Class 6 Chapter 7 Fractions Math Formulas

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Proper Fraction:-

Proper Fraction is the fraction what is less than 1 or where Numerator is less than Denominator.


For Example:- \frac{2}{3}


Improper Fraction:-

Improper Fraction is the fraction which is greater than 1 or where Numerator is greater than Denominator.


For Example:-\frac{7}{8}



Mixed Fraction:-

It is combination of whole number and a proper fraction.


For example:-4\frac{2}{3}, 3\frac{3}{5}



Converting mixed fraction to improper fraction:-

Formula for converting mixed fraction into proper fraction is:

\frac{Whole number \times Denominator + Numerator}{Denominator}


For Example:-
4\frac{2}{3} = \frac{4 \times 3 + 2}{3}


Converting improper fraction to mixed fraction:-

Use the quotient as the whole number.

Use the remainder as the numerator of the proper fraction.

The denominator will stay the same.


For Example:-

Convert  \frac{5}{4} to mixed Number

4 5

Hence the required mixed number is 1\frac{1}{4} .



Equivalent Fraction:-

Equivalent fractions are fractions that have the same value in its simplest form.


For example:-
\frac{1}{2}, \frac{2}{4}, \frac{3}{6}, \frac{4}{8}

Each one has same value\frac{1}{2} .


Like Fractions:-

Fractions having same denominators


Unlike Fractions:-

Fractions with different denominators


Comparing Like fraction:-

Numerator will decide the largest value.


For Example:-
\frac{4}{6} > \frac{2}{6}


Comparing Unlike fraction:-

Fractions having same numerator, the fraction with the lowest denominator is the greater number.


For Example:-

\frac{2}{5} and \frac{2}{6}  here \frac{5}{6}

So, \frac{2}{5} is grater than \frac{2}{6}.


Comparing fractions with different denominator and numerator:-

We need to convert each of the fractions into equivalent fraction such that they become like fractions. There are three steps

1 .Find the LCM of the denominators.
2. Convert each fraction into equivalent fraction such that denominator is the LCM.
3. Now both the fraction are converted into like fraction, so we can do the comparison easily


Adding Like Fraction:-

Keep the same value of denominator and add the value of numerator


For Example:-
\frac{1}{5} + \frac{2}{5} = \frac{3}{5}


Adding unlike fraction:-

First we need to convert the unlike fraction to like fraction using the LCM of the denominators. Then we can add the numerators and write the denominator same.


For example:-
\frac{1}{2} + \frac{2}{3} = \frac{1 \times 3 + 2 \times 2 }{6}[\latex]
=\frac{3 + 4}{6}[\latex]