subtract the additive inverse of 5/6 from the multiplicative inverse of -5/7 multiply 14/15
The Correct Answer and Explanation is:
Let’s break this problem down into smaller steps:
Step 1: Find the additive inverse of 5/6.
The additive inverse of a number is the opposite of that number. So, the additive inverse of 5/6 is -5/6.
Step 2: Find the multiplicative inverse of -5/7.
The multiplicative inverse of a number is its reciprocal, meaning you flip the numerator and denominator. Therefore, the multiplicative inverse of -5/7 is -7/5.
Step 3: Subtract the additive inverse of 5/6 from the multiplicative inverse of -5/7.
Now, we subtract -5/6 from -7/5:(−75)−(−56)=−75+56\left(-\frac{7}{5}\right) – \left(-\frac{5}{6}\right) = -\frac{7}{5} + \frac{5}{6}(−57)−(−65)=−57+65
To perform this addition, we need a common denominator. The least common denominator (LCD) of 5 and 6 is 30. We convert both fractions to have 30 as the denominator:−75=−4230,56=2530-\frac{7}{5} = -\frac{42}{30}, \quad \frac{5}{6} = \frac{25}{30}−57=−3042,65=3025
Now, we add them:−4230+2530=−42+2530=−1730-\frac{42}{30} + \frac{25}{30} = \frac{-42 + 25}{30} = \frac{-17}{30}−3042+3025=30−42+25=30−17
Step 4: Multiply the result by 14/15.
Next, we multiply the result -17/30 by 14/15:−1730×1415=−17×1430×15=−238450\frac{-17}{30} \times \frac{14}{15} = \frac{-17 \times 14}{30 \times 15} = \frac{-238}{450}30−17×1514=30×15−17×14=450−238
Simplify this fraction by finding the greatest common divisor (GCD) of 238 and 450, which is 2:−238450=−119225\frac{-238}{450} = \frac{-119}{225}450−238=225−119
Final Answer:
The final result is -119/225.
