Fraction Calculator

What is Fraction?

Fraction shows how many equal part of a whole and total amount. A fraction is a part of a whole. It represents one or more equal parts of a whole object.

Example: \( \frac{1}{4} \)

Here 1 is a numerator; shows how many of the total equal parts. 4 is the denominator; shows how many total equal parts are in the whole. \( \frac{1}{4} \) is fraction bar or division bar.

Pictorial Representation:

Fraction can have different values depending on a size or amount of the whole. When the numerator and denominator are same number, the fraction will have the same 1, or the whole.
A fraction is also a part of a set.

Three fourth \( \frac{3}{4} \) of the boxes are filled.

Types of Fractions

1- Proper fraction
2- Improper fraction
3- Mixed fraction

Proper Fraction: A fraction in which the numerator is less than the denominator is called proper fraction. For example, \( \frac{2}{8} \) here \( 2 < 8 \)

Improper Fraction: A fraction in which the numerator is greater than or equal to the denominator is called an improper fraction. For example, \( \frac{5}{3} \) here \( 5 > 3 \) and \( \frac{4}{4} \) here \( 4 = 4 \)

Mixed Fraction: A mixed fraction is a sum of a natural number and a proper fraction. For example, \( 1 + 1 + \frac{1}{2} => 2 + \frac{1}{2} => 2\frac{1}{2} \)

Unit Fraction

A fraction which has 1 as the numerator is a unit fraction.
Example: \( \frac{2}{3} \), \( \frac{1}{7} \), \( \frac{1}{12} \)

Like and unlike fraction

“Like and unlike fraction depend on denominator”

Like fraction:
Fractions with the same denominators are called like fractions. For example, \( \frac{1}{4} \), \( \frac{3}{4} \)

Unlike fraction:
Fractions with different denominators. For example, \( \frac{5}{8} \), \( \frac{5}{3} \), \( \frac{2}{7} \)

Importance of fraction / Why are fractions important?

Fractions are important because on the basis of it, we can assess what portion of a whole we required, there are few fields where fraction play vital role.
1- Medical field
2- Cooking(measuring ingredients in recipes)
3- Research
4- Statistics(probability)
5- Data representation in mathematics
6- Property division
7- Understanding of an equation( in understanding of an equations in order to proper understanding of equation, we first have a grip on fraction)
\(F = \frac{G m_1 m_2}{r^2} \)
\(K.E = \frac{1}{2}mv^2 \)
\(V = \frac{4}{3}πr^3\)
\(A = \frac{1}{2}bh\)
8- Petrol pumps (rates, like 249 \(\frac{9}{10}\) or RS 148 \(\frac{9}{10}\))
9- Price list
10- Time (8:45 also means quarter to nine)

A general example

Q: if a pizza has 8 pieces in it and you give 1 piece away, how many pieces of pizza do you have left?
Answer: let’s make this into a fraction if a fraction is written as \( \frac{a}{b} \), then this would be written as \( \frac{7}{8} \) in fraction.

Comparing fraction

Q: Which fraction is greater? \( \frac{2}{5} \) or \( \frac{6}{5} \)
Solution: As denominator is same so compare only numerator. Therefore; \( \frac{2}{5} < \frac{6}{5} \)

Q: Which fraction is greater? \( \frac{5}{6} \) or \( \frac{5}{7} \)
Solution: As denominators are different if numerator are same then lesser denominator fraction is the greater one. Therefore; \( \frac{5}{6} > \frac{5}{7} \) as \( 0.83 > 0.7 \)

Q: Which fraction is greater? \( \frac{3}{4} \) or \( \frac{2}{3} \)

Solution: Numerator and denominator are not same, so follow these methods:

(a) Convert each fraction into decimal.

(b) Comparing denominator and then numerator.

(c) Cross multiply

So, \(\frac{3}{4}\), \(\frac{2}{3}\) means \(9 > 8\) hence, \(\frac{3}{4} > \frac{2}{3}\)

Let’s verify the solution \(\frac{3}{4} > \frac{2}{3}\), its fraction values will be \(0.75 > 0.56\)

Q: Which fraction is greater? \( \frac{4}{9} \) or \( \frac{5}{7} \)

So, \(\frac{4}{9}\), \(\frac{5}{7}\) means \(28 < 45\) hence, \(\frac{4}{9} < \frac{5}{7}\)

Let’s verify the solution \(\frac{4}{9} < \frac{5}{7} => \frac{4 × 7}{9 × 7} < \frac{5 × 9}{7 × 9} => \frac{28}{63} < \frac{45}{63}\)

Fraction Tricks

Let’s take example of \(\frac{4}{5}\), \(\frac{2}{3}\), \(\frac{5}{6}\)

Solution:

Let’s take LCM of all denominator 5, 3, 6:

Now \(2 × 3 × 5 = 30\), make all denominator to 30 by multiplying any number to both numerator and denominator.

\(\dfrac{4 × 6}{5 × 6}\), \(\dfrac{2 × 10}{3 × 10}\), \(\dfrac{5 × 5}{6 × 5}\)

\(\dfrac{24}{30}\), \(\dfrac{20}{30}\), \(\dfrac{25}{30}\)

\(\dfrac{20}{30} < \dfrac{24}{30} < \dfrac{25}{30}\) Here all denominator are same now we can consider numerator only.
Hence, \(\dfrac{2}{3} < \dfrac{4}{5} < \dfrac{5}{6}\)

Changing an improper fraction into a mixed number

Convert \(\frac{9}{2}\) into a mixed number

Solution:

\(Mixed number = quotient + \dfrac{remainder}{division}\)

Its mean, \(\frac{9}{2} = 4\frac{1}{2}\)

Changing a mixed number into an improper fraction

Q: Convert \(5\frac{3}{9}\) into an improper fraction.

Solution:

\(\frac{(Natural Number × Denominator) + Numerator}{Denominator} => \frac{(5 × 9) + 3}{9} => \frac{45 + 3}{9} => \frac{48}{9} \)

FAQS