114 Part 2: Into the Unknown
WORLDLY WISDOM
When you add fractions, you need to have like denominators. When you add terms,
you need to have like terms. The denominator of a fraction tells you what kind of frac-
tion you have, and the numerator tells you how many of them you have. If you have the
same denominators, you can just add the numerators, but if the denominators are dif-
ferent, you can’t combine the fractions. The variable part of a term tells you what kind
of thing you have, and the coefficient tells you how many. If the variable parts are the
same, you can add the coefficients.If you have to subtract terms, you follow the same rule: you can only subtract like terms, and you
subtract the coefficients and keep the variable part exactly as it was. To subtract 8t – 11t, you
subtract 8 – 11 to get -3, and you keep the t. So 8t – 11t = -3t.
If you’re faced with an addition or subtraction problem and you realize that the terms are unlike,
you just leave the problem as it is, or you might say “this cannot be combined.”CHECK POINT
Is it possible to complete these additions and subtractions? Complete them if you can!
- 4x + 9x
- 3a^2 – 2a^3
- 5xy + 6xy
14. 120xy^2 – 80xy^2
15. 15z + 25x
Simplifying Expressions.......................................................................................................
Once you have terms, it’s natural to want to start doing things with them. You can add or subtract
terms if they’re like terms, and you can multiply terms by other terms, like or not. You can even
do both of these things, adding and then multiplying. When you start doing so many things with
terms, you soon need to stop and think about how you simplify the problems you’ve created.
Do you need a whole new set of rules? The good news is no. Your old friend PEMDAS
(Parentheses, Exponents, Multiply, Divide, Add, Subtract) will cover most situations. Let’s look
at a problem that’s not too complicated. Suppose you wanted to do 5x(3x + 7x). PEMDAS says
do what’s in the parentheses first, so look at the 3x + 7x part first. Those are like terms, so you
can add them and get 10x. Your expression 5x(3x + 7x) becomes 5x(10x). Exponents are next, but
there are none, so move on to multiplying and dividing. 5x(10x) = 5 × 10 × x × x = 50x^2.