Date: 11/16/98 at 21:58:05 From: Anna Martinez Subject: Using Parenthesis in Math problems Dear Dr. Math, I don't understand how to use parentheses. Can you explain it step by step so I can get it? Thanks, Anna
Date: 11/17/98 at 12:27:18 From: Doctor Peterson Subject: Re: Using Parenthesis in Math problems Hi, Anna. Did you ever see a Christmas package labelled "Open me first?" That's sort of what parentheses do. They wrap up some numbers and symbols, and tell us to do whatever is inside the package first, before we do anything else with those numbers. For instance, suppose we have this expression (we write multiplication as "*" to avoid confusion with the letter x): 2 * (3 + 4) That tells us we first calculate 3 + 4 = 7, and then put that number in place of the whole package (3 + 4): 2 * 7 Now we can do the multiplication, and calculate the answer as 14. If you like, you can think of parentheses as a funnel that pours some ingredients into the calculation at the right place: (3 + 4) \ / \ / 2 * ( 7 ) If we didn't use the parentheses, but had: 2 * 3 + 4 then the usual rules (called "order of operations") tell us that we should multiply 2 by 3 first, getting: 6 + 4 and then add, so the answer is 10. Why is it different? It's sort of like if you got a cat, a mouse, and a cage for Christmas. If they weren't wrapped right, you'd end up with an empty cage and a satisfied cat. But if you wrapped it like this: cat (mouse + cage) then you could first open the parenthesized package and put the mouse in the cage, then end up with a hungry cat and a caged mouse. That's probably what you really wanted! Here's a place in the Dr. Math FAQ to find out more about the order of operations: http://mathforum.org/dr.math/faq/faq.order.operations.html - Doctor Peterson, The Math Forum http://mathforum.org/dr.math/
Search the Dr. Math Library:
Ask Dr. MathTM
© 1994- The Math Forum at NCTM. All rights reserved.