Problems from Operations with integers

• They have different signs
• We calculate the absolute values of each number: $|+7|=7,$ $|-3|=3$
• We subtract the absolute values: $7-3=4$
• We put the sign of the number with the greatest absolute value. In this case, $7$ is greater than $-3$, therefore we put the $+$ sign: $+4$
• And so, the result is: $(+7)+(-3)=+4$

• They have the same sign
• We calculate the absolute values of each number: $|-5|=5$, $|-2|=2$.
• We add up the absolute values: $5+2=7$
• We put the sign they had before: $-7$
• So the result is: $(-5)+(-2)=-7$

• The minuend is $+7$, and the subtrahend is $+2$.
• The opposite of $+2$ is $-2$.
• We add up the minuend ($+7$) and the opposite of the subtrahend ($-2$): $(+7)+(-2)=+5$
• The result of the subtraction is $(+7)-(+2)=+5$

• The minuend is $+9$, and the subtrahend is $-6$.
• The opposite of $-6$ is $+6$.
• We add up the minuend ($+9$) and the opposite of the subtrahend ($+6$): $(+9)+(+6)=+15$
• The result of the subtraction is $(+9)-(-6)=+15$

We do the multiplication without signs: $8\cdot 4=32$ As both numbers have the same sign, the result has a positive sign. That is: $(+8)\cdot (+4)=+32$

We do the multiplication without signs: $2\cdot 7=14$ As both numbers have different signs, the result has a negative sign. That is: $(+2)\cdot (-7)=-14$

First we do the division without the signs: $21:3=7$ As both numbers have different signs, the result has a negative sign. Therefore: $(-21):(+3)=-7$

First we do the division without the signs: $64:8=8$ As both numbers have the same sign, the result has a positive sign. That is to say: $(-64):(-8)=+8$