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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

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
• 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
• 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
• 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