PRESENTATION 5 Common Fractions

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PRESENTATION 5Common Fractions
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COMMON FRACTIONS

• A fraction is a value that shows the number of
  equal parts taken of a whole quantity
• The symbol used to indicate a fraction is the
  slash (/) or bar ()
• A fraction indicates division

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COMMON FRACTIONS

• There are two parts to a fraction, called terms
• The numerator is the top number and shows how
  many equal parts of the whole are taken
• The denominator is the bottom number and shows
  how many equal parts are in the whole quantity

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COMMON FRACTIONS

• A proper fraction is a number less than 1
• For example 3/4, 5/8, 99/100 written with the
  slash or written with the bar
• An improper fraction is a number greater than 1
• For example

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FRACTION IN LOWEST TERMS

• Fractions can be expressed in lowest terms by
  dividing both the numerator and denominator by
  the same number without changing the value.
• For example
• To reduce to lowest terms, divide both the
  numerator and denominator by 2

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FRACTION IN LOWEST TERMS

• The fraction is still not in lowest terms, so
  find another common factor in the numerator and
  the denominator. In this case, divide by the
  factor of 2
• A fraction is in lowest terms when the numerator
  and denominator do not contain a common factor

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MIXED NUMBERS AS FRACTIONS

• A mixed number is a whole number plus a fraction
• To express a mixed number as an improper
  fraction
• Find the number of fractional parts contained in
  the whole number
• Add the fractional part to the whole number
  equivalent

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MIXED NUMBERS AS FRACTIONS

• Find the number of fractional parts contained in
  the whole number
• Add the fractional part

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FRACTIONS AS MIXED NUMBERS

• To convert fractions into mixed numbers, divide
  and place the remainder over the denominator

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FRACTIONS AS MIXED NUMBERS

• Example
• Divide and place the remainder over the
  denominator
• Reduce to lowest terms

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ADDITION OF FRACTIONS

• Fractions cannot be added unless they have a
  common denominator (the denominator of each
  fraction is the same)
• The lowest common denominator (LCD) is the
  smallest number that all denominators divide into
  evenly
• For example, the lowest common denominator of 4
  2 is 4 since 4 is the smallest number evenly
  divisible by both 2 and 4

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COMPARING VALUES OF FRACTIONS

• To compare values of fractions with like
  denominators, compare the numerators
• The fraction with the larger numerator is the
  larger fraction
• To compare fractions with unlike denominators,
  express the fractions as equivalent fractions
  with a common denominator and compare numerators

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ADDITION OF FRACTIONS

• To add fractions, express using the lowest common
  denominator
• Add the numerators and write their sum over the
  LCD
• Example

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ADDITION OF FRACTIONS, MIXED NUMBERS, AND WHOLE
NUMBERS

• To add fractions, mixed numbers, and whole
  numbers
• Express the fractional parts of the number using
  a common denominator
• Add the whole numbers
• Add the fractions
• Combine the whole number and the fraction and
  express in lowest terms

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SUBTRACTION OF FRACTIONS

• To subtract common fractions, express the
  fractions as equivalent fractions with a common
  denominator
• Subtract the numerators
• Reduce to lowest terms

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SUBTRACTION OF FRACTIONS

• Example

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SUBTRACTION OF FRACTIONS

• Express the fractions as equivalent fractions
  with 60 as the denominator
• Finally, subtract the numerators of the
  fractions

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MULTIPLICATION OF FRACTIONS

• Multiplication and division of fractions do not
  require a common denominator
• To multiply simple fractions, multiply the
  numerators and multiply the denominators
• Mixed numbers must be changed to improper
  fractions before multiplying

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MULTIPLICATION OF FRACTIONS

• Example
• Multiply the numerators and denominators

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MULTIPLICATION OF FRACTIONS

• Example
• Multiply numerators and denominators
• Express as mixed number in lowest terms

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DIVIDING BY COMMON FACTORS

• Problems involving multiplication of fractions
  are generally solved more quickly if a numerator
  and denominator are divided by any common factors
  before the fractions are multiplied
• This process is called cancellation

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DIVIDING BY COMMON FACTORS

• Example
• The factor 3 is common to both the numerator 3
  and the denominator 9, so divide
• The factor 4 is common to both the numerator 4
  and the denominator 8, so divide
• Multiply the numerators and denominators

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DIVISION OF FRACTIONS

• Division is the inverse of multiplication
• To divide fractions, invert the divisor, change
  to the inverse operation (multiplication), and
  multiply

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DIVISION OF FRACTIONS

• Example
• Invert the divisor, multiply, and reduce

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DIVISION OF FRACTIONS

• To divide any combination of fractions, mixed
  numbers, and whole numbers
• Write mixed numbers as fractions
• Write whole numbers over the denominator of 1
• Invert the divisor
• Change to the inverse operation
• Multiply

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DIVISION OF FRACTIONS

• Example
• Write
• Invert the divisor
• Change to the inverse operation and multiply

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ORDER OF OPERATIONS

• As with any arithmetic expression, the order of
  operations must be followed. The operations are
• Parentheses
• Exponents and roots
• Multiplication and division from left to right
• Addition and subtraction from left to right

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ORDER OF OPERATIONS

• Example
• First, add the fractions in ( )
• Next, multiply and divide
• Finally, subtract

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PRACTICAL PROBLEMS

• A baker prepares a cake mix that weighs 100
  pounds.
• The cake mix consists of shortening and other
  ingredients.
• The weights of the other ingredients are 20 1/2
  pounds flour, 29 3/4 pounds of sugar, 18 1/8
  pounds of milk, 16 pounds of whole eggs, and a
  total of 5 1/4 pounds of flavoring, salt, and
  baking powder.
• How many pounds of shortening are used in the
  mix?

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PRACTICAL PROBLEMS

• Add all the ingredients

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PRACTICAL PROBLEMS

• Subtract from the total weight of the cake mix
• There are pounds of shortening in the mix