Question

rule 2: multiplication and division rules are the same
same signs?=
different signs?=
how? a positive \square or \square by a positive is always
a negative \square or \square by a negative is always
a positive \square or \square by a negative is always
examples with numbers:
-2×2
\frac{10}{-2}
5(-20)
-7(-8)
-\frac{10}{2}
examples with variables:
-2(c)
-2(-c)
2c(2)
\frac{10}{-2}x
\frac{-18x}{3}
examples with distributing: (dont forget rule #1)
-2(c+4)
-2(c-3)
\frac{1}{2}(10x+-5)
x(-4-7)
-10(x-5)
examples with factoring: (dont forget rule #1)
2c+4
-2c-20
10x+-5
-4x+7x
-5x-5

Explanation:

Step1: Fill sign rules

Same signs?= Positive
Different signs?= Negative
How? A positive multiplied or divided by a positive is always positive
A negative multiplied or divided by a negative is always positive
A positive multiplied or divided by a negative is always negative

Step2: Solve number examples

• $-2 \times 2 = -4$
• $\frac{10}{-2} = -5$
• $5(-20) = -100$
• $-7(-3) = 21$
• $-\frac{10}{2} = -5$

Step3: Solve variable examples

• $-2(c) = -2c$
• $-2(-c) = 2c$
• $2c(2) = 4c$
• $\frac{10}{-2}x = -5x$
• $\frac{-18x}{3} = -6x$

Step4: Solve distribution examples

• $-2(c+4) = -2c - 8$
• $-2(c-3) = -2c + 6$
• $\frac{1}{2}(10x + -5) = 5x - \frac{5}{2}$
• $x(-4-7) = x(-11) = -11x$
• $-10(x-5) = -10x + 50$

Step5: Solve factoring examples

• $2c+4 = 2(c+2)$
• $-2c-20 = -2(c+10)$
• $10x + -5 = 5(2x - 1)$
• $-4x+7x = 3x = x(3)$
• $-5x-5 = -5(x+1)$

Answer:

Sign Rules:

Same signs?= Positive
Different signs?= Negative
How? A positive multiplied or divided by a positive is always positive
A negative multiplied or divided by a negative is always positive
A positive multiplied or divided by a negative is always negative

Examples with numbers:

$-4$, $-5$, $-100$, $21$, $-5$

Examples with variables:

$-2c$, $2c$, $4c$, $-5x$, $-6x$

Examples with Distributing:

$-2c - 8$, $-2c + 6$, $5x - \frac{5}{2}$, $-11x$, $-10x + 50$

Examples with Factoring:

$2(c+2)$, $-2(c+10)$, $5(2x - 1)$, $3x$, $-5(x+1)$