Those nasty negatives - always causing trouble.
1. It’s all in how you look at it. In your early math education when you were learning to add and subtract, a negative sign meant minus, subtract or take away. What you are really doing now in college is combining numbers and variables, some of them negative and some of them positive. In other words, you have to adjust your thinking and consider negative signs to belong to the number they are in front of. The negative sign is part of that number’s identity, making it a negative number. It no longer is telling you to do something like subtract.
For example, 4-2 can be understood as (+4) + (-2).
And for - 2(4x + 3), when you distribute the 2 to the 4x and the 3, make sure you are distributing (-2). In other words, (-2)(+4x) + (-2)(+3), or (-8x) + (-6). At this point, you can rid of the ( ) and the + sign because it is understood that you are combining -8x and -6, written as -8x -6.
If you had to simplify -2(4x - 3), you would think of it as (-2)(4x) + (-2)(-3), then (-8x) + (+6) or -8x + 6.
2. The basic rules:
When multiplying, if both signs are the same (positive or negative), the result is positive. If they are different, the result is negative. (You’ve heard two negatives make a positive. This is where it applies.)
When combining two positive numbers, the result is a larger number that is positive. (4 and 2 = + 6)
When combining two negative numbers, the result is a larger number that is negative. (-4 and -2 = -6)
When combining one negative number and one positive number, find the difference between the two numbers and assign that difference the sign of the larger number. (-4 and 2 = -2)
When multiplying (or dividing) both sides of an inequality by a negative number, reverse the inequality sign.
3. Do each step of your problems directly underneath the previous step, so you can bring down each member of the equation that you are not altering in that step, directly as it appears. It is very easy and common to make a copying error. This way of working problems helps you keep track of details like negative signs.
4. Visit a tutor. We’ve seen it all and we’re not grading you so there’s no need to feel self-conscious about your lack of understanding. And we’ve had a lot of practice quickly finding a student’s difficulties in case you have no idea where you are going wrong. We’re not in a hurry and we don’t care if you need lots of explanations. If we weren’t patient, we wouldn’t tutor. It’s also not too late. Many a student has taken an F (high F) at midterm time to a C for the course. Act 101 students can be tutored online evenings and weekends. Those of us who have used this find it to be super convenient and comfortable. After making an appointment, you just log into Blackboard, go to the ACT 101 shell and enter the virtual classroom through the collaborations tab within the communications tab. Math tutoring on campus is available all week and the schedule is on Keystone’s website.
5. Don’t get too discouraged or lose confidence. In math, it only takes one little misunderstanding to miss a lot of problems. You are probably better at math than you think.
6. Practice, practice, practice. Its kind of like learning to play an instrument or a sport.
I chose negative signs for this blog because I find through tutoring that people generally have some problems with them. If you have another topic/problem you would like me to address, email me at Kathy.Tuttle@keystone.edu.
Best of luck with midterms,
Kathy Tuttle