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PRESENTATION 5Common Fractions

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

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

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

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

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

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

MIXED NUMBERS AS FRACTIONS

- Find the number of fractional parts contained in

the whole number - Add the fractional part

FRACTIONS AS MIXED NUMBERS

- To convert fractions into mixed numbers, divide

and place the remainder over the denominator

FRACTIONS AS MIXED NUMBERS

- Example
- Divide and place the remainder over the

denominator - Reduce to lowest terms

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

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

ADDITION OF FRACTIONS

- To add fractions, express using the lowest common

denominator - Add the numerators and write their sum over the

LCD - Example

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

SUBTRACTION OF FRACTIONS

- To subtract common fractions, express the

fractions as equivalent fractions with a common

denominator - Subtract the numerators
- Reduce to lowest terms

SUBTRACTION OF FRACTIONS

- Example

SUBTRACTION OF FRACTIONS

- Express the fractions as equivalent fractions

with 60 as the denominator - Finally, subtract the numerators of the

fractions

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

MULTIPLICATION OF FRACTIONS

- Example
- Multiply the numerators and denominators

MULTIPLICATION OF FRACTIONS

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

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

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

DIVISION OF FRACTIONS

- Division is the inverse of multiplication
- To divide fractions, invert the divisor, change

to the inverse operation (multiplication), and

multiply

DIVISION OF FRACTIONS

- Example
- Invert the divisor, multiply, and reduce

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

DIVISION OF FRACTIONS

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

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

ORDER OF OPERATIONS

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

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?

PRACTICAL PROBLEMS

- Add all the ingredients

PRACTICAL PROBLEMS

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