- Multiply 0.2 with 10 it becomes 2 and divide by 10. Now it becomes `2/10` which is a proper fraction. This proper fraction can be simplified to least form. Problem Solution 0.2 =`(0.2.10) / 10` = `2/10` simplify by 2 on both numerator and denominator = `1/5` Practice problem 1. What is 0.7 in fraction form 2. What is 1.2 in fraction form 3.
- Convert decimal to fraction or fraction to decimal with the use of Digi-Key's conversion calculator. Additional calculators available at Digi-Key.
- Convert decimal to fraction or fraction to decimal with the use of Digi-Key's conversion calculator. Additional calculators available at Digi-Key.
Use calculator to divide the fraction's numerator by the denominator. For mixed numbers add the integer. 2/5 = 2 ÷ 5 = 0.4. 1 2/5 = 1 + 2 ÷ 5 = 1.4. Use long division to divide the fraction's numerator by the fraction's denominator. Calculate 3/4 by long division of 3 divided by 4.
What is a fraction?
In mathematics fraction is defined as a part of a certain whole. For instance when using one half (1/2) or three-quarters (3/4) you are actually using them.
A fraction contains an integer numerator which is positioned above the line (or on the left side of a slash) and a non-zero integer denominator positioned below the line. For instance 1/2 consists of the numerator 1 that indicates the fact that in this case is a single equal part and of the denominator 2 that indicates the facts that in this case the whole is made of 2 equal parts.
As the form of the fraction is now clear we should refer a bit to the set of rational numbers represented in mathematics by Q. This is the set of all numbers that can be written in the form of a fraction (numerator/denominator), more specifically as x/y with two condition that x and y are integer numbers AND that y is a non zero number. If one number can be written in this form then it is called a rational number.
Example of numbers and how can they be expressed as fractions:
■ For instance when you are referring to a decimal number such as 0.05, this is as fractional number even though you do not see its numerator and denominator as it can easily be written as 5/100.
■ For example when you are using a percentage such as 10%, this can be written as fraction too since any percentage is made of a numerator (in this case the numerator is 10) and a denominator which always 100; which in our case means that the fraction is 10/100.
■ Even when speaking about integer numbers such as 10, they can be expressed as fraction since every integer number has 1 as denominator, which means 10/1 = 10. Tuneskit screen recorder 1 0 16.
■ When you are using negative exponents numbers they can also be written as fractions. Let’s take the following negative exponent 10−2 that equals to 1/100.
![Videoscan 1 0 2 Fraction Videoscan 1 0 2 Fraction](https://1.bp.blogspot.com/-yxaXolrP2cc/WlOz-ffiKAI/AAAAAAAAam4/Bse5yQ-0YbgAj4fA8MkiFSGKsOVTv00jQCLcBGAs/s1600/Colorful%2BFractions%2BCircle1.jpg)
■ When you are referring to division such as 2 ÷ 5 this is actually a fraction as it is equal to 2/5.
■ Also when you use ratios such as ratio 5:6 this is actually the same with 5/6 which is a fraction.
How to multiply fractions?
Even though our fraction calculator allows you perform this calculation let’s answer on how to multiply fractions.
■ How to multiply a fraction by another fraction?
In order to multiply a fraction by another you have to multiply their numerators and multiply their denominators as shown in this example:
■ How to multiply a fraction by a whole number?
In case you have to multiply a whole number with a fraction you need to consider that the integer number can be written as a fraction having the denominator 1, and then simply multiply two fractions by following the rule explained above. For instance:
■ How to multiply mixed numbers?
In order to multiply mixed numbers the best way to do it is by converting the mixed number into a common fraction and then perform the calculation by following the standard multiplication rule. For instance:
- In case of a multiplication between an integer number and a mixed number:
- In case of a multiplication between a simple fraction and a mixed number you only have to convert the mixed number into a common fraction and then apply the standard multiplication rule. For instance:
How to add fractions?
The basic rule on how to add fractions says that you can perform an addition only if the denominator of the two fractions is the same. That is why you first have to ensure that both fractions get the same denominator, which means when they have different denominator you should see which is the closest common denominator and convert them.
■ How to add fractions having different denominators?
In order to add fractions containing different denominators you need to convert both fractions to the same denominator and the simplest way to do this is to multiply together the two denominators (bottom number). For instance:
■ How to add an integer number to a fraction?
To add an integer number to a fraction you have to first express the given number as a fraction and then convert it in a fraction having the same denominator as the one you need to add to. For instance:
How to subtract fractions?
The steps to follow in case of a subtraction between two fractions are similar to the ones as in case of an addition, which means you can subtract fraction only if they have the same denominator. This way the fraction that is obtained after subtraction will have that denominator while its numerator will be the result of subtracting the numerators of the initial fractions.
■ How to subtract fractions having different denominators?
In order to subtract fractions having different denominators you need to convert both of them to the same denominator and the simplest way to do this is to multiply together the two denominators (bottom number). For instance:
■ How to subtract an integer number from a fraction?
To subtract an integer number from a fraction you have to first write the given number as a fraction and then convert it in a one having the same denominator as the one you need to subtract from. For example:
How to divide fractions?
■ How to divide a fraction by a whole number?
In order to this calculation there are two approaches: you either choose to divide the numerator by the number only if the given value goes evenly into the numerator (a), or multiply the denominator by the given number (b). For example:
a)
b)
■ How to divide a number by a fraction?
In this case the solution is to multiply that number by the reciprocal of the given fraction, for example:
22 Feb, 2015 Learning Outcomes
- Write fractions that represent portions of objects
- Use fraction circles to make wholes given
- Use models to visualize improper fractions and mixed numbers.
Representing Parts of a Whole as Fractions
Andy and Bobby love pizza. On Monday night, they share a pizza equally. How much of the pizza does each one get? Are you thinking that each boy gets half of the pizza? That’s right. There is one whole pizza, evenly divided into two parts, so each boy gets one of the two equal parts.
In math, we write [latex]frac{1}{2}[/latex] to mean one out of two parts.
In math, we write [latex]frac{1}{2}[/latex] to mean one out of two parts.
On Tuesday, Andy and Bobby share a pizza with their parents, Fred and Christy, with each person getting an equal amount of the whole pizza. How much of the pizza does each person get? There is one whole pizza, divided evenly into four equal parts. Each person has one of the four equal parts, so each has [latex]frac{1}{4}[/latex] of the pizza.
On Wednesday, the family invites some friends over for a pizza dinner. There are a total of [latex]12[/latex] people. If they share the pizza equally, each person would get [latex]frac{1}{12}[/latex] of the pizza.
Fractions
A fraction is written [latex]frac{a}{b}[/latex], where [latex]a[/latex] and [latex]b[/latex] are integers and [latex]bne 0[/latex]. In a fraction, [latex]a[/latex] is called the numerator and [latex]b[/latex] is called the denominator.
A fraction is a way to represent parts of a whole. The denominator [latex]b[/latex] represents the number of equal parts the whole has been divided into, and the numerator [latex]a[/latex] represents how many parts are included. The denominator, [latex]b[/latex], cannot equal zero because division by zero is undefined.
In the image below, the circle has been divided into three parts of equal size. Each part represents [latex]frac{1}{3}[/latex] of the circle. This type of model is called a fraction circle. Other shapes, such as rectangles, can also be used to model fractions. Things 2 8 8 – elegant personal task management.
In the image below, the circle has been divided into three parts of equal size. Each part represents [latex]frac{1}{3}[/latex] of the circle. This type of model is called a fraction circle. Other shapes, such as rectangles, can also be used to model fractions. Things 2 8 8 – elegant personal task management.
Doing the Manipulative Mathematics activity Model Fractions will help you develop a better understanding of fractions, their numerators and denominators.
What does the fraction [latex]frac{2}{3}[/latex] represent? The fraction [latex]frac{2}{3}[/latex] means two of three equal parts.
Example
Name the fraction of the shape that is shaded in each of the figures.
Solution:
We need to ask two questions. First, how many equal parts are there? This will be the denominator. Second, of these equal parts, how many are shaded? This will be the numerator.
We need to ask two questions. First, how many equal parts are there? This will be the denominator. Second, of these equal parts, how many are shaded? This will be the numerator.
[latex]begin{array}{cccc}text{How many equal parts are there?}hfill & & & text{There are eight equal parts}text{.}hfill text{How many are shaded?}hfill & & & text{Five parts are shaded}text{.}hfill end{array}[/latex]
Five out of eight parts are shaded. Therefore, the fraction of the circle that is shaded is [latex]frac{5}{8}[/latex].
Five out of eight parts are shaded. Therefore, the fraction of the circle that is shaded is [latex]frac{5}{8}[/latex].
[latex]begin{array}{cccc}text{How many equal parts are there?}hfill & & & text{There are nine equal parts}text{.}hfill text{How many are shaded?}hfill & & & text{Two parts are shaded}text{.}hfill end{array}[/latex]
Two out of nine parts are shaded. Therefore, the fraction of the square that is shaded is [latex]frac{2}{9}[/latex].
Two out of nine parts are shaded. Therefore, the fraction of the square that is shaded is [latex]frac{2}{9}[/latex].
Example
Shade [latex]frac{3}{4}[/latex] of the circle.
Show SolutionSolution
The denominator is [latex]4[/latex], so we divide the circle into four equal parts ⓐ.
The numerator is [latex]3[/latex], so we shade three of the four parts ⓑ.
The denominator is [latex]4[/latex], so we divide the circle into four equal parts ⓐ.
The numerator is [latex]3[/latex], so we shade three of the four parts ⓑ.
[latex]frac{3}{4}[/latex] of the circle is shaded.
Try it
Shade [latex]frac{6}{8}[/latex] of the circle.
Show Solution
Shade [latex]frac{2}{5}[/latex] of the rectangle.
Show Solution
Watch the following video to see more examples of how to write fractions given a model.
In earlier examples, we used circles and rectangles to model fractions. Fractions can also be modeled as manipulatives called fraction tiles, as shown in the image below. Here, the whole is modeled as one long, undivided rectangular tile. Beneath it are tiles of equal length divided into different numbers of equally sized parts.
We’ll be using fraction tiles to discover some basic facts about fractions. Refer to the fraction tiles above to answer the following questions:
How many [latex]frac{1}{2}[/latex] tiles does it take to make one whole tile? | It takes two halves to make a whole, so two out of two is [latex]frac{2}{2}=1[/latex]. |
How many [latex]frac{1}{3}[/latex] tiles does it take to make one whole tile? | It takes three thirds, so three out of three is [latex]frac{3}{3}=1[/latex]. |
How many [latex]frac{1}{4}[/latex] tiles does it take to make one whole tile? | It takes four fourths, so four out of four is [latex]frac{4}{4}=1[/latex]. |
How many [latex]frac{1}{6}[/latex] tiles does it take to make one whole tile? | It takes six sixths, so six out of six is [latex]frac{6}{6}=1[/latex]. |
What if the whole were divided into [latex]24[/latex] equal parts? (We have not shown fraction tiles to represent this, but try to visualize it in your mind.) How many [latex]frac{1}{24}[/latex] tiles does it take to make one whole tile? | It takes [latex]24[/latex] twenty-fourths, so [latex]frac{24}{24}=1[/latex]. |
It takes [latex]24[/latex] twenty-fourths, so [latex]frac{24}{24}=1[/latex].
This leads us to the Property of One.
This leads us to the Property of One.
Property of One
Any number, except zero, divided by itself is one.
[latex]frac{a}{a}=1left(ane 0right)[/latex]
Doing the Manipulative Mathematics activity “Fractions Equivalent to One” will help you develop a better understanding of fractions that are equivalent to one
Example
Red giant vfx suite 1 0 38. Use fraction circles to make wholes using the following pieces:
- [latex]4[/latex] fourths
- [latex]5[/latex] fifths
- [latex]6[/latex] sixths
Show Solution
Try it
Use fraction circles to make wholes with the following pieces: [latex]3[/latex] thirds.
Show Solution
Use fraction circles to make wholes with the following pieces: [latex]8[/latex] eighths.
Show Solution
What if we have more fraction pieces than we need for [latex]1[/latex] whole? We’ll look at this in the next example.
Example
Use fraction circles to make wholes using the following pieces:
- [latex]3[/latex] halves
- [latex]8[/latex] fifths
- [latex]7[/latex] thirds
Solution
1. [latex]3[/latex] halves make [latex]1[/latex] whole with [latex]1[/latex] half left over.
1. [latex]3[/latex] halves make [latex]1[/latex] whole with [latex]1[/latex] half left over.
2. [latex]8[/latex] fifths make [latex]1[/latex] whole with [latex]2[/latex] fifths left over.
3. [latex]7[/latex] thirds make [latex]2[/latex] wholes with [latex]2[/latex] thirds left over.
try it
Use fraction circles to make wholes with the following pieces: [latex]5[/latex] thirds.
Show Solution
Use fraction circles to make wholes with the following pieces: [latex]5[/latex] halves.
Show Solution
Model Improper Fractions and Mixed Numbers
In an earlier example, you had eight equal fifth pieces. You used five of them to make one whole, and you had three fifths left over. Let us use fraction notation to show what happened. You had eight pieces, each of them one fifth, [latex]frac{1}{5}[/latex], so altogether you had eight fifths, which we can write as [latex]frac{8}{5}[/latex]. The fraction [latex]frac{8}{5}[/latex] is one whole, [latex]1[/latex], plus three fifths, [latex]frac{3}{5}[/latex], or [latex]1frac{3}{5}[/latex], which is read as one and three-fifths.
The number [latex]1frac{3}{5}[/latex] is called a mixed number. A mixed number consists of a whole number and a fraction.
The number [latex]1frac{3}{5}[/latex] is called a mixed number. A mixed number consists of a whole number and a fraction.
Mixed Numbers
A mixed number consists of a whole number [latex]a[/latex] and a fraction [latex]frac{b}{c}[/latex] where [latex]cne 0[/latex]. It is written as follows.
[latex]afrac{b}{c}text{, }cne 0[/latex]
Fractions such as [latex]frac{5}{4},frac{3}{2},frac{5}{5}[/latex], and [latex]frac{7}{3}[/latex] are called improper fractions. In an improper fraction, the numerator is greater than or equal to the denominator, so its value is greater than or equal to one. When a fraction has a numerator that is smaller than the denominator, it is called a proper fraction, and its value is less than one. Fractions such as [latex]frac{1}{2},frac{3}{7}[/latex], and [latex]frac{11}{18}[/latex] are proper fractions.
Proper and Improper Fractions
The fraction [latex]frac{a}{b}[/latex] is a proper fraction if [latex]a<b[/latex] and an improper fraction if [latex]age b[/latex].
Doing the Manipulative Mathematics activity “Model Improper Fractions” and “Mixed Numbers” will help you develop a better understanding of how to convert between improper fractions and mixed numbers.
Example
Name the improper fraction modeled. Then write the improper fraction as a mixed number.
Solution:
Each circle is divided into three pieces, so each piece is [latex]frac{1}{3}[/latex] of the circle. There are four pieces shaded, so there are four thirds or [latex]frac{4}{3}[/latex]. The figure shows that we also have one whole circle and one third, which is [latex]1frac{1}{3}[/latex]. So, [latex]frac{4}{3}=1frac{1}{3}[/latex].
Each circle is divided into three pieces, so each piece is [latex]frac{1}{3}[/latex] of the circle. There are four pieces shaded, so there are four thirds or [latex]frac{4}{3}[/latex]. The figure shows that we also have one whole circle and one third, which is [latex]1frac{1}{3}[/latex]. So, [latex]frac{4}{3}=1frac{1}{3}[/latex].
Example
Draw a figure to model [latex]frac{11}{8}[/latex].
Show SolutionSolution:
The denominator of the improper fraction is [latex]8[/latex]. Draw a circle divided into eight pieces and shade all of them. This takes care of eight eighths, but we have [latex]11[/latex] eighths. We must shade three of the eight parts of another circle.
The denominator of the improper fraction is [latex]8[/latex]. Draw a circle divided into eight pieces and shade all of them. This takes care of eight eighths, but we have [latex]11[/latex] eighths. We must shade three of the eight parts of another circle.
So, [latex]frac{11}{8}=1frac{3}{8}[/latex].
Try it
Draw a figure to model [latex]frac{7}{6}[/latex].
Show Solution
Draw a figure to model [latex]frac{6}{5}[/latex].
Show Solution
Example
Use a model to rewrite the improper fraction [latex]frac{11}{6}[/latex] as a mixed number.
Show SolutionSolution:
We start with [latex]11[/latex] sixths [latex]left(frac{11}{6}right)[/latex]. We know that six sixths makes one whole.
We start with [latex]11[/latex] sixths [latex]left(frac{11}{6}right)[/latex]. We know that six sixths makes one whole.
[latex]frac{6}{6}=1[/latex]
That leaves us with five more sixths, which is [latex]frac{5}{6}left(11text{sixths minus}6text{sixths is}5text{sixths}right)[/latex].
So, [latex]frac{11}{6}=1frac{5}{6}[/latex].
That leaves us with five more sixths, which is [latex]frac{5}{6}left(11text{sixths minus}6text{sixths is}5text{sixths}right)[/latex].
So, [latex]frac{11}{6}=1frac{5}{6}[/latex].
In the next video we show another way to draw a model that represents a fraction. You will see example of both proper and improper fractions shown.
Example
Use a model to rewrite the mixed number [latex]1frac{4}{5}[/latex] as an improper fraction.
![Fraction Fraction](https://prod-qna-question-images.s3.amazonaws.com/qna-images/question/e79d58fd-86be-4a93-b718-ae8a8475db5d/b5669e56-0b91-4fee-94b4-41a7ade4fe91/fo0k89d_processed.jpeg)
Videoscan 1 0 2 Fraction Calculator
Solution:
The mixed number [latex]1frac{4}{5}[/latex] means one whole plus four fifths. The denominator is [latex]5[/latex], so the whole is [latex]frac{5}{5}[/latex]. Together five fifths and four fifths equals nine fifths.
So, [latex]1frac{4}{5}=frac{9}{5}[/latex].
The mixed number [latex]1frac{4}{5}[/latex] means one whole plus four fifths. The denominator is [latex]5[/latex], so the whole is [latex]frac{5}{5}[/latex]. Together five fifths and four fifths equals nine fifths.
So, [latex]1frac{4}{5}=frac{9}{5}[/latex].