Adding & Subtracting Rational Numbers - Pre Algebra

1. What is the sum of any number and its opposite?

   $0$. For example, $-6.2 + 6.2 = 0$; opposites are additive inverses.

2. What is $-3.5 + (-1.25)$?

   $-4.75$. Both are negative, so add $3.5 + 1.25$ and keep the negative sign.

3. What is $-\frac{1}{4} - \frac{1}{2}$?

   $-\frac{3}{4}$. Rewrite as $-\frac{1}{4} + \left(-\frac{2}{4}\right)$.

4. What is $-\frac{2}{3} + \frac{1}{6}$?

   $-\frac{1}{2}$. Rewrite as $-\frac{4}{6} + \frac{1}{6} = -\frac{3}{6}$.

5. What is the rule for adding a positive number and a negative number?

   Subtract the smaller absolute value from the larger one, and give the result the sign of the number with the larger absolute value.

6. What is $2.4 - 5.1$?

   $-2.7$. Since $5.1 > 2.4$, the difference is negative: $5.1 - 2.4 = 2.7$.

7. On a horizontal number line, which direction do you move to add a negative number?

   Left. Adding a negative number decreases the value, so you move toward smaller numbers.

8. What is $-5 - 8$?

   $-13$. Rewrite as $-5 + (-8)$ and add the absolute values.

9. What is $6 - (-9)$?

   $15$. Subtracting $-9$ is the same as adding $9$.

10. What is $-7 + 4$?

    $-3$. The signs differ, so $7 - 4 = 3$ takes the sign of $-7$.

11. Subtracting a number is the same as adding what?

    Its opposite: $a - b = a + (-b)$. For example, $4 - 9 = 4 + (-9) = -5$.

12. What is the rule for adding two negative numbers?

    Add their absolute values and make the sum negative. For example, $-3 + (-5) = -8$.

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