Mastering Integer and Rational Addition

To solve 3 + -7, you add 3 and -7. This is the same as 3 - 7, which equals -4. Therefore, the correct answer is -4.

The temperature on Monday was 3°C. If it was 7.5 degrees lower on Tuesday, we calculate: 3 - 7.5 = -4.5°C. Therefore, the temperature on Tuesday was -4.5°C.

To find the missing number, we can rearrange the equation: -2 + x = -7. Adding 2 to both sides gives x = -7 + 2, which simplifies to x = -5. Thus, the missing number is -5.

To find the sum of 7 and 5, simply add the two numbers: 7 + 5 = 12. Therefore, the correct answer is 12.

To calculate -8 + (-3), add the two negative numbers: -8 + (-3) = -8 - 3 = -11. Therefore, the correct answer is -11.

To add \(\frac{3}{4} + \frac{1}{2}\), convert \(\frac{1}{2}\) to \(\frac{2}{4}\). Now, \(\frac{3}{4} + \frac{2}{4} = \frac{5}{4}\). However, this is incorrect; the correct addition is \(\frac{3}{4} + \frac{1}{2} = \frac{7}{4}\).

To subtract the fractions, find a common denominator. The least common multiple of 6 and 3 is 6. Rewrite \(\frac{1}{3}\) as \(\frac{2}{6}\). Now, \(\frac{5}{6} - \frac{2}{6} = \frac{3}{6} = \frac{1}{2}\). Thus, the correct answer is \(\frac{1}{2}\).