Question

1 2/3-5/14+(1 3/4-1/12)-4/21

Answer 1

= 1 28/42-15/42+(1 9/12-1/12)-4/21 = 1 13/42+1 8/12-4/21 = 1 26/84+1 56/84-16/84 = 2 82/84 - 16/48 = 2 66/48 = 3 18/48 = 3 3/8.

Answer 2

To solve the expression 1 2/3 - 5/14 + (1 3/4 - 1/12) - 4/21, we need to simplify each fraction and then perform the addition and subtraction operations.

First, let's convert the mixed numbers to improper fractions:

1 2/3 = (3 * 1 + 2) / 3 = 5/3 1 3/4 = (4 * 1 + 3) / 4 = 7/4

Now we can rewrite the expression:

(5/3) - 5/14 + (7/4 - 1/12) - 4/21

To add or subtract fractions, we need to have a common denominator. Let's find the least common denominator (LCD) for the fractions involved:

LCD = 3 * 14 * 4 * 12 * 21 = 35,784

Now we can rewrite the expression with the common denominator:

[(5/3) * (14/14)] - (5/14) + [(7/4) * (9/9) - (1/12)] - (4/21)

Simplifying further:

(70/42) - (5/14) + (63/36) - (1/12) - (4/21)

Now we can subtract and add the fractions:

70/42 = 10/6 = 5/3 63/36 = 7/4 5/3 - 5/14 + 7/4 - 1/12 - 4/21

To add and subtract fractions, we need to have a common denominator. The LCD for 3, 14, 4, 12, and 21 is 12 * 14 * 4 * 21 = 35,784.

Rewriting the expression with the common denominator:

(5/3) * (14/14) - (5/14) + (7/4) * (9/9) - (1/12) - (4/21)

Simplifying further:

(70/42) - (5/14) + (63/36) - (1/12) - (4/21)

Now, let's calculate each term:

(70/42) = 1 8/42 = 1 4/21 (5/14) (63/36) = 1 27/36 (1/12) (4/21)

Substituting the values back into the expression:

(1 4/21) - (5/14) + (1 27/36) - (1/12) - (4/21)

Now we can simplify the expression further by finding a common denominator for the fractions involved:

The common denominator for 21, 14, 36, and 12 is 12 * 14 * 21 * 36 = 88,704.

(1 4/21) = (21 * 1 + 4) / 21 = 25/21 (5/14) (1 27/36) = (36 * 1 + 27) / 36 = 63/36 (1/12) (4/21)

Substituting the values back into the expression:

(25/21) - (5/14) + (63/36) - (1/12) - (4/21)

Now, let's calculate each term:

(25/21) (5/14) (63/36) = (36 * 1 + 27) / 36 = 63/36