Order of Operations and Adding Negative Numbers
Date: 08/08/97 at 16:17:06 From: Dayna Chapman Subject: Adding negative numbers Dear Dr. Math, Can you help me better understand a problem? The problem is: 16 times 8 + 6 (-9 + -10) = ? I know the PEMDAS: parenthesis, exponents, multiply, divide, add, subtract. I also know that the parenthesis go first, but I am still having a little trouble. I just started school Thursday and I'm in 8th grade algebra. Thanks.
Date: 08/09/97 at 13:45:10 From: Doctor Mike Subject: Re: Adding negative numbers Hi Dayna, Okay, you have made a good start with the PEMDAS rule. Also you are right that it means for expressions inside of the parentheses to go first. So, what does (-9 + -10) mean? -19. Let's use * for times, so we have 16*8 + 6*(-19). There are no more expressions inside parentheses (just the number -19) and there are no exponents, so next we multiply and divide, left to right. That gives 128 + (-114), which equals 128 - 114 = 14. If there is some part of this you don't understand, write back. I'll just explain one more thing. You might get confused about what happens when 2 negatives are involved. It is true that -9 times -10 equals +90 (neg times neg is positive) but -9 plus -10 is -19 (neg plus neg is negative). For a while you might have to just remember the multiplication rule, but here's an easy way to get comfortable with the rule about adding negatives. Let's say you are measuring distances "up and down" from a spot on the surface of the earth. One way to do it is to use positive numbers for everything, like the flagpole is 25 feet high, and the well is 123 feet deep. Another common way is to use positive numbers for up and negative for down. That would put the top of the flag pole at +25 and the bottom of the well at -123. Okay, so you've got that, up is plus and down is minus. Now, let's say you and a few friends are being paid to dig a hole, and the first day you make it to 10 feet deep (bottom of hole now at -10). The next day you are all really tired from the first day and you only are able to dig it 9 feet DEEPER (-9 more). You can tell from common sense that if you dig it 10 feet deep, and then 9 feet deeper, it's going to be 19 feet deep. At that time you're going to take your money and leave, but my point is that "9 feet deeper" and "-9 more" are both ways of adding -10 and -9 together. So.... -10 + -9 equals -19. This is written in terms of the "-" sign meaning "negative". It can also be written in terms of the "-" sign meaning "subtraction" because : -10 + -9 = -10 - 9 That is, in words, "negative ten plus negative nine" is the same as "negative ten minus 9", and they both equal -19. This may be a little more than you wanted to know, but I hope it helps. P.S. If you dig the ten-foot-deep hole in your front yard (better ask permission!), then set up a ladder at the bottom of this new hole, and then climb up the steps of the ladder until your shoes are 15 feet above the bottom of the hole, how far above the level of your yard are your shoes? Right, -10 + 15 = +5 so they are 5 feet above the level of the yard. Now fill in the hole! -Doctor Mike, The Math Forum Check out our web site! http://mathforum.org/dr.math/
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