Question

-(19 4/15 - 21,095) + (8 1/5 - 18,975) - (-11 2/3 + 2,12)

Answer 1

$- (19 \frac{4}{15} - 21.095 )+ (8 \frac{1}{5} - 18.975) - ( - 11 \frac{2}{3} + 2.12) = - 19 \frac{4}{15} + 21.095+8 \frac{1}{5} - 18.975 + 11 \frac{2}{3} - 2.12 = \frac{3}{5} + 0 = \frac{3}{5} = 0.6\\ 1) \: \: \: - 19 \frac{4}{15} + 8 \frac{3}{15} + 11 \frac{10}{15} = \frac{ - 4 + 3 + 10}{15} = \frac{9}{15} = \frac{3}{5} \\ 2) \: \: \: 21.095 - 18.975 - 2.12 = 2.12 - 2.12 = 0$

Answer 2

Let's break down the expression step by step:

1. -(19 4/15 - 21,095): First, we need to subtract 21,095 from the mixed number 19 4/15. To do this, we need to convert 19 4/15 to an improper fraction.

19 4/15 = (19 * 15 + 4) / 15 = (286 + 4) / 15 = 290 / 15

Now, the expression becomes:

-(290/15 - 21,095)

To perform the subtraction, we need to find a common denominator, which is 15. So, we can rewrite 21,095 as 21,095 / 1, with 15 as the denominator:

-(290/15 - 21,095/1)

Now, we can subtract:

-(290/15 - 21,095/1) = -(290/15 - 21,095/15) = -((290 - 21,095) / 15) = -20,805 / 15 = -1387

2. (8 1/5 - 18,975): Similar to the previous step, let's convert 8 1/5 to an improper fraction:

8 1/5 = (8 * 5 + 1) / 5 = (40 + 1) / 5 = 41 / 5

Now, the expression becomes:

41/5 - 18,975

To perform the subtraction, we need to find a common denominator, which is 5. So, we can rewrite 18,975 as 18,975 / 1, with 5 as the denominator:

41/5 - 18,975/1 = 41/5 - 18,975/5 = (41 - 18,975) / 5 = -18,934 / 5 = -3,786.8

3. (-11 2/3 + 2,12): Again, convert -11 2/3 to an improper fraction:

-11 2/3 = -(11 * 3 + 2) / 3 = -(33 + 2) / 3 = -35 / 3

Now, the expression becomes:

-35/3 + 2,12

To perform the addition, we need to find a common denominator, which is 3. So, we can rewrite 2,12 as 2 + 12/100, and then convert to a fraction with 3 as the denominator:

2,12 = 2 + 12/100 = 2 + 12/100 * 3/3 = 2 + 36/300 = 2 + 36/300 = 2 + 6/50 = 2 + 3/25

Now, the expression becomes:

-35/3 + 2 + 3/25

To add these fractions, we need to find a common denominator, which is 75 (3 * 25):

-35/3 + 2 + 3/25 = -35/3 + 2 * 25/25 + 3/25 = -35/3 + 50/25 + 3/25 = (-35 + 50 + 3) / 25 = 18/25

Now, the final expression is:

-1387 + (-3,786.8) - 18/25

Now, let's perform the subtraction and addition:

-1387 - 3,786.8 - 18/25 ≈ -5171.8 - 18/25

To combine the whole numbers with the fraction, we find a common denominator, which is 25:

-5171.8 - 18/25 = -5171.8 * 25/25 - 18/25 = (-51718 - 18) / 25 = -51736 / 25

So, the final result is approximately:

-51736 / 25 ≈ -2069.44