Colegio Herma. Maths Bilingual Department Isabel Martos Martínez. 2015

1. Fraction

Is an expression like , where a and b are natural numbers

and b is not equal to 0.

A fraction can be expressed:

• As a part of the unit

The top number of the fraction tells us how many slices we have.

We call it numerator.

The bottom number tells us how many parts in the whole unit we

have. We call it the denominator

• As a ratio /quotient

To obtain its value you need to divide the numerator by the

denominator. YOU MUST DO THE DIVISION.

• As an operator

To obtain its value you need to multiply this number by the

numerator and then divide it by the denominator

Fractions can be:

• Proper fractions:

The numerator is less than the denominator

This fraction is lower than the unit.

• Improper fractions

The numerator is greater than the denominator

This fraction is greater than the unit

The improper fraction can be expressed as a MIXED NUMBER

MIXED NUMBER IS A WHOLE NUMBER AND A FRACTION

can be expressed as a mixed number because it is an

improper fraction.

9 4 = 2 +

1 2

+ +

2 +

whole number proper fraction

Comparing and Ordering fractions

• Fractions with the same denominator, look at their numerators.

The largest fraction is the one with the largest numerator.

• Fractions with the same numerator, look at their denominators.

The largest fraction is the one with the lowest denominator.

• If you want to compare more than two fractions with different

denominator, you have to find the LCM and this is the new

denominator.

2. Equivalent fractions

• Two fractions are said to be equivalent when simplifying both

of them produces the same fraction written in its simplest

terms.

• Equivalent fractions are fractions with identical values.

• To create a pair of equivalent fractions, you multiply (or

divide, cancelling down) the top (numerator) and bottom

(denominator) of a given fraction by the same number.

Two fractions are equivalent if the cross-products are

the same.

THE SIMPLEST FORM FRACTION (FRACCIÓN IRREDUCIBLE)

A fraction is in simplest form when the top and bottom cannot be any smaller

(while still being whole numbers).

The simplest form is a fraction that cannot be reduced, since numerator and

denominator have no common divisors.

Simplifying (or reducing) fractions means to make the fraction as simple as

possible.

You always have to obtain the SIMPLEST FRACTION in any operation with

fractions.

We obtain the SIMPLEST FRACTION by dividing the top and bottom by the

highest number that can divide into both numbers exactly (HCD)

REMEMBER:

REDUCE A

FRACTION WHEN

POSSIBLE

Exercises

1. Cancel down the following fractions into their simplest

terms:

2. Arrange these fractions in order of size, smallest first:

a) b) c)

3. Operations involving fractions

a. Adding and subtracting fractions

When adding (or subtracting) fractions with different denominators,

they must be rewritten to have the same denominator before

starting the addition.

b. Multiplying and dividing fractions

• To multiply: You must simply multiply the two top numbers, and

multiply the two bottom ones.

• To divide one fraction by another, turn the second fraction upside

down and then multiply them. (You cross-multiply)

• Don’t forget: To multiply or divide by a whole number, just treat

it like a fraction with a denominator of 1.

Pay atention to

order of

operation

BEDMAS

Bedmas song

4. Types of decimal numbers

There are three different types of decimal number: exact,

recurring and other decimals.

An exact or terminating decimal is one which does not go on

forever, so you can write down all its digits. For example:

0,125

A recurring decimal is a decimal number which does not stop

after a finite number of decimal places, but where some of the

digits are repeated over and over again. For example:

0,1252525252525252525...

it is a recurring decimal, where '25' is repeated forever.

There exist two types of recurring decimals:

Pure recurring decimal: It becomes periodic just after the decimal

point. Ex. 1,3535… ( 35 is called the period)

Eventually recurring decimal: When the period is not settled just

after the decimal point. There is a not repeating number placed

between the decimal point and the period.

Ex. 1,6353535… ( 6 is called anteperiod, and 35 is called the period)

Other decimals are those which go on forever and don't have digits

which repeat. For example

pi = 3,141592653589793238462643..

They are called irrational numbers.

Writing a decimal number ( a regular number) as a fraction

To convert regular number into a fraction you only have to

divide the integer number by 1 followed as many ceros as

digits this number has in the decimal part.

Example: write as a fraction 5,12

Step 1: Write down the decimal divided by 1, like this:

5,12

1

Step 2: Multiply both top and bottom by 10 for every number

after the decimal point. (In this case there are two numbers

after the decimal point, then use 100.)

512

100

Step 3: Reduce the fraction 512

100=

256

50=

153

25

Writing a recurring decimal number as a fraction

Now, we are going to convert one recurring decimal number into its corresponding fraction.

We will also indicate which kind of recurring decimal it is.

You have to use this formula:

Where:

E: integer part or the whole number portion

P: periodic part from the decimal portion

A: anteperiod from the decimal portion

9: write as many 9 as digits in the periodic part

0: write as many 0 as digits in the anteperiod part

𝐸𝐴𝑃 − 𝐸𝐴

9…0

E.g.

Give the corresponding fraction for 6,59

E: 6

A: 5

P: 9

9: one digit, one 9 659−65

90 = 594

90 =

99

15 =

33

5

0: one digit, one 0

5. Number sets

• All the numbers in the Number System are classified into

different sets and those sets are called as Number Sets.

• The set of real numbers is divided into natural numbers,

whole numbers, integers, rational numbers, and irrational

numbers.