Question

name_ adding integers practice — mixed positive & negative date_ directions: solve each problem. show your work using a number line or another 1. +9 + (-4) = 2. -7 + (+3) = 3. -5 + (-9) = 4. +12 + (+8) = 5. -10 + (+6) = 6. +4 + (-11) = 7. -15 + (-7) = 8. +18 + (-12) = 9. -9 + (+14) = 10. +20 + (-25) =

Explanation:

Step1: Recall integer - addition rule

When adding integers \(a + b\), if the signs are the same, add the absolute values and keep the sign. If the signs are different, subtract the smaller absolute - value from the larger absolute - value and take the sign of the number with the larger absolute value.

Step2: Solve problem 1

For \(+9+( - 4)\), the signs are different. \(|9| = 9\) and \(|-4| = 4\). \(9-4=5\), and since \(|9|>| - 4|\) and 9 is positive, the result is \(5\).

Step3: Solve problem 2

For \(-7+(+3)\), the signs are different. \(|-7| = 7\) and \(|3| = 3\). \(7 - 3=4\), and since \(|-7|>|3|\) and \(-7\) is negative, the result is \(-4\).

Step4: Solve problem 3

For \(-5+( - 9)\), the signs are the same. \(| - 5|+| - 9|=5 + 9=14\), and since the numbers are negative, the result is \(-14\).

Step5: Solve problem 4

For \(+12+(+8)\), the signs are the same. \(|12|+|8|=12 + 8=20\), and since the numbers are positive, the result is \(20\).

Step6: Solve problem 5

For \(-10+(+6)\), the signs are different. \(|-10| = 10\) and \(|6| = 6\). \(10-6 = 4\), and since \(|-10|>|6|\) and \(-10\) is negative, the result is \(-4\).

Step7: Solve problem 6

For \(+4+( - 11)\), the signs are different. \(| - 11| = 11\) and \(|4| = 4\). \(11-4 = 7\), and since \(| - 11|>|4|\) and \(-11\) is negative, the result is \(-7\).

Step8: Solve problem 7

For \(-15+( - 7)\), the signs are the same. \(| - 15|+| - 7|=15 + 7=22\), and since the numbers are negative, the result is \(-22\).

Step9: Solve problem 8

For \(+18+( - 12)\), the signs are different. \(|18| = 18\) and \(| - 12| = 12\). \(18-12 = 6\), and since \(|18|>| - 12|\) and 18 is positive, the result is \(6\).

Step10: Solve problem 9

For \(-9+(+14)\), the signs are different. \(|14| = 14\) and \(|-9| = 9\). \(14-9 = 5\), and since \(|14|>|-9|\) and 14 is positive, the result is \(5\).

Step11: Solve problem 10

For \(+20+( - 25)\), the signs are different. \(| - 25| = 25\) and \(|20| = 20\). \(25-20 = 5\), and since \(| - 25|>|20|\) and \(-25\) is negative, the result is \(-5\).

Answer:

1. \(5\)
2. \(-4\)
3. \(-14\)
4. \(20\)
5. \(-4\)
6. \(-7\)
7. \(-22\)
8. \(6\)
9. \(5\)
10. \(-5\)