Answer:
(-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
