Saturday, August 10, 2024

# What Does Fraction Mean In Math

## How Many Parts Are There In A Fraction

What is an Improper Fraction? | Math with Mr. J

A fraction has two parts, the numerator and the denominator.

• Numerator: The numerator represents the number that is placed above the fractional bar. For example, in 6/7, 6 is the numerator.
• Denominator: The denominator indicates the number that is placed below the fractional bar. For example, in 6/7, 7 is the denominator.

## Reciprocals And The Invisible Denominator

The reciprocal of a fraction is another fraction with the numerator and denominator exchanged. The reciprocal of 3 3 }} . The product of a fraction and its reciprocal is 1, hence the reciprocal is the multiplicative inverse of a fraction. The reciprocal of a proper fraction is improper, and the reciprocal of an improper fraction not equal to 1 is a proper fraction.

When the numerator and denominator of a fraction are equal , its value is 1, and the fraction therefore is improper. Its reciprocal is identical and hence also equal to 1 and improper.

Any integer can be written as a fraction with the number one as denominator. For example, 17 can be written as 17 1 }} , where 1 is sometimes referred to as the invisible denominator. Therefore, every fraction or integer, except for zero, has a reciprocal. For example. the reciprocal of 17 is 1

## How Are Fractions And Decimals Related

Fractions and decimals are different ways to represent numbers. Fractions are written in the form of p/q, where qâ 0, for example, 3/5 while in decimals, the whole number part and fractional part is connected with a decimal point, for example, 3.56. A fraction can be converted to a decimal if we divide the given numerator by the denominator. Similarly, to convert a decimal into a fraction, we write the given decimal as the numerator, we place a fractional bar below it. Then, we place 1 right below the decimal point followed by the number of zeros required accordingly. Then, this fraction can be simplified. For example, if we need to convert 0.5 to a fraction, we place 10 in the denominator and remove the decimal point which makes it 5/10. After reducing the fraction, we get / = 1/2.

Don’t Miss: What Is Big G In Physics

## Rules For Simplification Of Fractions

There are some rules we should know before solving the problems based on fractions.

Rule #1: Before adding or subtracting fractions, we should make sure that the denominators are equal. Hence, the addition and subtraction of fractions are possible with a common denominator.

Rule #2: When we multiply two fractions, then the numerators are multiplied as well as the denominators are multiplied. Later simplify the fraction.

Rule #3: When we divide a fraction from another fraction, we have to find the reciprocal of another fraction and then multiply with the first one to get the answer.

## Fraction On A Number Line

The representation of fractions on a number line demonstrates the intervals between two integers, which also shows us the fundamental principle of fractional number creation. The fractions on a number line can be represented by making equal parts of a whole, i.e., from 0 to 1. The denominator of the fraction would represent the number of equal parts in which the number line will be divided and marked. For example, if we need to represent 1/8 on the number line, we need to mark 0 and 1 on the two ends and divide the number line into 8 equal parts. Then, the first interval can be marked as 1/8. Similarly, the next interval can be marked as 2/8, the next one can be marked as 3/8, and so on. It should be noted that the last interval represents 8/8 which means 1. Observe the following number line that represents these fractions on a number line.

âRelated Articles

Also Check: Chapter 9 Review Algebra 2

## What Does A Horizontal Line Between Two Numbers Mean

A horizontal line placed over an expression to show that everything below the line is one group. In some countries it is the horizontal line used to separate the numerator and denominator in a fraction, also called a fraction bar.

How are fractions represented on a number line?

A fraction shows the equal parts of a collection or whole. The number line is a straight line with numbers placed at equal intervals along its length. Representing Fractions on Number Line means pointing the fractions on the number line. It shows the interval between two numbers.

What does the word fractional mean in English?

fractional An expression of a fractional number. In English, most ordinals double as fractionals u2014 third, fourth, and so on u2014 with the exception of second, whose corresponding fractional is half.

## How To Subtract Unit Fractions

The process of subtraction is similar to the addition, but instead of adding the numerators in step 3, we subtract them here and simplify the answer.

For example, lets subtract $\frac$ from $\frac$.

Step 1: Identify the LCM

Multiples of 4 = 4, 8, 12, 16, 20, 24 . . .

Multiples of 5 = 5, 10, 15, 20 . . .

So, the LCM here is 20.

Step 2: Convert each fraction to a fraction with the least common denominator.

$\frac = \frac \times \frac = \frac$

$\frac = \frac \times \frac = \frac$

Step 3: Subtract the fractions and simplify.

$\frac$ $$\frac = \frac$$ $\frac$

$= \frac$

Example 1: Find the sum of $\frac$ and $\frac$.

Solution:

Step 1:Identify the least common multiple of the denominators.

Multiples of 3: 3, 6, 9, 12, 15, 18, 21, 24

Multiples of 7: 7, 14, 21

So, the LCM is 21.

Step 2: Convert each fraction to an equivalent fraction with the least common multiple as the denominator.

Now, we convert the fractions into a denominator with the LCM.

$\frac = \frac \times \frac = \frac$

$\frac = \frac \times \frac = \frac$

$\frac + \frac$

$= \frac + \frac$

$= \frac$

Example 2. Subtract $\frac$ from $\frac$.

Solution:

Multiples of 8: 8, 16, 24, 32

Multiples of 6: 6, 12, 18, 24,

So, the LCM is 24.

Now, we convert the fractions into a denominator with the LCM.

$\frac = \frac \times \frac = \frac$

$\frac = \frac \times \frac = \frac$

$\frac$ $$\frac = \frac$$ $\frac$

$= \frac$

Recommended Reading: What Branch Of Science Does Physics Belong

## Definition Of Fraction In Maths

In Maths, a fraction is used to represent the portion/part of the whole thing. It represents the equal parts of the whole. A fraction has two parts, namely numerator and denominator. The number on the top is called the numerator, and the number on the bottom is called the denominator. The numerator defines the number of equal parts taken, whereas the denominator defines the total number of equal parts in a whole.

For example, 5/10 is a fraction.

Here, 5 is a numerator and 10 is a denominator.

## How To Convert Fractions To Decimals

How to Find the Mean of Fractions

As we already learned enough about fractions, which are part of a whole. The decimals are the numbers expressed in a decimal form which represents fractions, after division.

For example, Fraction 1/2 can be written in decimal form as 0.5.

The best part of decimals are they can be easily used for any arithmetic operations such as addition, subtraction, etc. Whereas it is difficult sometimes to perform operations on fractions. Let us take an example to understand

solution: 1/6 = 0.17 and 1/4 = 0.25

Hence, on adding 0.17 and 0.25, we get

0.17 + 0.25 = 0.42

You May Like: What Is Vf In Physics

## Adding Fractions With Different Denominators

If the denominators of the two fractions are different, we have to simplify them by finding the LCM of denominators and then making it common for both fractions.

Example: + ¾

The two denominators are 3 and 4

Hence, LCM of 3 and 4 = 12

Therefore, multiplying by 4/4 and ¾ by 3/3, we get

8/12 + 9/12

= 17/12

## What Is Proper Fraction And Example

Fraction is a unit of measurement that is used to describe how many of something there are in a given area. An example of a fraction is 1/3. There are three parts in a whole, sharecroppers would say. One part is the land, one part is the labor, and one part is the food. A fraction is a way of measuring these parts.

Don’t Miss: Holt Algebra 2 Lesson 6 2 Multiplying Polynomials

## The Basics Of Fractions

What exactly is a fraction, anyway? Have you ever dealt with fractions in either your schooling or your work? Well, a fraction is a part of a whole.

Say you ordered a pizza and there were a total of 8 slices. You were hungry that day and you had 5 of them, therefore eating 5 out of the 8 slices. That can be represented as a fraction.

## How To Simplify Fractions

To simplify the fractions easily, first, write the factors of both numerator and denominator. Then find the largest factor that is common for both numerator and denominator. Then divide both the numerator and the denominator by the greatest common factor to get the reduced fraction, which is the simplest form of the given fraction. Now, let us consider an example to find the simplest fraction for the given fraction.

For example, take the fraction, 16/48

So, the factors of 16 are 1, 2, 4, 8, 16.

Similarly, the factors of 48 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 48.

Thus, the greatest common factor for 16 and 48 is 16.

i.e. GCF = 16.

Now, divide both the numerator and denominator of the given fraction by 16, we get

16/48 = / = 1/3.

Hence, the simplest form of the fraction 16/48 is 1/3.

Don’t Miss: What Is Tfr In Human Geography

## Fraction: Relationship Between The Part And The Whole

Its the simplest interpretation and its obvious to children its the use of a fraction to refer to a part of a whole:

Its a common interpretation and thus, its usually the starting point for teaching sequences but it raises a problem when improper fractions are introduced: How am I going to take more pieces than whats there?.

But at the same time, its very representative. It relates a lot to real-life elements and situations and is relevant for children which makes modeling easy. Modeling is very important in the first levels of didactic sequencing for understanding what is being done and modeled.

## Proper And Improper Fractions

Common fractions can be classified as either proper or improper. When the numerator and the denominator are both positive, the fraction is called proper if the numerator is less than the denominator, and improper otherwise. The concept of an “improper fraction” is a late development, with the terminology deriving from the fact that “fraction” means “a piece”, so a proper fraction must be less than 1. This was explained in the 17th century textbook The Ground of Arts.

In general, a common fraction is said to be a proper fraction, if the absolute value of the fraction is strictly less than onethat is, if the fraction is greater than 1 and less than 1. It is said to be an improper fraction, or sometimes top-heavy fraction, if the absolute value of the fraction is greater than or equal to 1. Examples of proper fractions are 2/3, 3/4, and 4/9, whereas examples of improper fractions are 9/4, 4/3, and 3/3.

Recommended Reading: Infinite Algebra 1 Multi Step Inequalities

## Formal Definition Of Fractions

Fractions may be represented as ordered pairs of integers $$, b\ne 0, for which an equivalence relation has been specified , namely, it is considered that  =  if ad = bc. The operations of addition, subtraction, multiplication, and division are defined in this set of fractions by the following rules:$$\pm = ,\cdot = ,: = ,.

A similar definition of fractions is convenient in generalizations and is accepted in modern algebra .

## How To Multiply Fractions With Whole Numbers

Fractions as powers – what do they mean?

In order to multiply fractions with whole numbers, we write the whole number in the fraction form by placing 1 in the denominator and then we follow the usual procedure of multiplication of fractions. For example, let us multiply 5/8 Ã 3. Here 3 is a whole number and we will write it as 3/1. Now, let us multiply 5/8 Ã 3/1 = 15/8 = \

Don’t Miss: Pre Algebra Games Online For 8th Grade

## Proper Fractions And Improper Fractions

A proper fraction is one where the numerator is smaller than the denominator. It is what we normally think of as a fraction.

Remember that the numerator tells us the number of parts we want while the denominator tells us the total number of parts that the whole number is divided into.

Whole numbers can also be written as a fraction. For example, 4/4 means 4 out of 4 which is the same as 1 whole.

An improper fraction is one where the numerator is bigger than the denominator. This happens when we include the whole number from a mixed fraction into a fraction.

See the examples below.

An easy way to remember how to change a whole number into an improper fraction is to multiply the whole number by the denominator.

## What Is 3/4 As A Whole Number

3/4 as a whole number is a number that is three fourths of a whole number. This number is used to represent numbers that are larger than one but smaller than four. For example, if you have the number 12 and want to represent it as a whole number, you would divide 12 by 4 to get 3/4 as a whole number.

## It Also Means ‘divide’

Sometimes, a fraction is just another way of saying ‘divide’. For example is simply a way of saying ‘two divided by seven’.This is the same as writing

This happens a lot in algebra, when we divide whole expressions by something. For examplewhich comes out to

The top and/or bottom can both be algebra expressions. For example

## How To Add Fractions With Different Denominators

In order to add fractions with different denominators, we need to use the following steps. Let us add the fractions 4/5 + 6/7

• Step 1: Since the denominators in the given fractions are different, we will find the LCM of 5 and 7 to make them the same. LCM of 5 and 7 = 35.
• Step 2: After this step, we will multiply 4/5 with 7/7, that is, Ã = 28/35, and 6/7 with 5/5, Ã = 30/35. This step converts them to like fractions that have the same denominators.
• Step 3: Now, the denominators are the same, so we can add the numerators and keep the common denominator. The new fractions with common denominators are 28/35 and 30/35. So, 28/35 + 30/35 = /35 = 58/35 = \.

Don’t Miss: What Are Conjugates In Math

## Examples Of Numerator In A Sentence

numeratornumerator Forbesnumerator Forbesnumerator Fortunenumerator The New YorkernumeratorQuanta MagazinenumeratorScientific AmericannumeratorForbesnumerator San Diego Union-Tribune

These example sentences are selected automatically from various online news sources to reflect current usage of the word ‘numerator.’ Views expressed in the examples do not represent the opinion of Merriam-Webster or its editors. Send us feedback.

## What Does Fraction Mean In Math

Fraction is a mathematical term that is used to describe how many of one thing there are in a given number. In general, a number is considered fractional if it has a fractional component.

In math, fractions are everything. Theyre the building blocks of math and they help us understand how things work. For example, if you divide a number by two, you get a number that is half of the original number. If you divide a number by three, you get a number that is three times the original number.

In addition, fractions are a way to divide things up evenly. For example, if you have a number like 2 and 5, you can divide them by two to get 2/5 and 2/10, and so on. This is a great way to divide things up evenly, because it keeps things simple.

You May Like: Is There Math On The Real Estate Exam

## What Is A Unit Fraction

In math, a unit fraction can be defined as a fraction whose numerator is 1. It represents 1 shaded part of all the equal parts of the whole. The term unit means one.

For instance, if a pizza is divided into 4 equal portions and one person is eating one portion of it, it can be numerically represented as 1/4.

If a whole is divided into three equal parts, each part is represented by the fraction 1/3, written as one-third of the whole.

Similarly, if a whole is divided into four or five equal parts, each part is represented by the fraction 1/4 or 1/5, written as one-fourth or one-fifth of the whole.

## How Do You Simplify Fractions

How to Find the Mean | Math with Mr. J

In order to simplify a fraction, we first write down the factors for the numerator and the denominator. Then, determine the largest factor that is common between the two and divide the numerator and denominator by the Greatest Common Factor . The reduced fraction that we get is the simplest form of the given fraction. For example, in order to simplify 36/45, we will find the GCF of 36 and 45. The GCF of 36 and 45 = 9. Now, we will divide the numerator and the denominator by 9, that is, / = 4/5

Also Check: What Is Earthquake In Geography

## What Does Fraction Mean

A fraction is any part separated or distinct from its whole, as in After the party, just a fraction of the large cake was left.

A fraction can also be a very small part of a whole, as in We only understand a fraction of how the human mind works.

In mathematics, fraction is a number that is expressed as a proportion, as 1/2 or 2/3. The number on the bottom represents the total number of parts of one unit, while the number on the top is the portion of the unit being considered. For example, in 1/2 the 2 represents two halves of one whole and the 1 represents the amount of parts being observed, in this case one.

To fraction means to divide into sections or fractions, as in Politics often fractions people into self-interested groups.

Example: That announcement is only a fraction of whats in store tonight.