Final answer:
The expression 2(-4/5)+6(1/3) simplifies to the fraction 2/5. First, the multiplication is performed for both terms, then the results are added, with careful attention to the signs of the numbers involved.
Step-by-step explanation:
To evaluate the expression 2(-4/5)+6(1/3), you should follow the order of operations and multiply before you add. The multiplication of two negative numbers (as in the first term) or two positive numbers results in a positive product, while the multiplication of a positive number with a negative number results in a negative product. Here's a step-by-step breakdown:
- Multiply 2 by -4/5. Since one is positive and the other negative, the result is negative: 2 x -4/5 = -8/5.
- Multiply 6 by 1/3. Both numbers are positive, so the result is positive: 6 x 1/3 = 6/3 which can be simplified to 2.
- Now add the two results: -8/5 + 2. Converting 2 to a fraction with a common denominator of 5 gives us 10/5. So we have -8/5 + 10/5 = 2/5.
The final answer in simplest form as a fraction is 2/5.