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Blake Ayers
Mathematics
12 June, 07:38
How to simplify - 2 1/4 - 2/3 (-2+1/5)
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Alexzander Frederick
12 June, 07:59
0
(-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
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