How to simplify - 2 1/4 - 2/3 (-2+1/5)

(-21) / 20

Step-by-step explanation:

Simplify the following:

- (2 + 1/4) - 2/3 (1/5 - 2)

Put 2 + 1/4 over the common denominator 4. 2 + 1/4 = (4*2) / 4 + 1/4:

- (4*2) / 4 + 1/4 - 2/3 (1/5 - 2)

4*2 = 8:

- (8/4 + 1/4) - 2/3 (1/5 - 2)

8/4 + 1/4 = (8 + 1) / 4:

- (8 + 1) / 4 - 2/3 (1/5 - 2)

8 + 1 = 9:

-9/4 - 2/3 (1/5 - 2)

Put - 2 + 1/5 over the common denominator 5. - 2 + 1/5 = (5 (-2)) / 5 + 1/5:

-9/4 - 2/3 1/5 + (5 (-2)) / 5

5 (-2) = - 10:

-9/4 - 2/3 ((-10) / 5 + 1/5)

-10/5 + 1/5 = (-10 + 1) / 5:

-9/4 - 2/3 (1 - 10) / 5

-10 + 1 = - 9:

-9/4 - 2/3 * (-9) / 5

-2 (-9) = 18:

(-9) / 4 + 18 / (3*5)

3*5 = 15:

(-9) / 4 + 18/15

The gcd of 18 and 15 is 3, so 18/15 = (3*6) / (3*5) = 3/3*6/5 = 6/5:

(-9) / 4 + 6/5

Put (-9) / 4 + 6/5 over the common denominator 20. (-9) / 4 + 6/5 = (5 (-9)) / 20 + (4*6) / 20:

(5 (-9)) / 20 + (4*6) / 20

5 (-9) = - 45:

(-45) / 20 + (4*6) / 20

4*6 = 24:

(-45) / 20 + 24/20

-45/20 + 24/20 = (-45 + 24) / 20:

(-45 + 24) / 20

-45 + 24 = - 21:

Answer: (-21) / 20