Question

(9/19-(-5/21)÷(-2 9/14)​

Answer 1

(9/19-(-5/21):(-2 9/14) = -568/2109

1) (9/19-(-5/21) = 9/19+5/21 = (189+25)/399 = 284/399

2) 284/399 : (-2 9/14) = 284/399 : (-37/14) = 284/399 * (-14/37) = 284/57 * (-2/37) = -568/2109

Answer 2

To simplify the expression (9/19 - (-5/21)) ÷ (-2 9/14), let's break it down step by step.

First, let's simplify the subtraction part: 9/19 - (-5/21).

When we subtract a negative number, it is equivalent to adding the positive number. So, the expression becomes:

9/19 + 5/21

To add these fractions, we need to find a common denominator. The least common multiple of 19 and 21 is 399.

So, let's convert both fractions to have a denominator of 399:

(9/19) * (21/21) = 189/399 (5/21) * (19/19) = 95/399

Now, we can add the fractions:

189/399 + 95/399 = (189 + 95) / 399 = 284/399

Next, let's simplify the division part: (-2 9/14).

To perform division, we need to convert the mixed number into an improper fraction. Multiply the whole number (-2) by the denominator (14) and add the numerator (9). Then, put the result over the denominator:

(-2 * 14 + 9) / 14 = (-28 + 9) / 14 = (-19) / 14

Finally, let's divide the fraction we obtained above by (-19/14):

(284/399) ÷ (-19/14)

When we divide by a fraction, it is equivalent to multiplying by its reciprocal. So, the expression becomes:

(284/399) * (-14/19)

To multiply fractions, we multiply the numerators together and the denominators together:

(284 * -14) / (399 * 19) = -3976 / 7581

Therefore, the simplified expression (9/19 - (-5/21)) ÷ (-2 9/14) is -3976/7581.