divide the sum of 13/5 and -12/7 by the product of -31/7 and 1/-2 and add the result to (-2/3-1/3)
To solve this problem, follow these steps:
Step 1: Find the sum of 13/5 and -12/7
To add fractions, you need a common denominator. In this case, the common denominator is 35.
(13/5) + (-12/7) = (13/5) × (7/7) + (-12/7) × (5/5) (multiplying by 1 to maintain the value)
= (91/35) + (-60/35) (simplifying)
= (91 - 60)/35 (combining the numerators)
= 31/35 (simplifying the numerator)
Step 2: Find the product of -31/7 and 1/-2
To multiply fractions, multiply the numerators together and the denominators together.
(-31/7) × (1/-2) = (-31 × 1)/(7 × -2) (multiplying the numerators and denominators)
= -31/-14 (simplifying)
= 31/14 (cancelling the negatives)
Step 3: Add the result from Step 1 to (-2/3 - 1/3)
(-2/3 - 1/3) = (-2 - 1)/3 (subtracting the numerators)
= -3/3 (simplifying the numerator)
= -1 (simplifying)
Now, add the result from Step 2 to the result from Step 3:
(31/35) + (-1) = (31/35) + (-1 × 35/35) (multiplying -1 by 35/35 to maintain the value)
= (31/35) + (-35/35) (simplifying)
= (31 - 35)/35 (combining the numerators)
= -4/35 (simplifying the numerator)
Therefore, the final answer is -4/35.
(13/5-12/7)/(-31/7*-1/2) + (-2/3-1/3) =
(91/35-60/35)/(31/14) + (-1) =
(31/35)/(31/14) - 1 = ?