## FRACTION

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FRACTION

By Mushadi Iksan, M.Ed.

3.1 FRACTION

A fraction is a number that represents a part of a whole. It is written as , where a and b are whole numbers and b 0. is read as “ a over b”

Example:

1. is read as “three over four” or “ three quarter”

2. is read as “ one over three” or “one third”.

3.1.1 Representing Fractions with Diagrams

· Fractions can be represented with diagrams and number lines.

In the left diagram, the shaded parts are 1 out of 4 equal parts, that is Example:

· In any fraction, the top number is called the numerator and the bottom number is called the denominator.

Example:

Denominator

Numerator

· The numerator represents the number of equal parts that are shaded and the denominator represents the total number of equal parts in one whole.

· When the numerator is the same as the denominator, the value of the fraction is equal to 1.

Example:

3.1.2 Equivalent Fractions

· Equivalent fractions are fractions having the same value.

Example:

=

=

· Equivalent fractions can be obtained by multiplying the numerator and denominator by the same whole numbers (greater than 1).

Example:

Since,

, , , and

· To determine whether two given fractions are equivalent or not, we can use calculation.

Fractions and are equivalent if ad = bc

Example :

Determine whether and are equivalent.

Solution:

Cross-multiplying

The products are the same

Therefore, and are equivalent

3.1.3 Comparing the Values of Two Fractions

· When comparing two fractions having the same denominator, the fraction with the bigger numerator is greater in value.

Example:

and

has greater value, because 7 > 5 and their denominator are the same.

· When comparing two fractions having the same numerator, the fraction with the smaller denominator is greater in value.

Example:

and

has greater value, because 12 <>

· Alternative method of comparing two fractions having different numerators and denominators.

Fractions and ;

If ad > bc then >

If ad <> Þ >

3.1.4 Simplifying Fraction

· A fraction is in its lowest terms if the numerator and denominator have no common factor except 1.

· To simplify a fraction to its lowest term, divide the numerator and the denominator by their HCF.

· All answer must be given in their lowest term.

Example:

Simplify to its lowest terms.

Solution:

13 is the HCF of 13 and 39

3.2 PROPER FRACTIONS, IMPROPER FRACTION AND MIXED NUMBERS

3.2.1 Proper Fractions and Improper Fractions

· A proper fraction has a numerator which is smaller than the denominator.

Example:

· An improper fraction has a numerator which is the same as or greater than the denominator.

Example:

3.2.2 Converting Whole Numbers to Improper Fractions

· All whole numbers are improper fractions with 1 as their denominators.

Example:

, ,

· Whole numbers can be converted to improper fractions with other denominators.

Example:

= =

3.2.3 Mixed Number

· A mixed number is a number consisting of a whole number and a fraction.

· All mixed numbers are greater than.

Example:

, , ,

3.2.4 Converting Mixed Numbers to Improper Fractions.

· To change a mixed number to an improper fraction, multiply the whole number by the denominator and then add the product to the numerator. The denominator remains the same.

Example:

a.

b.

3.2.5 Converting Improper Fractions to Mixed Numbers

· To change an improper fraction to a mixed number, divide the numerator by the denominator.

· The quotient obtained is the whole number part and the remainder is the numerator of the fractional part.

Example:

Þ Remainder = 2

Therefore,

· Where possible, simplify the improper fraction to its lowest terms before converting it to the mixed number.

Example:

3.1 FRACTION

A fraction is a number that represents a part of a whole. It is written as , where a and b are whole numbers and b 0. is read as “ a over b”

Example:

1. is read as “three over four” or “ three quarter”

2. is read as “ one over three” or “one third”.

3.1.1 Representing Fractions with Diagrams

· Fractions can be represented with diagrams and number lines.

In the left diagram, the shaded parts are 1 out of 4 equal parts, that is Example:

· In any fraction, the top number is called the numerator and the bottom number is called the denominator.

Example:

Denominator

Numerator

· The numerator represents the number of equal parts that are shaded and the denominator represents the total number of equal parts in one whole.

· When the numerator is the same as the denominator, the value of the fraction is equal to 1.

Example:

3.1.2 Equivalent Fractions

· Equivalent fractions are fractions having the same value.

Example:

=

=

· Equivalent fractions can be obtained by multiplying the numerator and denominator by the same whole numbers (greater than 1).

Example:

Since,

, , , and

· To determine whether two given fractions are equivalent or not, we can use calculation.

Fractions and are equivalent if ad = bc

Example :

Determine whether and are equivalent.

Solution:

Cross-multiplying

The products are the same

Therefore, and are equivalent

3.1.3 Comparing the Values of Two Fractions

· When comparing two fractions having the same denominator, the fraction with the bigger numerator is greater in value.

Example:

and

has greater value, because 7 > 5 and their denominator are the same.

· When comparing two fractions having the same numerator, the fraction with the smaller denominator is greater in value.

Example:

and

has greater value, because 12 <>

· Alternative method of comparing two fractions having different numerators and denominators.

Fractions and ;

If ad > bc then >

If ad <> Þ >

3.1.4 Simplifying Fraction

· A fraction is in its lowest terms if the numerator and denominator have no common factor except 1.

· To simplify a fraction to its lowest term, divide the numerator and the denominator by their HCF.

· All answer must be given in their lowest term.

Example:

Simplify to its lowest terms.

Solution:

13 is the HCF of 13 and 39

3.2 PROPER FRACTIONS, IMPROPER FRACTION AND MIXED NUMBERS

3.2.1 Proper Fractions and Improper Fractions

· A proper fraction has a numerator which is smaller than the denominator.

Example:

· An improper fraction has a numerator which is the same as or greater than the denominator.

Example:

3.2.2 Converting Whole Numbers to Improper Fractions

· All whole numbers are improper fractions with 1 as their denominators.

Example:

, ,

· Whole numbers can be converted to improper fractions with other denominators.

Example:

= =

3.2.3 Mixed Number

· A mixed number is a number consisting of a whole number and a fraction.

· All mixed numbers are greater than.

Example:

, , ,

3.2.4 Converting Mixed Numbers to Improper Fractions.

· To change a mixed number to an improper fraction, multiply the whole number by the denominator and then add the product to the numerator. The denominator remains the same.

Example:

a.

b.

3.2.5 Converting Improper Fractions to Mixed Numbers

· To change an improper fraction to a mixed number, divide the numerator by the denominator.

· The quotient obtained is the whole number part and the remainder is the numerator of the fractional part.

Example:

Þ Remainder = 2

Therefore,

· Where possible, simplify the improper fraction to its lowest terms before converting it to the mixed number.

Example: