Question

(7 1/2+2 2/3-12 1/4:7/9):6+3 1/8+5 2/7

Answer 1

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Answer 2

Let's break down the expression step by step:

1. Calculate the sum of the first three fractions: 7 1/2 + 2 2/3 - 12 1/4

To add mixed fractions, we first convert them into improper fractions:

7 1/2 = (7 * 2 + 1) / 2 = 15/2 2 2/3 = (2 * 3 + 2) / 3 = 8/3 12 1/4 = (12 * 4 + 1) / 4 = 49/4

Now, subtract the last two fractions from the first one:

15/2 + 8/3 - 49/4

To add these fractions, we need to find a common denominator. The common denominator for 2, 3, and 4 is 12:

(15/2)(6/6) + (8/3)(4/4) - (49/4)*(3/3) = 90/12 + 32/12 - 147/12 = (90 + 32 - 147) / 12 = -25 / 12

So, the result of the first part is -25/12.

2. Calculate the division of the previous result by 7/9: (-25/12) / (7/9)

To divide by a fraction, we multiply by its reciprocal:

(-25/12) * (9/7)

Now, multiply the numerators and denominators:

= (-25 * 9) / (12 * 7) = -225 / 84

We can simplify this fraction:

= -75 / 28

So, the result after the division is -75/28.

3. Add the next three numbers: 6 + 3 1/8 + 5 2/7

To add mixed fractions, convert them into improper fractions:

3 1/8 = (3 * 8 + 1) / 8 = 25/8 5 2/7 = (5 * 7 + 2) / 7 = 37/7

Now, add the three fractions:

6 + 25/8 + 37/7

To add these fractions, we need to find a common denominator. The common denominator for 8 and 7 is 56:

(6 * 56/56) + (25/8)(7/7) + (37/7)(8/8) = 336/56 + 175/56 + 296/56 = (336 + 175 + 296) / 56 = 807 / 56

Now, the final step is to add the result of the division to this sum:

-75/28 + 807/56

To add these fractions, we need to find a common denominator. The common denominator for 28 and 56 is 56:

(-75/28)(2/2) + (807/56)(1/1) = -150/56 + 807/56 = (807 - 150) / 56 = 657 / 56

The final result is 657/56.