Negative Numbers in Equations
Date: 11/20/2001 at 22:53:03 From: Stacey Merrow Subject: Algebra Hi! I have just recently started home schooling, and I don't know how to do some of the homework I am getting. Here are some examples of confusing equations: -30 = -37 + b/15 b= ? -c/4 - 8 = -48 c= ? How do I figure out how to solve the equation? My grandpa has helped me try to understand how to do some of them, but these are really confusing. 5+r/-2 = -6 r = 17 Is this correct? How would I do this equation? -a - -3/3 = 10 a = ?
Date: 11/21/2001 at 16:53:48 From: Doctor Sarah Subject: Re: Algebra Hi Stacey - thanks for writing to Dr. Math. It's always great to hear from a home-schooler! Let's work through your equations. Your goal is to collect like terms (get the numbers together, and get the variables together) and to move the numbers to a different side of the equation from the variables by doing the same thing to both sides. (1) -30 = -37 + b/15 add 37 to both sides of the equation: 7 = b/15 multiply both sides of the equation by 15: 105 = b (2) -c/4 - 8 = -48 add 8 to both sides of the equation: -c/4 = -40 multiply both sides by 4: -c = -160 multiply both sides by -1: c = 160 (3) 5 + r/-2 = -6 subtract 5 from both sides: r/-2 = -11 multiply both sides by -2: r = 22 For why a negative times a negative = a positive, see the Dr. Math FAQ: http://mathforum.org/dr.math/faq/faq.negxneg.html For adding/subtracting positive/negative integers (you'll need this in problem 4), see the Dr. Math archives: Subtracting Numbers by Walking a Number Line http://mathforum.org/dr.math/problems/stephanie.09.12.01.html (4) -a - -3/3 = 10 simplify the fraction: -a - -1 = 10 -a + 1 = 10 subtract 1 from both sides: -a = 9 multiply both sides by -1: a = -9 The final step when you solve any equation is to plug the number you get back into the equation to see if it works! Let's try #4 to see if -9 is the right answer: -a - -3/3 = 10 - -9 - -3/3 = 10 9 + 1 = 10 (could you follow the shortcuts?) Does this help? - Doctor Sarah, The Math Forum http://mathforum.org/dr.math/
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