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• TO COMPARE NUMBERS

Find the first number on the number line

Find the second number on the number line

If the second number is to the right use less than <

If the second number is to the left use greater than >

TO ORDER NUMBERS

Put a dot for each number on the number line

If least to greatest put an arrow from left to right

If greatest to least put an arrow from right to left

Start at eh binning of the arrow and write the number of the dots in order following the path of the arrow

TO CLASSIFY RATIONAL NUMBERS

Look for a decimal point or a fraction bar

If you see one, the number is a rational number only

If not and you see a negative sign, then the number is an integer and rational

If you don’t see a decimal point, fraction bar or a negative, then the number is whole, integer and rational

Find Least Common Multiple

1. List multiples for each number

2. Circle the numbers that are the same on each list

3. Identify the smallest of the circled numbers

1. Check the signs of both numbers

2. If both numbers have the same sign add the values
3. If they have different signs subtract the values
4.  Answer will have the sign of the biggest number

Subtracting Integers
1. Leave the first number the same
3. Change the sign of the second number

Breaking down word problems
2. Circle the numbers
3. Underline question
4. Box math action words
5. Expression or equation needed?
6. Solve the problem

Multiplying Integers
1. Multiply factors to get product
2. Use tic tac toe chart to find the sign of the product

Dividing Integers
1. Divide like normal
2. Use tic tac toe chart to find the sign of the quotient

Converting fractions to decimals
1. Write the fraction
2.  denominator (long division symbol) numerator.00
3. Divide like normal
4. If it was a mixed number, add the whole number back in front of the decimal

Multiplying decimals
1. Rewrite problem as long number x short number
2. Multiply like normal
3. Count how many numbers are behind the decimal in the factors do the same for the answer
4. Use tic tac toe chart for the sign

Multiplying Fractions
1. Make sure both numbers are written as fractions
2. Multiply numerator x numerator to get the new numerator
3. Multiply denominator x denominator to get the new denominator
4. Use tic tac toe chart for the sign

Dividing Decimals

1. Write problem divisor (long division symbol) dividend
2. Move decimal in divisor to the right to make it a whole number
3. Move decimal in dividend to the right the same number of places
4. Bring decimal in dividend up and divide like normal
5. Use tic tac toe chart for the sign

Divide Fractions
1. Make all number fractions
2. Keep first fraction the same
3. Change divide to multiply
4. Flip second fraction
5. Multiply straight across

If the denominators are the same
1.  Keep the denominator
If the denominators are different
1. Make both numbers fractions
2. Swoop: Multiply denominators together
3. Cross: bottom R x top L
4. Cross: bottom L x top R
5. Order of operations

1. Line up the decimal points

Subtracting Fractions
If the denominators are the same
1.  Keep the denominator
If the denominators are different
1. Make both numbers fractions
2. Swoop: Multiply denominators together
3. Cross: bottom R x top L
4. Cross: bottom L x top R
5. Order of operations

Subtracting Decimals
1. Line up the decimal points
2. Subtract like normal

Simplifying Variable Expressions
1. Distribute to get rid of parentheses
2. Identify variable terms and move them to the left side
3. Identify constants and move them to right side
4. Do the required operations

To Factor
1. Find a number that can be divided out of both terms
2. Write that number outside of parentheses
3. Inside parentheses goes quotients

Distribute
Multiply the number in front of  parentheses times each term inside parentheses

Solving one step equations
1. Separate equation at the equal sign
2. Identify operation happening to variable
3. Do the inverse operation to both sides of equation
4. What you do to one side, do to the other
5. Answer is variable = number

Solving two step equations
1. Split the equation and identify the variable
2. Do the opposite of addition or subtraction on both sides
3. Do the opposite of multiplication or division on both sides
4. Answer is variable = number

Solving one step inequality
1. Separate at sign on equality
2. On side with variable do the inverse operation
3. What you do to one side, do to the other
4. Bring the sign of equality down
5. If you multiplied or divided by a negative number, flip the sign of equality

Graphing inequalities
1. Draw axis
2. Place answer in middle of axis
3. Circle around number
4. If variable is in gator mouth shade right, if number is in gator mouth shade left
5. If line is under sign of equality fill in circle, if not leave it blank

Writing 2 step inequalities
1. Set up problem (time)x+(constant)    (total)
2. Fill in total amount
3.  Fill in initial amount
4. Last value or time value goes in front of x
5. Choose sign of equality based on context clues

Solving 2 step inequalities
1. Separate at sign of equality and identify side with variable
2. On side with variable do opposite of +/-
3. On side with variable do opposite of x/ ÷
4. What you do to one side do to other
5. Bring down sign of equality
-- flip if multiplied or divided by negative

Ways to write ratios
word form: 3 to 2
Fraction form: 3/2
Ratio form: 3:2

Way to find equivalent ratios
1. Write the ratio in fraction form
2. Either multiply or divide top and bottom by the same number

Finding Unit Rate
1. Rewrite question as unit1 per unit2
2. Create division problem
for decimal unit 2 (bracket) unit 1
for fraction unit 1  ÷ unit 2
3. Divide
4. Answer followed by unit 1 per unit 2

Identifying Constant rate of Change
1. Create fractions for each set of data
money or distance is a numerator
time is the denominator
or in the order it is given in the problem
2.  Divide each fraction
bottom (bracket) top.00
--if same then proportional
--if different then non-proportional

How to create proportionality equation
1. Create fractions from data
--money, distance or y is numerator
--time or x is denominator
2. Divide all fractions
--bottom goes outside
--top goes inside division sign add decimal and 0's if necessary
3.  If answers are the same it is proportional
4. If answers are different it is non-proportional
5. Write equation y = k x

A graph is proportional if:
1.  it is a straight line
2. it goes through the origin
3. increases from left to right

To create an equation from a graph
1. Identify a point on the graph
2. Divide y  ÷ x
3. Use answer for k value in y = k x

To change percent to decimal
1. Erase percent sign
2. Move decimal point 2 units to the left
3. If necessary put 0 in front of decimal point

To change decimal to percent
1. Move decimal 2 units to the right
2. Add  percent sign to number

To change percent to fraction
1. Erase percent sign
2. Put number over 100
3. Simplify fraction

To change fraction to percent
1. Divide numerator  ÷ denominator
2. Move decimal point in quotient 2 units to the right
3. Add percent sign to number

To solve percent problems
1. set up proportion is / of = % / 100
2. Fill in values
3. Cross multiply
4. Divide by number in front of x

To find percent change
1. Subtract the values
2. Divide the total by the starting amount
3. if the numbers got bigger write increase
if the numbers got smaller write decrease

To find markup or markdown
1. Change percent to a decimal
2. Multiply original amount times decimal
3. If markdown or discount or decrease
If markup, tax, or tip or increase

To find interest
1. Write equation i=Prt
2. Plug in the number they give you in for i, P, r, t
3. Multiply
4. Divide by number in front of variable
5. To find total add interest amount to principal

Long Division
1. How many times can divisor be subtracted from first number in dividend
---write answer above that digit in dividend
2. Multiply 'answer' times divisor write product under dividend
3. Subtract
---difference should be less than divisor
4. Bring down next number in dividend
---if you run out of numbers and still have remainder add decimal to dividend and 3 zeros
5. Repeat 1-4 until either you have 3 numbers after the decimal or you have 0 remainder and no more numbers to bring down.

To use scale factor
1. Set up proportion fake/real=scale factor as a fraction
2. Plug in scale factor in order it was given
3. Line up the units and plug in other value
4. Cross multiply
--a/b=c/d becomes a*d=b*c
5. Divide by number in front of x on both sides

To determine if it is a triangle
1. Two shortest sides must add to be greater than third side
-- if s1+s2 less than s3
2. If they give you 1 side between two angles it is a unique triangle
3. If they give you 3 angles it could make many different triangles
4. The 3 angles in a triangle add up to 180 degrees

Finding Area and circumference of a Circle
1.  Divide diameter by 2 to get radius
2.  Remember pi= 3.14
3.  Identify which equations to use
-- Area = pi*r*r
-- Circumference= 2*pi*r
4.  Plug in values for radius and multiply
-- if directions say 'in terms of pi' stop here
5. Plug in 3.14 for pi and multiply

Finding area of composite figures
1. Break figure into shapes
-- circles, triangles, squares, rectangles, quadrilaterals, trapezoids
2. Redraw shapes independently with their dimensions and identify type of shape
3. Identify correct equation
4. Plug numbers into equations
5. Find the area of each shape and add them together

Finding Volume of Prisms
1. Identifying the shape of the base
2. Redraw the base with dimensions
3. Find the area of the base
4. Multiply area times depth of the figure

Finding Surface Area of Prisms
1. Identify the base of the prism
2. Redraw base with dimensions
3. Find area and perimeter of base
--if circle use 2*pi*r
4. Multiply area of base x2
multiply perimeter of base x height

Using data to predict the future
1. Setup two fractions    specific sample/total sample=specific population/total population
2. Cross multiply  a/b= c/d  becomes axd=bxc
3. Divide both sides by coefficient

To find the mean absolute deviation
2. Divide sum by number of values added
3. Subtract this mean from original data values
5. Divide sum by number of values added

To find Probability
1. Identify the total number of options or choices
2. Identify what you are looking for
3. Create probability (what you are looking for)/ (total choices)
4. Reduce fraction

Compound Probability
1.  Theoretical Probability
number of ways an event CAN occur (over) the total number of likely outcomes
2.  Experimental Probability
number of ways an event HAS occured (over) the total number of likely outcomes
3.  Prediction = probability x total possibilities