Final answer:
To simplify the expression 7/8 + (-2/3) ÷ 5/6, you divide -2/3 by 5/6, which is the same as multiplying by its reciprocal, and then add the result to 7/8 with a common denominator, simplifying to the fraction 3/40.
Step-by-step explanation:
To simplify 7/8 + (-2/3) ÷ 5/6, let's first deal with the division part. Division by a fraction is the same as multiplication by its reciprocal. Therefore, -2/3 ÷ 5/6 becomes -2/3 × 6/5. Next, we multiply the numerators and denominators separately: (-2 × 6) / (3 × 5) equals -12/15, which can be simplified to -4/5.
Now, we need to add this result to 7/8. To do this, we need a common denominator. The least common denominator for 8 and 5 is 40. We convert both fractions to have this common denominator: (7/8 × 5/5) + (-4/5 × 8/8) equals 35/40 + (-32/40). Adding these together yields 3/40.
So, 7/8 + (-2/3) ÷ 5/6 simplifies to 3/40 when expressed as a fraction in simplest form.