**Put rational numbers in order :**

- Convert integers and mixed numbers to improper fractions.
- Find the least common denominator LCD of all the fractions.
- Rewrite fractions as equivalent fractions using the GCD.
- Order the new fractions by the numerator.
- In case we have decimals, we have to convert it into fraction.

Let us see some examples to understand the above concept.

**Example 1 :**

Write the following rational numbers in order from greatest to least.

19/25 is already a fraction, so we can leave it as it is. |
= 19/25 |

For converting the second number 0.33 into fraction, we have to multiply both numerator and denominator by 100. |
0.33 x (100/100) = 33/100 |

68% can be written as 68/100 |
= 68/100 |

Since 14/20 is already in fractional form, we don't have to convert this |
14/20 |

50% can be written as 50/100 |
50/100 |

The denominators of the above fractions are 25, 100, 100, 20 and 100.

Since the denominators are different, we have to find least common multiple.

L.C.M = 100

19/25 (1) ==> (19/25) x (4/4) = 76/100

0.33 (2) ==> (33/100)

68% (3) ==> (68/100)

14/20 (4) ==> (14/20) x (5/5) = 70/100

50% (5) ==> (50/100)

The rational numbers from greatest to least is 76/100, 70/100, 68/100, 50/100, 33/100

Hence the required order is 19/25, 14/20, 68%, 50%, 0.33

**Example 2 :**

Write the following rational numbers in order from greatest to least.

5/6 is already a fraction, so we can leave it as it is. |
= 5/6 |

For converting the second number 0.121 into fraction, we have to multiply both numerator and denominator by 1000. |
0.121 x (1000/1000) = 121/1000 |

8/9 is already a fraction, so we can leave it as it is. |
= 8/9 |

70% can be written as 70/100 |
70/100 |

11/12 is already a fraction, so we can leave it as it is. |
11/12 |

The denominators of the above fractions are 6, 1000, 9, 100 and 12.

Since the denominators are different, we have to find least common multiple.

L.C.M = 3 x 2 x 5 x 2 x 5 x 10 x 3 = 9000

5/6 (1)==> (5/6) x (1500/1500) = 7500/9000 **(3)**

0.121 (2)==> 0.121 x (1000/1000) = 121/1000 **(5)**

8/9 (3)==> (8/9) (1000/1000) = 8000/9000 **(2)**

70% (4)==> (70/100) x (90/90) = 6300/9000 **(4)**

11/12 (5)==> (11/12) x (750/750) = 8250/9000 **(1)**

The rational numbers from greatest to least is 8250/9000, 8000/9000, 7500/9000, 6300/9000, 121/9000

Hence the required order is 11/12, 8/9, 5/6, 70%, 0.121

**Example 3 :**

Write the following rational numbers in order from least to greatest.

3/4 is already a fraction, so we can leave it as it is. |
= 3/4 |

13/17 is already a fraction, so we can leave it as it is. |
= 13/17 |

To convert 0.888 as fraction, we have to multiply both numerator and denominator by 1000 |
0.888 x (1000/1000) = 888/1000 |

11/15 is already a fraction, so we can leave it as it is. |
11/15 |

77.7% can be written as 77.7/100. In order to convert this into fraction, we have to multiply both numerator and denominator by 10. |
(77.7/100) x (10/10) = 777/1000 |

The denominators of the above fractions are 4, 17, 1000, 15 and 1000.

Since the denominators are different, we have to find least common multiple.

L.C.M = 5 x 2 x 2 x 5 x 17 x 10 x 3 x 10 = 510000

3/4 (1)==>(3/4)x(127500/127500) = 382500/510000 **(3)**

13/17 (2)==>(13/17)x(30000/30000)=390000/510000 **(4)**

0.888(3)==>

(8/1000)x(510/510)=4080/510000 **(1)**

11/15 (4)==>

(11/15)x(34000/34000)=374000/510000 **(2)**

77.7 (5)==>

(777/1000) x (510/510) = 396270/510000 **(5)**

The rational numbers from greatest to least is 8250/9000, 8000/9000, 7500/9000, 6300/9000, 121/9000

Hence the required order is 0.888, 11/15, 3/4, 13/17, 77.7%

After having gone through the stuff given above, we hope that the students would have understood "Put rational numbers in order".

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