Question

adding integers discovery lab
name:
directions: use the counters and number lines to solve the problems. write your answers

1. 5 + 3 = 8
2. 6 + 4 = 10
3. - 5+( - 2)=
4. - 3+( - 3)=
5. - 2+( - 4)=
6. - 1+( - 2)

what do you notice about adding integers that have the same sign? what pattern(s) do you see?

1. 5+( - 3)=
2. 6+( - 4)=
3. 2+( - 1)=
4. - 3 + 3=
5. - 4 + 2=
6. - 5 + 1=

what do you notice about adding integers that have different signs? what pattern(s) do you see?
what other operation could you use instead of adding a negative?
try solving these without the number line or counters! test the patterns you noticed
a) 15+( - 13)=
b) - 16 + 4=
c) - 5+( - 20)=
d) 3+

Explanation:

Step1: Add integers with same - sign

When adding two negative integers, we add their absolute values and keep the negative sign. For example, for \(-5+( - 2)\), the absolute values of \(-5\) and \(-2\) are \(5\) and \(2\) respectively. \(5 + 2=7\), so \(-5+( - 2)=-7\). Similarly, for \(-3+( - 3)\), \(|-3|+|-3| = 3+3 = 6\), so \(-3+( - 3)=-6\), for \(-2+( - 4)\), \(|-2|+|-4|=2 + 4=6\), so \(-2+( - 4)=-6\), and for \(-1+( - 2)\), \(|-1|+|-2|=1 + 2 = 3\), so \(-1+( - 2)=-3\).

Step2: Add integers with different - sign

When adding integers with different signs, we subtract the smaller absolute value from the larger absolute value and take the sign of the number with the larger absolute value. For example, for \(5+( - 3)\), \(|5|-|-3|=5 - 3 = 2\), and since \(|5|>|-3|\) and \(5\) is positive, \(5+( - 3)=2\). For \(6+( - 4)\), \(|6|-|-4|=6 - 4 = 2\), and since \(|6|>|-4|\) and \(6\) is positive, \(6+( - 4)=2\). For \(2+( - 1)\), \(|2|-|-1|=2 - 1 = 1\), and since \(|2|>|-1|\) and \(2\) is positive, \(2+( - 1)=1\). For \(-3 + 3\), \(|3|-|-3|=3 - 3=0\). For \(-4 + 2\), \(|-4|-|2|=4 - 2 = 2\), and since \(|-4|>|2|\) and \(-4\) is negative, \(-4 + 2=-2\). For \(-5 + 1\), \(|-5|-|1|=5 - 1 = 4\), and since \(|-5|>|1|\) and \(-5\) is negative, \(-5 + 1=-4\).

Step3: Alternative operation for adding a negative

Adding a negative integer is the same as subtracting a positive integer. For example, \(a+( - b)=a - b\).

Step4: Solve additional problems

For \(15+( - 13)\), \(|15|-|-13|=15 - 13 = 2\), so \(15+( - 13)=2\). For \(-16 + 4\), \(|-16|-|4|=16 - 4 = 12\), and since \(|-16|>|4|\) and \(-16\) is negative, \(-16 + 4=-12\). For \(-5+( - 20)\), \(|-5|+|-20|=5 + 20 = 25\), so \(-5+( - 20)=-25\).

1. \(-7\)
2. \(-6\)
3. \(-6\)
4. \(-3\)
5. \(2\)
6. \(2\)
7. \(1\)
8. \(0\)
9. \(-2\)
10. \(-4\)

a) \(2\)
b) \(-12\)
c) \(-25\)

Pattern for adding same - sign integers: Add the absolute values and keep the common sign.
Pattern for adding different - sign integers: Subtract the smaller absolute value from the larger absolute value and take the sign of the number with the larger absolute value.
Alternative operation for adding a negative: Subtraction of a positive.

Answer:

Step1: Add integers with same - sign

When adding two negative integers, we add their absolute values and keep the negative sign. For example, for \(-5+( - 2)\), the absolute values of \(-5\) and \(-2\) are \(5\) and \(2\) respectively. \(5 + 2=7\), so \(-5+( - 2)=-7\). Similarly, for \(-3+( - 3)\), \(|-3|+|-3| = 3+3 = 6\), so \(-3+( - 3)=-6\), for \(-2+( - 4)\), \(|-2|+|-4|=2 + 4=6\), so \(-2+( - 4)=-6\), and for \(-1+( - 2)\), \(|-1|+|-2|=1 + 2 = 3\), so \(-1+( - 2)=-3\).

Step2: Add integers with different - sign

When adding integers with different signs, we subtract the smaller absolute value from the larger absolute value and take the sign of the number with the larger absolute value. For example, for \(5+( - 3)\), \(|5|-|-3|=5 - 3 = 2\), and since \(|5|>|-3|\) and \(5\) is positive, \(5+( - 3)=2\). For \(6+( - 4)\), \(|6|-|-4|=6 - 4 = 2\), and since \(|6|>|-4|\) and \(6\) is positive, \(6+( - 4)=2\). For \(2+( - 1)\), \(|2|-|-1|=2 - 1 = 1\), and since \(|2|>|-1|\) and \(2\) is positive, \(2+( - 1)=1\). For \(-3 + 3\), \(|3|-|-3|=3 - 3=0\). For \(-4 + 2\), \(|-4|-|2|=4 - 2 = 2\), and since \(|-4|>|2|\) and \(-4\) is negative, \(-4 + 2=-2\). For \(-5 + 1\), \(|-5|-|1|=5 - 1 = 4\), and since \(|-5|>|1|\) and \(-5\) is negative, \(-5 + 1=-4\).

Step3: Alternative operation for adding a negative

Adding a negative integer is the same as subtracting a positive integer. For example, \(a+( - b)=a - b\).

Step4: Solve additional problems

For \(15+( - 13)\), \(|15|-|-13|=15 - 13 = 2\), so \(15+( - 13)=2\). For \(-16 + 4\), \(|-16|-|4|=16 - 4 = 12\), and since \(|-16|>|4|\) and \(-16\) is negative, \(-16 + 4=-12\). For \(-5+( - 20)\), \(|-5|+|-20|=5 + 20 = 25\), so \(-5+( - 20)=-25\).

1. \(-7\)
2. \(-6\)
3. \(-6\)
4. \(-3\)
5. \(2\)
6. \(2\)
7. \(1\)
8. \(0\)
9. \(-2\)
10. \(-4\)

a) \(2\)
b) \(-12\)
c) \(-25\)

Pattern for adding same - sign integers: Add the absolute values and keep the common sign.
Pattern for adding different - sign integers: Subtract the smaller absolute value from the larger absolute value and take the sign of the number with the larger absolute value.
Alternative operation for adding a negative: Subtraction of a positive.