Fractions

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Fractions

• Learning Intentions– the meaning of fractions– the equivalence of fractions– how to arrange fractions in order– simplifying fractions– adding and subtracting fractions

Meaning of Fractions

• A fraction indicates a part of a whole.• Fractions have a numerator and a

denominator• The denominator indicates the number of

parts that the whole has been divided into• The numerator indicates the number of parts

that you have• Example:

83

Equivalence of Fractions

• Two fractions can have the same value, even though they may be written differently.

• For example:

• They are the same because when you multiply or divide both the top and bottom by the same number, the fraction keeps its value.

84

42

21

Simplest Form

• We say a fraction is in its simplest form if the numerator and denominator do not share a common factor.

• For example:– A fraction not in its simplest form is

– A fraction in its simplest form is

156

138

Simplifying Fractions

• We can simplify a fraction by dividing the numerator and denominator by the same number.

• If we keep dividing until we can’t go any further then we have simplified the fraction

Comparing Fractions

• To compare fractions we must write them with the same denominator.

• Which fraction is the largest?– or

• Write each fraction as an equivalent fraction with the same denominator.

• The larger fraction then has the larger numerator

83

125

Mixed Numbers

• A number that consists of a fraction and a whole number is called a mixed number.

• For example: 1 41

Improper Fractions

• An improper fraction is a fraction with a larger numerator than a denominator

• For example • This indicates that you have more than one

whole.• In this case you have five quarters. That is one

whole (four quarters) and one quarter.

45

Improper Fractions

• To convert a mixed number to an improper fraction– Multiply the whole number part by the fraction's

denominator.– Add that to the numerator– Then write the result on top of the denominator

• Example: Write 3 as an improper fraction52

Improper Fraction

• To convert an improper fraction to a mixed number– Divide the numerator by the denominator.– Write down the whole number answer– Then write down any remainder above the

denominator.• Example: Convert to a mixed number

411

Adding Fractions

• There are four steps to be taken when adding fractions– Change mixed numbers to improper fractions– Change the fractions into equivalent fractions with

the same denominator– Add the numerators, keeping the denominator the

same– Simplify the fraction

Adding Fractions

• Examples: +

1 +

21

41

31

65

Subtracting Fractions

• There are four steps to be taken when adding fractions– Change mixed numbers to improper fractions– Change the fractions into equivalent fractions with

the same denominator– Subtract the numerators, keeping the

denominator the same– Simplify the fraction

Subtracting Fractions

• Examples: –

1 – 65

31

21

41