When you evaluate an expression, you find it's numerical value. To avoid confusion, mathmeticians have agreed on a set of rules called the Order of Operations.
The problem is: 6-(5-3)+10. First, do the parenthesis.
5-3=2. So it becomes: 6-2+10. Then do: 6-2, and it will become 4. So now it is: 4+10. Add. 4+10=14.
Remember, some problems will have all 6 operations. Just follow PEMDAS for the right answer
If a=5, b=4, and c=8
This is actually: 4(5)- 3(4)+1 or 4x5-3x4+1
Evaluate 4x5 and 3x4. 20 and 12. Subtract. 20-12= 8. Add the 1. 9. The final answer is nine (9).
Note: N(N) means multiply. (N is a variable for any number)
A mathematical sentence that contains an equal (=) sign is called an equation.
Ex. 7+8=15 3(6)= 18 x+2=5 (x is a variable)
Properties are open sentences that are true for any numbers.
Commutative Property looks like this.
a+(b+c)= a(b)+a(c) (Remember, that means multiply)
If a=b and b=c, then a=c also.
If 2+4=6 and 6=3*2, then 3+4=3*2
Negative numbers- any number less than 0.
Negative numbers like -86 and positive numbers like +125 and zero are members of the set of intergers. Integers can be represented as points on the number line.
a 15 yard loss = -15
3 inches above normal = +3
Try it Out
Using the greater than less than signs,(>) (<) compare the integers.
Try your own
The absolute value is the distance the number is from 0 on the number line. 4 is 4 units from 0, so the absolute value is 4. If you would like to practice these, refer to your math book.
The absolute value sign is a bar on each side of the number it looks ike the picture on the left.
Note: the x is a variable that stands for any number. Even with negatives, the absolute value will look like that. Ex. -2 absolute value is 2.
Find: -4+(-2). Using a number line is a great way to solve these problems. Starting from -4, go two units to the left (since it's a negative). The answer will be -6.
Remember, a negative plus a negative is always a negative.
To subtract an integer, add its opposite or additive inverse. Ex. 4-7 is the same as 4+(-7), which is -3.
Practice some of these problems in your book.
6(-8)=-48. Just multiply regularly and add the negative sign. A negative times a positive is always a negative.
-4(-3)= 12. A negative times a negative equals a positive.
Five years older than her brother
Five years (5) older (+) her brother's age (a)
So the expression will be: 5+a
a number less than 8 is 22
a number (n) less than 8 (-8) is 22 (=22)
So the equaton will be n-8=22
x+3=7. We know that a number added to 3 will be 7. So to solve for x, we will subtract 3 from 7.
7-3=4. So x=4.
Solve 35d= 210
Divide each side by 35
35d/ 35 and 210/35
35/35=1 and 210/35= 6
Multiply each side by -3.
-3*-3=9 (this gets crossed out). -7*-3=21.
This is the end of Chapter 1. For extra practice, refer to the problems in your math book. Study the Flash Cards and take the Quiz if you want :). I wish you the best on the OAA's!
Chapter 2 coming soon.