Question

5 1/16-1 1/8 (5/6+3/14)

Answer 1

51/16 - 11/8 × 22/21

51/16 - 11/4 × 11/21

51/16 - 121/84 = 587/336

Answer 2

To simplify the expression, let's break it down step by step:

First, let's simplify the fraction within the parentheses: 5/6 + 3/14.

To add these fractions, we need to find a common denominator. The least common multiple (LCM) of 6 and 14 is 42, so we'll use that as our common denominator.

Converting the fractions to have a common denominator:

5/6 = (5/6) * (7/7) = 35/42 3/14 = (3/14) * (3/3) = 9/42

Now, we can add the fractions:

35/42 + 9/42 = 44/42

Next, let's subtract the result of the fraction within the parentheses from 5 1/16:

5 1/16 - 1 1/8

To perform this subtraction, we need to convert the mixed numbers to improper fractions.

5 1/16 = (5 * 16 + 1) / 16 = 81/16 1 1/8 = (1 * 8 + 1) / 8 = 9/8

Now, we can subtract the fractions:

81/16 - 9/8

To subtract fractions, we need a common denominator. The LCM of 16 and 8 is 16. Let's convert the fractions:

81/16 = (81/16) * (1/1) = 81/16 9/8 = (9/8) * (2/2) = 18/16

Subtracting the fractions:

81/16 - 18/16 = 63/16

Finally, let's multiply the result by the fraction we simplified earlier, 44/42:

(63/16) * (44/42)

To multiply fractions, we simply multiply the numerators together and the denominators together:

(63 * 44) / (16 * 42) = 2772/672

To simplify this fraction, we can divide both the numerator and denominator by their greatest common divisor, which is 84:

(2772/84) / (672/84) = 33/8

Therefore, the simplified expression is 33/8.