Question

Simplify: 1/21 +[1/21÷{1/4-(1/5-1/30)}]​

Answer 1

Answer:

(13/21)

Step-by-step explanation:

Simplify the following:

1/21 + 1/(21 (1/4 - (1/5 - 1/30)))

Put 1/5 - 1/30 over the common denominator 30. 1/5 - 1/30 = 6/30 - 1/30:

1/21 + 1/(21 (1/4 - 6/30 - 1/30))

6/30 - 1/30 = (6 - 1)/30:

1/21 + 1/(21 (1/4 - (6 - 1)/30))

6 - 1 = 5:

1/21 + 1/(21 (1/4 - 5/30))

The gcd of 5 and 30 is 5, so 5/30 = (5×1)/(5×6) = 5/5×1/6 = 1/6:

1/21 + 1/(21 (1/4 - 1/6))

Put 1/4 - 1/6 over the common denominator 12. 1/4 - 1/6 = 3/12 - 2/12:

1/21 + 1/(21 (3/12 - 2/12))

3/12 - 2/12 = (3 - 2)/12:

1/21 + 1/(21 ((3 - 2)/12))

3 - 2 = 1:

1/21 + 1/(21 (1/12))

21 (1/12) = (21/12):

1/21 + 1/((21/12))

The gcd of 21 and 12 is 3, so 21/12 = (3×7)/(3×4) = 3/3×7/4 = 7/4:

1/21 + 1/((7/4))

((7/4))^(-1) = (1/(7/4)):

1/21 + (1/(7/4))

1/(7/4) = (4/7)^1:

1/21 + (4/7)

1/21 + (4/7) = (1/21 + 4/7):

(1/21 + 4/7)

Put 1/21 + 4/7 over the common denominator 21. 1/21 + 4/7 = 1/21 + (3×4)/21:

(1/21 + (3×4)/21)

3×4 = 12:

(1/21 + 12/21)

1/21 + 12/21 = (1 + 12)/21:

((1 + 12)/21)

1 + 12 = 13:

Answer: (13/21)

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Answer 2

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