Rules for adding and subtracting negative numbers with the rules for multiplying and dividing negative numbers

Question

There are two sets of rules for negative numbers.

1. Adding and subtracting negative numbers
2. Multiplying and dividing negative numbers

Students frequently make the algebra mistake of confusing these two sets of rules. They use the multiplication rules for addition and vice versa. Let's take a look at an example mistake

−3−5=8

Here the student saw the two minus signs and made the answer positive. This is the rule for multiplying negative numbers, not addition/subtraction of negative numbers.

The correct answer is

−3−5=−8

For addition and subtraction of negative numbers, you must think about the number line.

 

A minus sign means move left. A plus sign means move right. So in our case, we move left 3 spaces from 0, landing on -3. We then move an additional 5 spaces to the left, landing on -8. Let's look at one more example

3−5=−2

In this case, we move 3 spaces to the right, landing on +3. We then move 5 spaces to the left, landing on -2.

For multiplication, there are two rules to learn

1. (−)∗(−)=+
2. (−)∗(+)=−

If you multiply two identical signs (two minus's or two plus's) you get a positive number. If you multiply two opposite signs, you get a negative number. 

Answer 1

-3 times -5 = 15

two negative numbers' product is always positive

one negative and one positive number multiplied together is always negative

product of opposite signs is negative

product of same signs is positive

-3 -5 = -8

-3 -5 = (-3)+(-5) =-(3+5)

if the signs are the same, just add the numbers (ignoring the sign), then stick the same sign in front of the sum

if the two numbers have opposite signs, subtract the two numbers (ignoring the signs) then stick the sign of the bigger number with the result (bigger meaning the absolute value of the number, ignoring the sign)

-3 +5 = +(5-3)= 2

3-5 = -(5-3) = -2

just another way of thinking of addition and multiplication of numbers involving negative signs

Answer 2

There are two sets of rules for negative numbers.

1. Adding and subtracting negative numbers
2. Multiplying and dividing negative numbers

Students frequently make the algebra mistake of confusing these two sets of rules. They use the multiplication rules for addition and vice versa. Let's take a look at an example mistake

−3−5=8

Here the student saw the two minus signs and made the answer positive. This is the rule for multiplying negative numbers, not addition/subtraction of negative numbers.

The correct answer is

−3−5=−8

For addition and subtraction of negative numbers, you must think about the number line.

 

A minus sign means move left. A plus sign means move right. So in our case, we move left 3 spaces from 0, landing on -3. We then move an additional 5 spaces to the left, landing on -8. Let's look at one more example

3−5=−2

In this case, we move 3 spaces to the right, landing on +3. We then move 5 spaces to the left, landing on -2.

For multiplication, there are two rules to learn

1. (−)∗(−)=+
2. (−)∗(+)=−

If you multiply two identical signs (two minus's or two plus's) you get a positive number. If you multiply two opposite signs, you get a negative number.