Download Unit 1 – Number Relationships

Unit 1 – Number Relationships
Divisibility Rules
A number is divisible by 2, if it is an even number (ends in 0,2,4,6,8).
A number is divisible by 3, if the sum of the digits is divisible by 3.
A number is divisible by 4, if the last two digits are divisible by 4.
A number is divisible by 5, if it ends in a 0 or a 5.
A number is divisible by 6, if it is divisible by 2 and 3.
A number is divisible by 8, if the last three digits are divisible by 8.
A number is divisible by 9, if the sum of the digits is divisible by 9.
A number is divisible by 10, if the last digit is a 0.
Unit 2 – Fractions
Equivalent Fractions
1) Divide or Multiply the numerator and denominator by the same number – you get to choose what
operations you do and by what number.
2) What you do to the top, you to do the bottom.
Lowest Terms
1) Divide the numerator and denominator by the largest number that will divide evenly into both.
2) To find the largest number make a factor tree
3) Divide the numerator and denominator by the largest number.
Changing an Improper Fraction to a Mixed Number
Improper fraction – when the numerator is larger than the denominator.
Mixed number – a whole number and a fraction.
1) The denominator stays the same.
2) Ask myself, “How many times does the denominator go into the numerator?” - the answer to the
question is the whole number
3) The remainder is the numerator.
Changing a Mixed Number into an Improper Fraction (SMA)
1. The denominator stays the same.
2. Multiply the denominator and the whole number.
3. Add the numerator to your answer to get your new numerator.
Adding and Subtracting Fractions with the Same Denominators
1) Denominator stays the same.
2) Add or subtract the numerators (depending on the question)
Adding and Subtracting Fractions with the Different Denominator
1) Create a common denominator.
- the easiest way to do this is multiply the denominators together
2) What you do to the bottom, you do to the top.
3) Add or subtract the numerators and place your answer over the new denominator (common
denominator).
Adding and Subtracting Mixed Numbers
Adding 1) focus on the fractions – if the denominators are the same follow the rules.
- if the denominators are different follow the rules.
2) If your answer is an improper fraction turn it into a mixed number.
3) After adding the fractions, add the whole numbers
Subtracting – 1) Turn into an improper fraction.
2) Follow the rules for adding and subtracting fractions.
3) Remember to turn your answer back into a mixed number.
Unit 3 – Decimal Numbers
When adding or subtracting with decimals – line up the decimals and then do the work. Be sure to move
the decimal down into your answers.
7.1
27.9
+ 6.4
- 15.3
13.5
12.6
When multiplying with decimals – line up the last digit in each number. Do the multiplication then total
the number of decimal places in your question and put that many decimal places in your answer.
14.1 – 1 place
x
5 – 0 places
70.5 - 1 place
When dividing with a decimal in the dividend – move the decimal directly above to the answer and then do
the work.
7.1
5) 35.5
- 35
05
When dividing with a decimal in the divisor – move the decimal as many times needed to the right to make
it a whole number. Then move the decimal in the dividend as many times as you did in the divisor.
______
___5.76
0.85 ) 4.90
85 ) 490.00
- 425
650
- 595
550
How to write terminating decimals as a fractions
- remove the decimals from the number, the new number becomes your numerator
- the denominator will be a power of ten (10, 100, 1000, etc.). To determine what
the denominator will be, you need to look back at the original decimal number. However many
places after the decimal there were, that is how many zeros will be in your power of ten
numerator.
Ex. 0.6 = 6/10
0.12 = 12/100
0.375 = 375/1000
How to write repeating decimals as fractions.
- when a decimal is repeating, you follow the same rules as above, except of the denominator is a
nine.
- to determine the number of nines you put as your denominator, refer back to the original number.
The number of places after the decimal will be the number of nines in the denominator.
Ex. 0.1 . . . = 1/9
0.123 . . . = 123/999
1. Do operations in brackets first.
2. Evaluate exponents.
3. Do division and multiplication in the order they appear – from left to right.
4. Do addition and subtraction in the order they appear – from left to right.
B – Brackets ( )
E – Exponents 3³
D – Division ÷
M- Multiplication x
A – Addition +
S- Subtraction –
- When you see ‘half of #’ in the equation it means you can divide by 2 or multiply by 0.5
- ( ) ( ) = Multiplication
Unit 4 - Percent
Percent to Fraction
Fraction to Percent
30% = 30 = 3
100 10 (in lowest terms)
7 = 14 = 14%
50 100
Percent to Decimal
Decimal to Percent
78% = 78 = 0.78
100
whole = %
part
100
0.03 = 0.03 = 3 = 3%
1
100
* Cross multiply and divide
Unit 5 – Measurement
Square / rectangle
P = s1 + s2 + s3 + s4
a=LxW
Parallelogram
P = s1 + s2 + s3 + s4
A=bxh
Triangle
P = s1 + s2 + s3
A=bxh÷2
Circle
P (circumference) = π x d
A=πxrxr
Unit 6 – Integers
(1) When adding integers with the same signs:
 Add and keep the sign the same
Example:
(-5) + (-4) = (-9)
(+5) + (+4) = (+9)
(2) When adding integers with opposite signs:
 1st:subtract the smaller number from the larger number to get the difference
 2nd: add the sign (- or +) from the larger number to the difference
 3rd: Vola! You have the answer!!
Example:
(-5) + (+6) = +1
(3) When subtracting integers add it’s opposite:
 1st:
Keep the first integer the same
 2nd: Change the subtraction sign to an addition sign
 3rd: Change the second integer to it’s opposite
 4th: Use the rules for addition of integers to complete to find the answer
Example 1:
(-5) - (+4) = ?
(-5) + (-4) = -9
Unit 7 – Geometry
Translation/Slide
– The original figure and its image are congruent (same size and shape).
– The image faces the same way as the original figure
– the slide happens along straight lines – left or right, up or down
1. If x is positive (+) then it will move right
2. If x is negative (-) then it will move left
3. If y is positive (+) then it will move up
4. If y is positive (-) then it will move down
Reflection/Flip
– The original figure and its image are congruent (same size and shape).
– The line the shape is flipped in is called the line of reflection or the mirror image line
– The image is the same distance from the line of refection as the figure but is on the opposite side
of the line.
Rotation/Turn
– The original figure and its image are congruent (same size and shape).
– Each point on a shape is moved about a fixed point
– Rotations can be clockwise or counter clockwise
– ¼ = 90° ½ = 180°
¾ =270° full = 360°
Unit 8 – Statistics
The range is the difference between the highest and lowest values in a
set of data.
Example:
Data set: 4, 8, 2, 9, 3, 3, 1
Data set arranged from least to greatest: 1, 2, 3, 3, 4, 8, 9
Range: 9 – 1 = 8
The mode is the number that occurs most frequently in a set of data.
Example:
Data set: 4, 8, 2, 9, 3, 3, 1
Mode: 3
The median is the middle value when the data are arranged in numerical
order. If the number of pieces of data is even, the median is the average of the 2 middle values.
Example:
Data set: 4, 8, 2, 9, 3, 3, 1
Data set arranged from least to greatest: 1, 2, 3, 3, 4, 8, 9
Median: 3
The mean is calculated by finding the sum of the data and dividing by the number of pieces of data
Example:
Data set: 4, 8, 2, 9, 3, 3, 1
Mean: 4 + 8 + 2 + 9 + 3 + 3 + 1 = 30
An outlier is a data value that is far from the other data.
Example: Data set: 14, 18, 16, 19, 21, 14, 2, 18, 14, 15, 23, 17, 15
Data set arranged from least to greatest (or plot the data on
a line plot : 2, 14, 14, 14, 15, 15, 16, 17, 18, 18, 19, 21, 23
Outlier: 2
Unit 9 – Linear Relations and Linear Equations
Algebraic Expression (also known as a Pattern Rule)
Example: 3n + 4
Algebraic Equations
Example: y = 3n + 4
Variable: a quantity that changes
 y = 3n + 4
 y and n are variables
Constant Term: a quantity that does not change; stays the same
 y = 3n + 4
 4 is a constant term
Numerical Coefficient: the number that is multiplied by the variable
 y = 3n + 4 (3n means 3 × n)
 3 is a numerical coefficient
Writing an Equations from a diagram:
Explanation:
When you go from Figure 1 to Figure 2 you add 3 blocks and when you go from Figure 2 to Figure 3 you
add 3 blocks; therefore the variable coefficient is 3.
Unit 10 – Probability
Unit 11 – Circle Graphs