how do you know when to add or subtract integers

Question

example -10p+9p=12

Answer 1

Hi Melanie,

 

In this problem, there are two types of terms: two terms with a "p" and one term that's just a number, the 12 on the right. Take the two terms with the p and pull the p out, or factor it.

 

-10p + 9p = 12

p(-10 + 9) = 12

 

If you notice, what you have in the parenthesis is a simple arithmetic problem! 

 

p(-1) = 12 or p = -12

 

See, its not so much adding and subtracting integers, I think what you may be confused about is adding and subtracting like terms. The -10p and 9p are like terms because each has a "p", which you need to find. You can factor out the p and reduce the problem to arithmetic, something you're already familiar with.

Answer 2

if both integers are positive you add them together and the answer is positive

7+9=16

(+4)+(+8)=+12 or 12

a positive + a positive is positive

 

if both integers are negative you add their absolute values and put a negative sign in front of the sum

-6+(-5)=-[abs value(-6)+abs value(-5)]=-[6+5]=-[11]=-11

-12+(-13)=-[abs value(-12)+abs value(-13)]=-[12+13]=-[25]=-25

don't forget, absolute value is always greater than or equal to zero, but never negative

a negative + a negative is negative

 

if one integer is positive and one integer is negative, subtract their absolute values and use the sign of the number having the greater absolute value(or in other words, use the sign of the number farthest away from zero on the number line)

-8+10=abs value(10)-abs value(-8)=10-8=+2 or 2 (10, the positive integer, has the greater abs value)

-9+6=abs value(-9)-abs value(6)=9-6=3, and now put a negative sign in front of the 3: -3 is the answer  (-9 has the greater abs value, or -9 is farther away from zero than +6)

15+(-11)=abs value(15)-abs value(-11)=15-11=+4 or 4 (15 has a greater abs value than -11)

13+(-18)=abs value(-18)-abs value(13)=18-13=5, and now put a negative sign in front of the 5: -5 is the answer (-18 has the greater abs value, or -18 is farther away from zero than 13; -18 is 18 units from zero while 13 is only 13 units from zero)

-7+7=0 (any number plus its opposite is 0)

Answer 3

This is an algebraic expression. The "p" is a variable, and you simply add the coefficients up using standard arithmetic.

 

The first term, -10p, is negative. The second term, 9p is positive, and because adding is commutative, you can put the positive term first if you like, keeping track of the negative signs in the process:

 

9p + -10p = 12

9p - 10p = 12

-p = 12, and making the variable positive, you get:

 

p = -12

 

Answer 4

Hi Melanie;

Subtraction is the adding of negative numbers.

-10p+9p=12

9p-10p=12

-1p=12

p=-12