Algebra Know-It-ALL

In this chapter we’ll explore the mechanics of multiplication and division. Multiplication is a shortcut for repeated addition. ...

Suppose p is an integer and n is a positive integer. From the above facts, you can see that whenever you multiply p by n, you ad ...

at the point representing 2. If you start with −10 and divide by 5, you cut your distance from the “number reflector” by a facto ...

you want to get, say, 3? How many times must you add 0 to itself to get anything but 0? No integer can do this trick. In fact, n ...

absolute value of the multiplier is 2, we double our distance from the “number reflector” with each jump. Expressed as equations ...

Identity, Grouping, and Signs Let’s review how signs work in multiplication and division. Then we’ll proceed to the three major ...

and a/1=a The sign-changing element When you multiply or divide any integer by −1, you reverse the sign but do not change the ab ...

Signs in multiplication and division Here is a set of rules for multiplication and division by any integer except −1, 0, or 1. R ...

Group all the divisions Do all the divisions from left to right Convert all the subtractions to negative additions Do the addit ...

It works when you multiply The fact that you can multiply two integers in either order and get the same result is called the com ...

Are you confused? Suppose you see an expression where you have to divide repeatedly, with no parentheses telling you which divis ...

It works when you multiply Here’s how a mathematician would formally state the associative law in its most basic form. For any t ...

In this case, it simplifies to 100/2 = 50. Now let’s try this: 4,000 / (40/10) / 5 We do the division in parentheses first, gett ...

Here’s another challenge! Based on the commutative law for multiplication of two integers, and on the associative law for multip ...

Multiplication over subtraction The distributive laws also work with subtraction. For any three integers a, b, and c a(b−c)=ab−a ...

but 24/4− 24/2 = 6 − 12 =− 6 The right-hand law works with division If you have a sum or difference as the dividend and the sing ...

Next, we expand e back into its original form and substitute it into the above expression twice, getting (a+ b)c+(a+ b)d We can ...

82 Multiplication and Division Show at least one situation where you can say that (ab)/c=a(b/c) where a, b, and c are integers. ...

You can always divide an integer by another integer, except when the divisor is 0. Then you get a fraction. A fraction might not ...

84 Fractions Built of Integers Improper or proper? In a fraction, the dividend is called the numerator, and the divisor is calle ...