Math OAA's Studying Flashcards

If a=5, b=4, and c=8

4a-3b+1

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.

Algebra 

a+b=b+a

Arithmetic

6+1=1+6

Algebra

a+(b+c)=(a+b)+c

or

a*(b*c)=(a*b)*c

Arithmetic

2+(3+8)=(2+3)+8

or

3*(4*5)=(3*4)*5

Algebra

a+(b+c)= a(b)+a(c) (Remember, that means multiply)

or

a(b-c)=a(b)-a(c)

Arithmetic

4(6+2)=4*6+4*2

3(7-5)= 3*7-3*5

Algebra

a+0=a

or

a*1=a

Arithmetic

9+0=9

5*1=5

Algebra

If a=b and b=c, then a=c also.

Artithmetic

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

1. a gain of 2 dollars
2. 10 degrees below zero

Using the greater than less than signs,(>) (<) compare the integers.

• Ex. 1 > -6
• -4 < -2

Try your own

1. -5 and 4
2. -3 and 2
3. -1 and 1

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.

1. 9-12
2. -6-8
3. 7-(-15)

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.

1. -9(2)
2. 5(-3)
3. -8(6)

-4(-3)= 12. A negative times a negative equals a positive.

Pratice

1. -3(-7)
2. 6(4)
3. -5²

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

1d=6. d=6

Practice

1. 8x=72
2. -4n=28

Solve a/-3=-7.

Multiply each side by -3.

-3*-3=9 (this gets crossed out). -7*-3=21.

a=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.