Algebra Demystified 2nd Ed

Chapter 4 NegaTive NuMberS 89

DeMYSTiFieD / algebra DeMYSTiFieD / HuttenMuller / 000-0 / Chapter 4

Summary

Table 4-1 summarizes the rules we learned for arithmetic with negative numbers.

TABLE 41 arithmetic with negative numbers

Let a and b be positive numbers, so −a and −b are negative numbers.

Rule Example

−− =− +ab ()ab −− =− +=− 53 () 53 8

When adding a negative to a

positive take the difference.

The sum has the same sign as

the “larger number.”

24 +− =() 10 14

61 +− =−() 59

ab−=+−ab() 37 −=+− =− 37 () 4 ;

10 +− =−() 2102 = 8

−− =()aa −− =()44

()−−=ab()ab ()()−−== 23 ()() 23 6

− =

− =−

a

b

a

b

a

b

− =

−

(^2) =−
5
2
5
2
5
−
− =
a
b
a
b
−
− =
2
15
2
15
In this chapter, we also learned how to
• Add a negative number to a positive number. Take the difference of the num-
bers. The sign on the sum is the same as the sign on the “larger” number.
• Subtract a larger positive number from a smaller positive number. Momen-
tarily disregarding the negative sign. Find the difference of the numbers.
The sign on the difference is negative.
• Subtract a positive number from a negative number. Momentarily disregarding
the negative sign, add the two numbers. The sign on the sum is negative.
• Interpret a double negative. Negating a quantity means using the opposite,
so the opposite of the opposite is the original number.
• Rewrite a subtraction problem as an addition problem. Rewrite a subtraction
problem as an addition problem by changing the sign of the second term.