- Fraction
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- Proper Fraction
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- Mixed Fraction
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- Improper Fraction
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- How to convert Mixed Fractions to Improper Fractions
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- How to convert Improper Fractions to Mixed Fraction
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- How to Represent Fraction on Number Line?
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- Comparison, Addition and subtraction of Fraction

$\frac {3}{11}$

3 out of 11 parts

3 -> Called Numerator

11 -> Called Denominator

Example

$\frac {1}{3}$

$\frac {2}{3}$

$\frac {4}{5}

$\frac {1}{3}$

$\frac {2}{3}$

$\frac {4}{5}

$8 \frac {4}{9}$

$\frac {11}{5}$

$\frac {5}{4}$

$\frac {10}{9}$

Step1 |
Obtain the mixed fraction. Let the mixed fraction be 5^{2}/_{6} |

Step 2 |
Identify the whole number and the numerator (top) and denominator (bottom) of the proper fraction. Whole Number=5 Numerator=2 Denominator=6 |

Step 3 |
Apply the formula $\frac {(Whole \times Denominator) + Numerator}{Denominator}$ Example $ 5\frac {2}{6}$ =$\frac {32}{6}$ |

Step 1 |
Obtain the improper fraction. |

Step 2 |
Divide the numerator by the denominator and obtain the quotient and remainder. |

Step 3 |
Write the mixed fraction as $Quotient \frac {Reminder}{denominator}$ |

$\frac {11}{3}$

Here Numerator is greater than denominator, So Improper fraction

Now dividing 11 by 3, we get reminder as 2

So $\frac {11}{3}=3 \frac {2}{3}$

- $\frac {9}{4}$
- $\frac {11}{2}$
- $\frac {37}{18}$
- $\frac {99}{44}$
- $\frac {103}{9}$
- $\frac {17}{3}$

Now, divide the gap between 0 and 1 into two equal parts. The point of division represents 1/2.

To represent 1/4 on a number line, we divide the gap between 0 and 1 into 4 equal parts

First point will represent ½

Second point will represent 2/4 =1/2

Third point will represent 3/4

1) If the numerator and the denominator of a fraction have no common factor except, then it is said to be in its simplest form or lowest form.

$\frac {1}{3}$

$\frac {2}{3}$

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

$\frac {2}{6} \;,\; \frac {1}{3} \;,\; \frac {6}{18}$ are equivalent fractions as they have same value

$\frac {2}{3}$

Equivalent Fraction can be obtained by multiplying both the numerator and the denominator of the given fraction by the same number.

$\frac {2}{3} = \frac {2 \times 3}{{3 \times 3}= \frac {6}{9}$

$\frac {2}{3} = \frac {2 \times 5}{3 \times 5}= \frac {10}{15}$

$\frac {2}{3} = \frac {2 \times 7}{3 \times 7}= \frac {14}{21}$

Like Fractions |
Fractions with the same denominators are called like fractions. Example $\frac {1}{3}$, $\frac {2}{3}$ are Like Fractions $\frac {1}{4}$ ,$\frac {3}{4}$ are like Fractions |

Unlike Fraction |
Fractions with different denominators are called unlike fractions. Example $\frac {1}{3}$ , $\frac {2}{5}$ are Unlike Fractions |

$ \frac {5}{6} > \frac {2}{6}$

$ \frac {3}{6} > 0 $

$ \frac {1}{6} < \frac {6}{6} $

$ \frac {8}{6} < \frac {5}{6} $

Addition: The numerator adds to provide the final fraction value.

$\frac {1}{5} + \frac {1}{5} = \frac {2}{5}$

$\frac {1}{6} + \frac {4}{6} = \frac {5}{6}$

$\frac {9}{11} + \frac {1}{11} = \frac {10}{11}$

Subtraction: The Numerator subtract to provide the final fraction value.

$\frac {4}{5} - \frac {1}{5} = \frac {3}{5}$

$\frac {5}{6} - \frac {4}{6} = \frac {1}{6}$

$\frac {9}{11} - \frac {1}{11} = \frac {8}{11}$

And then it works like “like” Fraction

Let us check few example to make it clear

1)Compare $\frac {2}{3}$ and $\frac {5}{7}$

LCM of denominator is 3 and 7 is 21

So converting them equivalent Like fractions

$\frac {2}{3} = \frac {2 \times 7}{3 \times 7} = \frac {14}{21}$

$\frac {5}{7} = \frac {5 \times 3}{7 \times 3} = \frac {15}{21}$

Now $\frac {15}{21} > \frac {14}{21}$

So $\frac {5}{7} > \frac {2}{3}$

2)Perform the below Addition

$\frac {1}{2} + \frac {1}{3}$ Solution

LCM of 2 and 3 is 6

So converting them into equivalent Like Fractions

$\frac {1}{2} =\frac {1 \times 3}{2 \times 3} =\frac {3}{6}$

$\frac {1}{3} =\frac {1 \times 2}{3 \times 2} =\frac {2}{6}$

So

$\frac {1}{2} + \frac {1}{3} = \frac {3}{6} + \frac {2}{6} =\frac {5}{6}$

- $\frac {1}{5} + \frac {1}{6}$
- $\frac {1}{5} - \frac {1}{6}$
- $\frac {1}{2} + \frac {1}{3} + \frac {1}{4}$
- $\frac {1}{3} + \frac {1}{4} + \frac {1}{5}$

- Two mixed fraction can be added or subtracted by adding or subtracting the whole number of the two fractions and then adding or subtracting the fractional parts together.

- Two mixed fractions can also be converted into improper fractions and then added or subtracted.

1)Perform the below Addition

$1\frac {1}{2} + 2\frac {1}{3}$ Solution

We add the whole number and add the fractional part

$1\frac {1}{2} + 2\frac {1}{3}$ =$1 + 2+ \frac {1}{2} +\frac {1}{3}$ =$3 +\frac {1}{2} +\frac {1}{3}$ Now LCM of 2 and 3 is 6

So converting them into equivalent Like Fractions

$\frac {1}{2} =\frac {1 \times 3}{2 \times 3} =\frac {3}{6}$

$\frac {1}{3} =\frac {1 \times 2}{3 \times 2} =\frac {2}{6}$

So

=$3+ \frac {1}{2} + \frac {1}{3} = 3 + \frac {3}{6} + \frac {2}{6} =3 +\frac {5}{6} =3\frac {5}{6}$

We convert them into improper fraction

$1\frac {1}{2} + 2\frac {1}{3}$

=$\frac {3}{2} + \frac {7}{3}$

Now LCM of 2 and 3 is 6

So converting them into equivalent Like Fractions

$\frac {3}{2} =\frac {3 \times 3}{2 \times 3} =\frac {9}{6}$

$\frac {7}{3} =\frac {7 \times 2}{3 \times 2} =\frac {14}{6}$

So

=$\frac {9}{6} + \frac {14}{6}$

=$\frac {23}{6} =3\frac {5}{6}$

- 1$\frac {1}{5} + 1\frac {1}{6}$
- 3$\frac {1}{5} - 2\frac {1}{6}$
- 1$\frac {1}{2} + 2\frac {1}{3} + 3\frac {1}{4}$
- 4$\frac {1}{3} + 5\frac {1}{4} + 6\frac {1}{5}$

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