# Fractional Numbers

## NUMBERS AND OPERATIONS

A fractional number or fraction expresses a certain number of portions that are taken from a whole divided in equal parts.

It is represented by a dividing bar (oblique or horizontal), also called the "fraction line" that separates the first quantity (numerator) from the second (denominator).

#### Recognize the terms of a fraction

Do you know what a fraction is? And could you explain what the numerator and denominator represent? Don't worry, we offer you the explanation, an interactive game and some worksheets in PDF for you to practice and understand easily.

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We define the concept of fraction as "the number obtained by dividing a natural number (positive integer) into equal parts"

ELEMENTS OF A FRACTION

- The numerator (top number) of a fraction indicates the number of parts that are chosen from the unit.

- The denominator (bottom number) represents the number of equal parts the unit is divided into.

We present you some printable activities accompanied by their explanation and an educational game so that you can learn to read and write any fraction.

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HOW TO READ AND WRITE FRACTIONS

To correctly read and write any fraction, initially, we will read the numerator and then the denominator:

- The numerator is read and written using the cardinal numbers or natural numbers: one, two, three, four, five, thirty-six, hundred fifteen, nine hundred and eighty four...

- The denominator is read and written using the partitive numbers:

2 = half / halves

3 = third/s

4 = quarter/s

5 = fifth/s

6 = sixth/s

7 = seventh/s

8 = eighth/s

9 = ninth/s

10 = tenth/s

We present a visual scheme to facilitate the assimilation of learning to read and write fractional numbers:

There are two exceptions that have their own words: half (1/2) and quarter (1/4):

Remember that he denominator is an ordinal number (e.g., third, fifth, sixth...) and you can use “fourths” in place of “quarters”.

And when should you write fractions as words and when should you write them as numerals?

As a general rule, we will write the fractions in words in the main text of a document and we will use the numerals to write the fractions in measurements, tables of results, equations, and other primarily numerical data.

#### Interpret fractions as dividing two whole numbers

Every fraction of two natural numbers (positive integers) always represents the division between these numbers.

To express the quotient of a fraction (also called "result"), we will divide the numerator by the denominator obtaining as a result quotients with whole numbers or quotients with decimal numbers.

FRACTIONS WITH WHOLE QUOTIENT

The "fractions with whole quotient" are those in which, when dividing the numerator by the denominator, the quotient of the division is a positive integer because the division is exact (the remainder is zero):

FRACTIONS WITH DECIMAL QUOTIENT

The "fractions with decimal quotient" will be those fractions in which, after dividing the numerator by the denominator, the quotient of the division is a decimal number since the division is inexact (there is a leftover remainder):

#### Interpret and represent fractions graphically

FRACTIONS LESS THAN ONE

We teach you to graphically represent fractions less than one, that is, those fractions in which the numerator is less than the denominator.

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NUMERATOR < DENOMINATOR

FRACTIONS GREATER THAN ONE

We show you how to graphically represent fractions greater than one, that is, those fractions in which the numerator is greater than the denominator.

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NUMERATOR > DENOMINATOR

#### Compare fractions of the same denominator (like fractions) with each other

When comparing different fractions with the same denominator (also called "like fractions") with each other, the fraction with the greater numerator will be greater.

View the lesson to understand it in a simple way and practice with the activities in PDF using great than (>), less than (<) and equal to (=) signs.

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In the following example, the fraction 5/9 will be greater than 4/9 because its numerator is greater ( 5 > 4 ):

#### Compare fractions of the same numerator with each other

When comparing different fractions with the same numerator (also known as "same numerator fractions") with each other, the fraction with lower denominator will be greater.

View the lesson for quick understanding and solve our activities to keep improving your fraction comparisons.

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In the lesson that we propose, the fraction 1/2 will be greater than 1/4 because its denominator is smaller ( 2 < 4 ):

#### Compare fractions of different numerator and denominator (unlike fractions) with each other

To compare fractions with different numerator and denominator (known as "unlike fractions"), you have to transform them by finding the equivalent fraction so that both fractions have the same denominator.

The equivalent fraction with the largest numerator will be greater.

Watch the lesson and we will explain how to do it correctly using various examples.

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#### Compare fractions to one

To compare any fraction to unity, we will compare the numerator and denominator with each other. The following three situations can happen:

1) If the numerator and denominator are equal (for example 8/8), the fraction will be equal to one.

2) If the numerator is less than the denominator (for example 4/8), the fraction will be less than one.

3) If the numerator is greater than the denominator (for example 12/8), the fraction will be greater than one.

#### Identify the largest and smallest number in a series of fractions

After explaining how to compare fractions with the same numerator, same denominator, and different numerator and denominator with each other, use and apply these teachings to identify the largest and smallest fraction in a series of disordered fractions.

#### Order a series of fractions by comparison and graphical representation

Apply the rules for comparing fractions learned and solve the exercises proposed by ordering from greatest to least (and vice versa) any group of fractions.

#### Calculate the fraction of a number

Do you know the method to find the fraction of a quantity? In the following explanatory video we show you step by step how to do it and, so that you can continue practicing, we propose some printable educational tasks in PDF format.

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Steps to find the fraction of a number:

1) We will multiply the whole number ( 18 ) by the numerator of the fraction ( 4 ), that is, 18 x 4 = 72

2) We will divide the result of the previous multiplication ( 72 ) by the denominator of the fraction ( 6 ), giving as a result 12 , obtained at from the operation 72: 6 = 12

You can also solve the operations in reverse and the result will be the same:

1) We will divide the whole number ( 18 ) by the denominator of the fraction ( 6 ), that is, 18: 6 = 3

2) We will multiply the result of the previous division ( 3 ) by the numerator of the fraction ( 4 ), resulting in 12, obtained at starting from the operation 3 x 4 = 12

#### Solve word problems with fractions of a quantity

We present you some word problems with fractions of a quantity so that you can easily understand how to solve them. Also, we explain step by step what is the resolution process based on various examples.

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#### Recognize and interpret equivalent fractions through their graphic representation

We teach you how to recognize and interpret when two fractions are equivalent to each other through their graphical representation to make it easier for you to learn. Remember that two or more fractions will be equivalent if, even though their numerator and denominator are different, they represent the same portion of the unit.

In the proposed example, you can see that the fractions 1/3 and 2/6 represent graphically the same part of the unit (equivalent portions):

Therefore, it will be the same to eat one-third of a cake as two-sixths of the same cake.

#### Identify fractions equivalent to each other

Do you know what equivalent fractions are? And how to calculate them? We explain it to you:

Two or more fractions are equivalent to each other when the cross products of their terms are equal, representing the same part of the unit.

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#### Obtain fractions equivalent to a given fraction: Amplification

Do you know how to amplify a fraction? An equivalent fraction by the amplification method is obtained by multiplying the numerator and denominator of the fraction itself by the same number.

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#### Obtain fractions equivalent to a given fraction: Simplification

Do you know how to simplify a fraction? An equivalent fraction by the simplification method is obtained by dividing the numerator and denominator by the same number (remember, both must be divisible by the same number).

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#### Obtain the irreducible fraction to a given fraction

An irreducible fraction (also known as "fraction in lowest terms", "simplest form" or "reduced fraction") is a fraction that cannot be simplified further. We propose the explanation accompanied by some PDF exercises so that you can learn to find the irreducible fraction.

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#### Reduce fractions to a common denominator by the cross products method

We present you a tutorial, an interactive game and some downloadable tasks so that you can practice reducing fractions to a common denominator following the cross-multiplication system.

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#### Reduce fractions to a common denominator by the least common multiple method

We propose a lesson, a didactic game and some printable worksheets so that you can practice reducing fractions to the Least Common Multiple (LCM) of the denominators.

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#### Classify fractions: proper, improper, and mixed

In Math, we use three categories to classify fractions: proper, improper, and mixed.

- In proper fractions the numerator is less than the denominator (for example 2/5) and its decimal result will always be between 0 and 1.

- In improper fractions the numerator is equal to or greater than the denominator (for example 7/3) and its decimal result will always be equal to or greater than 1.

- A mixed number is the combination of a whole number and a proper fraction (for example 4 ones and 3/6).

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#### Express fractions greater than one as a mixed number and vice versa

We provide you with the explanation, a game and some worksheets in PDF so that you understand and practice the mathematical procedure of the expression of fractions as mixed numbers and vice versa.

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To convert a fraction to a mixed number:

1) We will divide the numerator by the denominator of the fraction.

2) The quotient digit will be the integer part, the remainder digit will correspond to the numerator and, finally, the divisor figure will be the denominator.

To convert a mixed number to a fraction:

1) The number of the numerator of the new fraction will be found by multiplying the number of the whole part by the denominator and, to the result, we will add the number of the numerator.

2) The digit of the denominator of the new fraction will correspond to the denominator of the mixed number.

#### Adding fractions of the same denominator (like fractions) by graphing

We show you how to solve the addition of fractions with the same denominator using their graphical representation. Remember, we will only add the numerators of each fraction and keep the denominator common.

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#### Add fractions of the same denominator (like fractions)

To solve any sum of fractions with the same denominator, we will add the numerators of each fraction leaving the same denominator that they have in common.

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#### Add fractions with different denominators (unlike fractions)

To solve a sum of fractions with different denominator, we will find the least common multiple (LCM) of the two denominators. Next, we will replace the original fractions by equivalent fractions starting from the common denominator. Finally, we will add the numerators.

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#### Add fractions to one or more natural units

To solve an addition of a fraction and a whole number , we will find the least common multiple (LCM) of the two denominators, where the value of the denominator of the whole number will always be 1. Next, we will proceed to solve the operation following the method of adding fractions with different denominators (unlike fractions).

#### Subtracting fractions of the same denominator (like fractions) by graphing

We show you how to solve the subtraction of fractions with the same denominator using their graphical representation. Remember, we will only subtract the numerators from each fraction and keep the denominator common.

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#### Subtract fractions of the same denominator (like fractions)

To solve any subtraction of fractions with the same denominator, we will subtract the numerators of each fraction leaving the same denominator that they have in common.

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#### Subtract Fractions of Different Denominators (unlike fractions)

To solve a subtraction of fractions with different denominator, we will find the least common multiple (LCM) of the two denominators. Next, we will replace the original fractions by equivalent fractions starting from the common denominator. Finally, we will subtract the numerators.

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#### Subtract fractions to one or more natural units

To solve an subtraction of a fraction and a whole number, we will find the least common multiple (LCM) of the two denominators, where the value of the denominator of the whole number will always be 1. Next, we will proceed to solve the operation following the method of subtracting fractions with different denominators (unlike fractions).

#### Add and subtract fractional number combined operations with parentheses

We propose a tutorial and a series of activities so that you can practice solving combined operations of addition and subtraction with fractions either with the same or with different denominator.

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#### Multiply whole numbers and fractions with each other

To solve any multiplication of a natural number by a fraction, we will multiply the natural number by the numerator of the fraction and leave the same denominator.

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#### Multiply fractions by each other

To solve a multiplication of a fraction by another fraction, we will multiply the numerator by the numerator and the denominator by the denominator.

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#### Divide whole numbers and fractions by each other

To solve a division of a fraction by a natural number , we will multiply the terms of the fractions by a cross, with the value of the denominator of the natural number will always be 1.

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#### Divide fractions by each other

To solve a division of a fraction by another fraction, we will multiply the terms of the fractions by a cross.

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