Download RATIONAL NUMBERS: Know the definitions of whole numbers

RATIONAL NUMBERS: Know the definitions of whole numbers, integers, natural numbers and
rational numbers. Be able to give an example of each.
Give an example of a natural number: 1
Give an example of a whole number: 1
Give an example of a rational
number that is not an integer: 1
3
ABSOLUTE VALUE: Know that absolute value means “how far from zero”.
Know which number has the highest absolute value: -30, 0, 25, -10
Because 30 is farther from zero than 0, 25 or 10.
Answer: -30
Know what two numbers give you an absolute value of 7 (or any other number). What two numbers
are 7 units from zero on the number line? Answer: 7 and - 7
Simplify ( combine all like terms): | -7 + 3 | - | - 2 |
Answer: | 4 | - | - 2 | = 4 – 2 = 2
COORDINATE PLANE: Be able to draw the coordinate plane and graph and label points.
Draw a coordinate plane and label the following points: (-1, 1), (0, 3), (3,0), (-2, -2)
NUMBER LINE: Be able to order the numbers from greatest decrease (smallest) to greatest increase
(largest) on a number line. Show your increments on the number line and then graph the points.
Graph two points on a number line so that both points have an absolute value of 3 (both numbers are 3
units from zero).
Order the numbers from greatest decrease to greatest increase on a number line: 0, -3, 3, -1, 1
3 2
ADDING, SUBTRACTING, MULTIPLYING AND DIVIDING INTEGERS:
Know the rules: Adding: Same signs- add and keep the sign
Different signs- find the difference and take the sign of the larger number
Subtracting: Change the – to + and change the number behind the – to its opposite.
Now you have an addition sentence so use the addition rules
Multiplying and: Multiply or divide as usual
Dividing
same signs = answer will be +
Different signs = answer will be –
LIKE TERMS, DISTRIBUTIVE PROPERTY AND 2-STEP EQUATIONS:
LIKE TERMS:
Simplify (combine what you can combine): Use the rules, draw counters, pictures or draw arrows or
whatever it takes to get all the like terms together: 4e + (-7) – 5e + 3 =
4e – 5e = 4e + (-5e) = -1e
+(-7) + 3 = - 7 + 3 = - 4
Answer: -1e – 4
DISTRIBUTIVE PROPERTY: Multiply everything on the outside of the parenthesis ( ) by everything
inside the parenthesis ( ).
Example: 3(2a – 5) + 4 ( -2a + 6) =
6a – 15 + ( -8a) + 24 =
6a + (-8a) = -2a
-15 + 24 = 9
Answer: -2a + 9
Example: (2c – 3a + 4) – ( 3c + 4a – 3) =
(change – to + and take the opposite of every number behind the – sign, don’t change the operation)
2c – 3a + 4 + (-3c) + (-4a) – (-3) = 2c – 3c = -1c
-3a + (-4a) = -7a
4 – (-3) = 4 + 3 = 7
Answer: -1c -7a +7
2-STEP EQUATIONS: Solve for the variable (find out what the variable is equal to)
-a – 4 = 10
2
add 4 to both sides of the equal sign: now you have – a = 14
2
Multiply both sides by 2: now you have –a = 28
You can never have a negative variable so divide both sides
By -1: now you have a = -28 (or just switch the signs on both sides)
WORD PROBLEMS: Read the problem carefully, write down any important facts. Draw a picture if
you need to.
Example: Joe went from Atlanta to Disney World which was a distance of A + 500 miles. He then
drove to Fort Lauderdale Florida to the beach which was a distance of 2A + 300 miles. The total
distance he drove was 2600 miles. How far is it from Atlanta to Disney World?
A + 500 + 2A + 300 = 2600
Simplify: A + 2A = 3A
500 + 300 = 800
3A + 800 = 2600 (now you have a 2-step equation)
Subtract 800 from both sides of the equal sign: now you have 3A = 1800
Divide both sides by 3: now you have A = 600
Now that you know what A is put 600 back in the original sentence for Atlanta to Disney World
A + 500 = 600 + 500 = 1100 miles from Atlanta to Disney World.