Math 047J (adding & subtracting integers)

What do we mean by "terms"?

"Terms" are quantities joined together by addition or subtraction signs.

(A) How many terms do you see? (B) Simplify. -2 + -2 + -2 + -2

(A) = four terms (B) = -8 Because... "terms" are values joined together by add or subtract signs and "simplify" just means to perform the operation(s) you see.

(A) How many terms do you see? (B) Simplify. -2 - (-2) - (-2)

(A) = three terms (B) = positive two Because... in additive form the problem is: -2 + (+2) + (+2).

(-10) - (-10z)

= (-10) + 10z or... (-10) - (-10z) Because... unlike terms may not be added nor subtracted.

-12 - 12

= - 24 Because.... in additive form this problem is -12 + (-12)

-3 - 5 - 2

= -10 Because... in additive form this problem is: -3 + (-5) + (-2)

-5 + 7y + -5

= -10 + 7y or... 7y + -10 Because.... we can only add like terms (-5 + -5) but the 7y cannot add to anything.

-4 + -4 + -4

= -12 Because... all values are negative and they add up to a bigger negative.

-25 + (-100)

= -125 Because... both numbers have the same signs so we simply add them and keep the sign the same.

-25 - 100

= -125 Because... in additive form this problem is -25 + (-100)

2y - 14y

= -12y Because..... these are like terms but in additive form the problem is 2y + -14y. We still cannot add but we can subtract keep the sign of the larger looking number.

-15 + 2

= -13 Because.... the signs are opposite so we subtract a difference. With -15 being further from zero than 2, we have a balance of negative value.

What is the sum of -18 and 4?

= -14 Because... the word "sum" means add but we cannot add numbers with opposite signs; we subtract instead.

-7 + -8

= -15 Because... both numbers are negative so they add up to a greater negative value.

Fill in the blank space to make the statement true: 15 + ( ) = zero

= -15 Because.... adding opposite values always equals zero.

-120x - 30x

= -150x Because.... in additive form this would be -120x + -30x.

-17xy - 17y

= -17xy - 17y or... -17xy + -17y Because... unlike terms may not be added nor subtracted.

-12 + -7

= -19 Because... two negatives add up to equal a greater negative.

(-10) + (-10)

= -20 Because... two negatives add up to a bigger negative.

-p - 19p

= -20p Because... they are like terms but in additive form the problem would be: -p + -19p.

-7 + -7 + -7

= -21 Because... these are all like terms and all negative, so we just add them and keep the sign the same. NOTE: we can also use multiplication here: (-7)(3).

11 - 33

= -22 Because... in additive form the problem is: 11 + (-33)

-9 - (13)

= -22 Because... in additive form this problem is really -9 + -13.

-21a + -7ab + -a

= -22a + -7ab Because... only the (-21a) and (-a) terms are alike so we can add those but not the (-7ab) term.

7 - 30

= -23 Because.... in additive form this problem is 7 + (-30). This is like overdrawing your checkbook. If you have 7 dollars but write a check for $30... you are in the whole by $23.

-11 + -13

= -24 Because.... the problem is addition with signs that are the same, so add and keep the sign the same.

Find the difference between 10 and 35.

= -25 Because... the problem translates to be 10 - 35 which in additive form is: 10 + (-35).

0 - 27

= -27 Because.... you are trying to remove 27 units from nothing. In additive form it would be: 0 + -27.

12 - 40

= -28 Because... in additive form the problem would be 12 + (-40)

20 + -100 + 50

= -30 Because... the two positive integers = (+70) which is then subtracted from -100.

-6p + -26p

= -32p Because... two negative numbers added up to a larger negative.

-17 - 17

= -34 Because... in additive form the problem is -17 + (-17).

-x + -x + -x

= -3x Because... these are all like terms and all negative.

10 - 20 - 30

= -40 Because... in additive form this problem is: 10 + (-20) + (-30)

Find the sum of -17 and -30.

= -47 Because... the word "sum" means add. Here the two values are both negative so the sum is a greater negative value.

-2 - 3

= -5 Because.... in additive form it would be: -2 + (-3).

20 - 70

= -50 Because... in additive form the problem would be 20 + -70 and opposites signs cannot be added.

-5x + 4y

= -5x + 4y Because...the x and y variables are different terms.

11 + -17

= -6 Because... with different signs we subtract the smaller looking number from the larger looking number and keep the sign of the larger looking number.

-30 + -30x + -30

= -60 + -30x Because... we can only combine the like terms (-30 + -30).

-w + (-5w)

= -6w Because... these are both like terms and both negative.

7 + 7 + -21

= -7 Because... 7 + 7 = 14 but 14 + -21 cannot be added; we subtract and keep the sign of the greater absolute value.

-8 + 10 - 10

= -8 Because 10 - 10 equals zero but the -8 would still remain.

Which number has the greater "absolute value"? 18 or -81

= -81 Because... -81 is farther from zero than 18.

12 + -21

= -9 Because... integers with opposite signs cannot be added.

-30 + -30 + -30

= -90 Because... all are like terms and all are negative so just add them all up and keep the sign negative.

-2 + 3

= 1 Because.... the signs are different thus we cannot add them together but we can subtract.

-xy - (-16yx)

= 15xy or... 15yx Because... xy & yx ARE LIKE TERMS! Remember that the commutative property tells us we can reverse the order.

-6 + 8

= 2 Because.... you cannot add numbers with different signs. Subtract smaller from larger, use sign of larger number.

50 + -30

= 20 Because... opposite signs do not add; we subtract and use the sign of the greater absolute value.

-5 + 25

= 20 Because.... the signs of the numbers are different so take a difference between them but use the sign of the bigger number.

What is the difference between -5 and -8?

= 3 Because... this problem translates to be -5 - (-8) which in additive form is really: -5 + (+8).

x - (-x) - (-x)

= 3x Because... in additive form this problem would actually be: x + x + x.

x + x + x

= 3x Because... these are all like terms and all positive.

-7x - 3y + 10x

= 3x - 3y or... -3y + 3x Because... only the like terms (-7x + 10x) may be combined.

-w - (-5w)

= 4w Because... in additive form the problem is: -w + (+5w)

-3 + 8

= 5 Because.... you cannot add a negative to a positive, but you can subtract a difference; keep the sign of the number with greater absolute value.

60 - (-5)

= 65 Because..... in additive form this problem would be 60 + (+5)

-25 + 100

= 75 Because... opposite signs do not add; we subtract 25 from 100 and use the sign of the number with the greatest absolute value.

What is the sum 70 and 15?

= 85 Because... this question asks: 70 + 15.

-3x - (-11x)

= 8x Because... in additive form this problem is: -3x + 11x

-5y + 13y

= 8y Because... these are like terms but being opposite signs they cannot be added; we subtract instead.

7 - (-2)

= 9 Because... in additive form this is really 7 + (+2).

9 - 9 - (-9)

= 9 Because.... in additive form the problem would be 9 + -9 + 9

-x - (-10x)

= 9x Because... in the additive form this would be -x + (+10x). We cannot add them because their signs are different but we can subtract and use the sign of the greater absolute value.

-120 - 30x

= Cannot simplify. Because.... they are not like terms.

-25n - 100m

= Cannot simplify. Because: each value has a different variable so we cannot add nor subtract them.

(-10) - (-10)

= zero Because... in additive form the problem is actually (-10) + (+10). Being exact opposites, they cancel out.

-Z - (-Z)

= zero Because... in additive form the problem would be: -Z + Z. These opposite values cancel when added.

-12 - (-12)

= zero Because.... in additive form this problem is -12 + (+12). The two values are exact opposites so they cancel through addition.

-3x - (-11y)

Cannot simplify. Because... -3x and -11y are not like terms.

What do we mean by "change to the additive form"?

Change all subtraction signs to addition and the signs of each number that follows a subtraction sign to its opposite.

When two negative numbers are added together the result is... (positive or negative)?

Negative! Because... if you add debt to debt the debt gets bigger!

What is the name of the property illustrated in the below example: a + b = b + a

The commutative property of addition.

-7x - 3y + 10xy

You cannot simplify more because none of these terms are alike.