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Gelneren [198K]
3 years ago
6

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

Mathematics
1 answer:
lesya [120]3 years ago
5 0

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

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