Question

5 2/7 + 3/8 - 51/56-(5 1/24 - 4 1/18)

Answer 1

..............................

Answer 2

To solve the given expression, we'll first convert all mixed fractions into improper fractions and then perform the arithmetic operations step by step. Let's break it down:

Step 1: Convert mixed fractions to improper fractions 5 2/7 = (7 * 5 + 2) / 7 = 37 / 7 5 1/24 = (24 * 5 + 1) / 24 = 121 / 24 4 1/18 = (18 * 4 + 1) / 18 = 73 / 18

Now the expression becomes: 37 / 7 + 3 / 8 - 51 / 56 - (121 / 24 - 73 / 18)

Step 2: Find a common denominator for all fractions (in this case, it is 504, which is the least common multiple of 7, 8, 56, and 24).

Step 3: Perform the arithmetic operations:

1. Convert all fractions to have a denominator of 504: (37 / 7) * (504 / 1) = 2136 / 7 (3 / 8) * (504 / 1) = 189 / 2 (51 / 56) * (504 / 1) = 459 / 4 (121 / 24) * (504 / 1) = 2521 / 2 (73 / 18) * (504 / 1) = 1827 / 2

2. Subtract the mixed fractions: (2521 / 2) - (1827 / 2) = 694 / 2 = 347

Step 4: Now, simplify the expression: 2136 / 7 + 189 / 2 - 459 / 4 - 347

Step 5: Convert the result back to a mixed fraction:

First, find the common denominator for the remaining fractions (in this case, it is 28, which is the least common multiple of 7 and 4).

(2136 / 7) * (4 / 4) = 2136 / 28 (189 / 2) * (14 / 14) = 189 / 28 (459 / 4) * (7 / 7) = 459 / 28

Now, the expression becomes: (2136 / 28) + (189 / 28) - (459 / 28) - 347

Now, combine the fractions: (2136 + 189 - 459) / 28 - 347

Simplify the numerator: (2136 + 189 - 459) = 1866

Final result: 1866 / 28 - 347

Now, simplify the fraction further: 1866 ÷ 28 = 66.642857...

So the final result is approximately: 66.64 - 347 ≈ -280.36