QUICK MATH REVIEW

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QUICK MATH REVIEW TIPS1

• Basic Facts Rules To Remember

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Word of Advise

• For a good and lasting foundation in Math, know
  your multiplication tables by all means.
• Knowing multiplication translates to being able
  to figure out division problems in the shortest
  amount of time.
• Working with fractions, algebra, ratios and
  percentages also become easy to handle.
• Start solving Math problems using the facts, the
  rules information you already know to guide
  you.

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• If you multiply two negative numbers
• the result will be positive
• -4 -9 36
• -3 -9 27
• -7 -8 56
• -6 -9 54

4

• If you multiply a negative and a
• positive number the result will be
• negative
• -4 x 9 -36
• 4 x -9 -36
• 5 x -8 -40

5

• If you subtract a larger number from a
• smaller number the result will be
• negative
• 12 - 25 -13
• 18 - 38 -20

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• If you add two negative numbers the
• answer will be a bigger negative number
• -5 -7 -5 (-7) -12
• -23 -12 -23 (-12) -35
• -51 -10 -61
• ( If you owe money and you borrow more you will
  owe more money. More negative )

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• Any number multiplied by ONE gives
• the same number
• 5 x 1 5
• 100 x 1 100

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• Any number multiplied by ZERO gives
• ZERO as the result
• 3 x 0 0
• 12 x 0 0
• A x 0 0
• 10,000 x 0 0

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• If you divide two negative numbers the
• answer will be positive
• -24 -8 3
• -42 6
• -7
• -72 9
• -8

10

• If you divide a negative number by a
• positive number the answer will be negative
• -24 8 -3
• -42 -6
• 7
• -72 -9
• 8

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• If you divide a positive number by a negative
• number the answer will be negative
• 24 -8 -3
• 42 -6
• -7
• 72 -9
• -8

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• 18 6 is the same as 18
• 6
• 24 3 is the same as 24
• 3
• 18 is the same as 18 3
• 3

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Some tips on Simplification

• Minus, Minus is Plus
• 5 - -8 5 8 13
• Minus, Plus is Minus
• 15 - 8 15 - 8 7
• Plus, Minus is Minus
• 15 - 8 15 - 8 7
• The easiest way to simplification problems
  involving order of operations is to use the
  BEDMAS or PEDMAS or PEMDAS approach. Learn and
  use the one you can easily remember.
• PEMDAS is short for Parenthesis Exponents
  Multiplication Division Additions Subtraction
• BEDMAS is short for Brackets Exponents Division
  Multiplication Additions Subtraction
• PEDMAS is short for Parenthesis Exponents
  Division Multiplication Additions Subtraction
• This means when working on long simplification
  problems, do Brackets or Parenthesis first, then
  Exponents, then Division, then Multiplication,
  followed by Addition and finally Subtraction

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Practice Questions

• (4(12 - 4) 10) 7
• Calculate 113 3(3 2)2 12 2

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How Percentages, Fractions and Decimals relate to
each other

• 2 is the same as 2 which is the same as
  0.02
• 100
• 25 is the same as 25 which is the same as
  0.25
• 100
• 10 is the same as 10 which is the same as
  0.10
• 100
• 12.5 is the same as 12.5 and also be written as
  0.125
• 100
• Notice that when you write the percentage as a
  fraction each zero in the denominator represent a
  single move of the decimal point to the left in
  the numerator when you convert it to decimals.

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Some Tips Tricks in Converting fractions to
decimals.

• In the absence of a calculator always check to
  see if the denominator of the fraction can be
  converted to a ten, a hundred, a thousand and so
  forth by multiplying by a number.
• If you can multiply the denominator by a number
  to get 10, 100, 1000 etc., then multiply both
  the numerator and denominator by this number.
• Now convert the numerator to the decimal number
  by moving the decimal point to the left as many
  times as there are zeros in the denominator.
• Note that each zero in the denominator represents
  a one decimal place move to the left.
• If the numerator did not originally contain a
  decimal point, start by assuming that there is a
  decimal point right after the last digit.
• (14 is the same as 14.0 or 14.)

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Examples

• Write 3 as a decimal.
• 5
• First we look at the denominator
• We can convert this to 10 by multiplying by 2.
• We have to also multiply the numerator
• by 2 so the value of the fraction remains the
• same
• 3 3 x 2 6 0.6
• 5 5 x 2 10

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• Write 7 as a decimal.
• 20
• 7 7 x 5 35 0.35
• 20 20 x 5 100

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THE OF KEYWORD

• A given percentage OF a certain quantity is
• equal to the Percentage multiplied by that
• quantity.
• 10 of a certain quantity can be expressed as
  (10 x the quantity )
• 10 of 200
• 10 200
• 10 200 20
• 100 1

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• A given Fraction OF a certain quantity is equal
  to
• the Fraction multiplied by that quantity
• ¾ of a certain quantity can be expressed as
• (¾ x the quantity )
• ¾ of 20
• ¾ 20
• 3 205 15
• 41 1

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EXAMPLES

• 1.) What is 15 of 500 ?
• Answer
• 15 of 500
• 15 x 500 15 x 5 75
• 100 1 1 1
• 2.) What is two-fifth of 80 ?
• Answer
• 2 of 80
• 5
• 2 x 8016 2 x 16 32
• 51 1 1 1

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• 3.) What percentage of 250 is 40 ?
• Answer
• Lets represent what percentage which we dont
  yet know with
• the letter p ( you can use any letter).
• Then we can write the following
• p of 250 is 40
• p x 250 40 (We can now solve for p)
• 100 1
• 2.5p 40
• p 40 16
• 2.5
• So 16 of 250 is equal to 40

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• 5.) 55 of the students in a school are boys. If
  there are 330 boys, what is the total number of
  students in the school?
• Answer
• We ask ourselves, What is the unknown here?
• The unknown is the total number of students
• Lets represent the total number of students by T.
• We can write the following mathematical
  statement
• 55 of T is equal to 330
• 55 x T 330
• 100
• 0.55T 330
• T 330 600

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What is a Reciprocal?

• The reciprocal of a whole number is 1 divided by
  the whole number.
• So the reciprocal of 5 will be 1
• 5
• As you can see, the reciprocal of a whole number
  becomes a fraction.
• The reciprocal of a fraction is the fraction you
  get when the numerator and denominator switch
  places.
• So the reciprocal of 7 will be 9
• 9 7

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LEAST COMMON MULTIPLE (LCM)

• In LCM we are looking at the multiples of two or
  more numbers to find out which of the multiples
  appear in all (COMMON) the numbers and at the
  same time the smallest.
• For example to find the LCM of 8 and 12 lets
  write out the multiples of each to a point
• 8gt8,16,24,32,40, . . .
• 12gt12,24,36,48, . . .
• Right away you notice that 24 is the first
  multiple of both 8 and 12. It is also the
  smallest or least of the multiples.
• So the LCM of 8 and 12 is 24
• To summarize 24 is both the Common Multiple and
  the Least.

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Finding LCM using the traditional method

• Start out by making a list of the multiples of
  each given number
• Look through the multiples for each given number
  and find which of the multiples appear in both
  lists or are common to both numbers.
• For example we want to find the LCM of 16 and 24
• 16 16, 32, 48, 64, 80 .
• 24 24, 48, 72, 96 ..
• We notice that 48 is the first multiple that is
  common to both 16 and 24 so 48 is our LCM

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• LEAST COMMON MULTIPLE (LCM) IN FOUR STEPS
• 1.)Write out the prime factors of each given
  number.
• 2.) Look for each COMMON factor and write it
  down only once for each time the common factor
  appears.
• 3.)Look for each Non-Common factor and write it
  down once.
• 4.)Multiply the factors from steps 2. and 3.
  above.
• For example to find the LCM of 16 and 24, write
  each number
• using its prime factors
• 16 2.2.2.2
• 24 2.2.2.3
• LCM 2.2.2.2.3 48

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Practice Questions

• What is the least common multiple of 4, 6 and 10
  ?
• What is the least common multiple of 6,10 and
  14?
• Try using both method to arrive at your answers
  and see which one is faster.

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GREATEST COMMON FACTOR (GCF)

• In GCF we are looking at the factors of two or
  more given numbers to determine which of the
  multiples appear in all (COMMON) the given
  numbers. This common factor should also be the
  greatest or largest or highest.
• GCF is also referred to as HCF (Highest Common
  Factor). They both mean the same thing.
• For example to find the GCF or HCF of 8 and 12
  lets write out the factors of each number
• 8gt1, 2, 4,8
• 12gt1, 2, 3, 4, 6, 12
• We notice from the list of factors that 1, 2 and
  4 are common to both lists. Of these three common
  factors 4 is the greatest or highest.
• So the GCF of 8 and 12 is 4
• To summarize two or more given numbers may have
  more than one factor which is common to them but
  we are only interested in the greatest of the
  common factors.

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GCF or HCF using the traditional method

• Start out by making a list of the factors of each
  given number.
• Look through the factors for each number and find
  which of the factors appear in both lists.
• The largest or highest of the common factors is
  the GCF or HCF.
• For example we want to find the GCF or HCF of 16
  and 24
• 16 1,2,4,8,16
• 24 1,2,3,4,6,8,12,24
• We notice that of the common factors 1,2,4,8
  the greatest or highest one is 8 so 8 is our GCF
  or HCF.

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• Greatest Common Factor (GCF) or Highest Common
  Factor (HCF) in THREE STEPS
• 1.) Write out the given number as a product of
  its prime factors
• 2.) Look for each prime factor that is COMMON to
  all the given numbers and write it down only once
  for each time that the factor appears common.
• 3.) Multiply the common prime factors from steps
  2 to get the GCF or HCF.
• e.g.
• 16 2222
• 24 2223
• The GCF is 222 8
• What is the greatest common factor of 9, 12 and
  15?
• Find the GCF of 24, 36 and 54