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PRESENTATION 5 Common Fractions

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Title: PRESENTATION 5 Common Fractions


1
PRESENTATION 5Common Fractions
2
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

3
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

4
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

5
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

6
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

7
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

8
MIXED NUMBERS AS FRACTIONS
  • Find the number of fractional parts contained in
    the whole number
  • Add the fractional part

9
FRACTIONS AS MIXED NUMBERS
  • To convert fractions into mixed numbers, divide
    and place the remainder over the denominator

10
FRACTIONS AS MIXED NUMBERS
  • Example
  • Divide and place the remainder over the
    denominator
  • Reduce to lowest terms

11
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

12
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

13
ADDITION OF FRACTIONS
  • To add fractions, express using the lowest common
    denominator
  • Add the numerators and write their sum over the
    LCD
  • Example

14
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

15
SUBTRACTION OF FRACTIONS
  • To subtract common fractions, express the
    fractions as equivalent fractions with a common
    denominator
  • Subtract the numerators
  • Reduce to lowest terms

16
SUBTRACTION OF FRACTIONS
  • Example

17
SUBTRACTION OF FRACTIONS
  • Express the fractions as equivalent fractions
    with 60 as the denominator
  • Finally, subtract the numerators of the
    fractions

18
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

19
MULTIPLICATION OF FRACTIONS
  • Example
  • Multiply the numerators and denominators

20
MULTIPLICATION OF FRACTIONS
  • Example
  • Multiply numerators and denominators
  • Express as mixed number in lowest terms

21
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

22
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

23
DIVISION OF FRACTIONS
  • Division is the inverse of multiplication
  • To divide fractions, invert the divisor, change
    to the inverse operation (multiplication), and
    multiply

24
DIVISION OF FRACTIONS
  • Example
  • Invert the divisor, multiply, and reduce

25
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

26
DIVISION OF FRACTIONS
  • Example
  • Write
  • Invert the divisor
  • Change to the inverse operation and multiply

27
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

28
ORDER OF OPERATIONS
  • Example
  • First, add the fractions in ( )
  • Next, multiply and divide
  • Finally, subtract

29
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?

30
PRACTICAL PROBLEMS
  • Add all the ingredients

31
PRACTICAL PROBLEMS
  • Subtract from the total weight of the cake mix
  • There are pounds of shortening in the mix
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