12 As An Improper Fraction

Improper Fractions

Fractions were first used in Ancient Arab republic of egypt around 1600 BC, which makes the concept quite erstwhile. Fractions are of dissimilar types. When the numerator is smaller than the denominator i.eastward. i/2, information technology is a proper fraction. All the same, when the denominator is smaller than or equal to the numerator, then it is an improper fraction. An example of this is sixteen/15.

An improper fraction is one type of fraction in which the numerator is equal to or greater than the denominator. Its value is e'er i or greater than one. Improper fractions are unremarkably written in mixed number class in a simplified fashion, as mixed fractions are easier to cover.

i.	What is an Improper Fraction?
2.	Improper Fraction and Mixed Fraction
3.	Converting Improper Fractions to Decimals
iv.	Converting Improper Fraction to Mixed Numbers
5.	How to Solve Improper Fractions?
6.	FAQs on Improper Fractions

What is an Improper Fraction?

An improper fraction is a type of fraction where the numerator is greater than or equal to the denominator. For instance, 5/2 and 8/5, are improper fractions. Every fraction has two parts, numerator, and denominator. In mathematics, there are 2 principal types of fractions based on the values of numerator and denominator, and those are proper fractions and improper fractions.

Improper Fraction Definition

A fraction whose numerator is greater than or larger than the denominator is defined equally an improper fraction such as 7/iii and 12/5. Improper fractions are easier to solve using addition and subtraction compared to the blazon of fractions such as mixed fractions.

Improper Fraction and Mixed Fraction

An improper fraction is a fraction whose numerator is greater than or equal to its denominator. For example, 9/4, 4/3 are improper fractions. Numerically, they are ever equal to or greater than 1. On the other hand, a mixed fraction is a fraction that is written every bit a combination of a natural number and a proper fraction. It is a simplified form of an improper fraction. For example, \( 21\dfrac{4}{v}, sixteen\dfrac{2}{3}\) are mixed fractions. Numerically, a mixed fraction is always greater than 1. Also, any mixed fraction can be written equally an improper fraction.

Generally, in existent life, mixed fractions are easier to interpret and compare, as compared to improper fractions. Nosotros can easily convert any improper fraction to a mixed number or mixed fraction to an improper fraction by following some basic steps that you will study in later on sections on this page.

Converting Improper Fractions to Decimals

Fractions and decimals are ii ways to stand for numbers. Improper fractions can exist converted to decimals easily by dividing the numerator with the denominator. Let's look at a quick and easy example of how we tin can convert improper fractions to decimals. Allow's consider the post-obit case.

Example: Convert the given improper fraction to a decimal: 10/4.

The first step is to divide 10 past 4. When nosotros do and so, we will get 10 ÷ 4 = 2.5.

Converting Improper Fraction to Decimal

Hither, x/4 is an improper fraction and two.5 is a decimal. Similarly, the value of 3/ii is 1.5 in decimals and 5/2 is 2.v in decimals. When we convert an improper fraction to a decimal, the decimal value is ever greater than 1.

Converting Improper Fractions to Mixed Numbers

The denominator of the mixed fraction form of an improper fraction is always the same as that of the original fraction. Mixed numbers are considered as the simplified class of improper fractions, that is why information technology is of import to learn this conversion. For converting an improper fraction to a mixed number, we have to follow the below-listed steps:

Step i- Carve up the numerator with the denominator.
Step 2- You lot volition get values of caliber and balance.
Footstep 3- Arrange those values of the quotient, remainder, and divisor in the following fashion to express a fraction as a mixed number: \(Caliber\dfrac{Remainder}{Divisor}\).

Allow's look at a quick and easy example of how nosotros tin catechumen improper fractions to mixed numbers. Allow'due south say you lot have an improper fraction, 13/4. The get-go step is to divide thirteen by iv. We get iii as the quotient with a rest of 1. Next, nosotros will place 1 as the numerator, 4 equally the denominator, and 3 as the whole number. Thus, we get the mixed fraction: \( 3\dfrac{1}{iv}\).

Converting Improper Fractions to Mixed Numbers

Similarly, let's solve some other example. Here, we have an improper fraction: 9/2. On dividing 9 by 2, we get four as the caliber with a remainder of i. Again, we will repeat the same procedure. We will place ane as the numerator, 2 as the denominator, and iv equally the whole number. Thus, nosotros get the mixed fraction: \(4\dfrac{1}{two}\).

How to Solve Improper Fractions?

Solving improper fractions mean performing arithmetics operations on them and simplifying the value of the answer so obtained. There are mainly 4 arithmetic operators in mathematics and those are addition, subtraction, multiplication, and division. Solving an improper fraction is the same equally solving whatever other proper fraction, the only difference is that, here, we accept to simplify the answer and write it in mixed numbers.

Let'due south solve the improper fraction: 4/3 + seven/3.

Step 1: We have the same denominator for both the fractions. Therefore, we will straight add the numerators 4 and vii. We go 11. Thus, on calculation improper fractions, we become xi/3.

Footstep 2: Simplifying the improper fraction (dividing 11 by iii), we volition get 3 as a whole, two equally a numerator, and 3 equally the denominator.

The reply is \(iii\dfrac{2}{iii}\).

Related Articles on Improper Fractions

Cheque the following topics related to the concept of improper fractions.

Improper Fraction to Mixed Number
Mixed Number to Improper Fraction
Improper Fraction to Mixed Number Calculator
Types of Fractions

Improper Fraction Examples

Example i: Place improper fractions out of the following: 12/5, 3, i/9, iv/2, 4/5.

Solution:

Improper fractions are the ones in which the numerator is either equal to or greater than the denominator. Out of the given fractions, 12/v, 3, and 4/ii are improper fractions. As, in 12/v, 12 > 5, 3 can be written as three/1 where 3 > 1, and 4/two can be simplified every bit ii/1 where ii > ane.
Example 2: There are v-fourth liters of plainly milk in the refrigerator. Convert the given quantity into a mixed number.

Solution:

To convert the given improper fraction 5/four to a mixed number, we have to split 5 by 4. By dividing, we will get 1 as the quotient, and 1 equally the remainder. Therefore, the answer is \(i\dfrac{1}{iv}\).
Example 3: What is four one/iii as an improper fraction?

Solution:

To convert the given mixed number to an improper fraction, we have to first multiply the denominator and the whole number and so we need to add together the numerator to the sum.
⇒ \(4\dfrac{i}{3}\) = (4 × 3 + 1)/three
⇒ (12 + 1)/3
⇒ 13/3
Therefore, \(four\dfrac{1}{3}\) is equivalent to 13/three.

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Practice Questions on Improper Fractions

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FAQs on Improper Fractions

What is an Improper Fraction?

Fractions in which the numerator is equal to or less than the denominator are known as improper fractions in math. 3/2, 6/5, 18/eleven are a few examples of improper fractions.

What is Proper Fraction and Improper Fraction?

Proper fractions are those in which the numerator is less than the denominator, while improper fractions are opposite of proper fractions where numerator ≥ denominator.

Are Whole Numbers Examples of Improper Fraction?

Yes, whole numbers are examples of improper fractions, every bit we tin write any whole number in the form of a fraction in which the numerator is greater than the denominator. For instance, 3= 3/i, 5= v/1, etc.

How can we Add Improper Fractions?

The improver of ii like improper fractions is done by adding the values of their numerator and writing the common denominator as the denominator of the sum obtained. While, in the example of two unlike improper fractions, we offset take the LCM of the denominators and catechumen them into similar fractions. So, we add those 2 fractions. Let's take an example of improver of improper fractions v/4 and 7/4.

Footstep 1: We have the same denominator in these fractions v/iv + 7/4. Therefore, we will simply add the numerators 5 and 7. We get 12 equally the sum. Thus, on adding, we take 12/4.
Step two: By simplifying the improper fraction (dividing 12 past four), nosotros go 3 as the answer.

How do we Simplify an Improper Fraction?

Simplification of improper fractions means finding the lowest value of the fraction past dividing the numerator with the denominator. Let us accept an example to understand how to simplify an improper fraction. Consider the fraction 100/5. Past dividing 100 past 5, we get 20 as the answer. Thus, 100/5 = 20 in the simplified form.

How to Subtract Improper Fractions?

Subtraction of two like improper fractions is done by subtracting the values of their numerator and writing the common denominator as the denominator of the difference obtained. While, in the case of two unlike improper fractions, we first take the LCM of the denominators and convert them into like fractions. Then, we decrease those two fractions.

How to Convert Improper Fraction to Mixed Numbers?

Improper fractions are converted to mixed numbers by dividing the numerator with the denominator and write the respond in this form: \(Quotient\dfrac{Remainder}{Divisor}\).

How to Multiply Improper Fractions?

The numerator and denominator of an improper fraction are multiplied with the numerator and denominator of the other fraction to find the product. After multiplying, nosotros simplify the fraction so obtained. In this mode, nosotros multiply ii improper fractions.