/17.