How to express Rational Numbers in Standard Form

Definition:

If in a rational number, numerator and denominator have no common factor other than 1, and its denominator is a positive integer then the rational number will be in a standard form.

Standard form is also known as simplest form or lowest form. 

Example: 1. Convert the rational number 15/25 into standard form.

15/25 is a rational number, simplest form of 15/25 is

= (15 ÷ 5)/(25 ÷ 5)

= 3/5

Here, 3 and 5 can not have any common factor, but the common factor between numerator 3 and denominator 5 is only one. 

Therefore, we can say that rational number 3/5 is in standard form so standard form of 15/25 is 3/5.

2. Convert the rational number -14/49 into standard form.

-14/49 is a rational number, simplest form of -14/49 is

= (-14 ÷ 7)/(49 ÷ 7)

= -2/7

Here, 2 and 7 can not divided any common factor, and common factor between numerator 2 and denominator 7 is only one.

Therefore, we can say that rational number -2/7 is in standard form so standard form of -14/49 is -2/7.

3. Convert the rational number -39/-52 into standard form.

-39/-52 is a rational number, simplest form of -39/-52 is 

= (-39 ÷ 13)/(-52 ÷ 13)

= -3/-4

= 3/4

standard form of -39/-52 is 3/4.

4. Convert the rational number 22/24 into standard form.

= 22/24

= (22 ÷ 2)/(24 ÷ 2)

= 11/12

standard form of 22/24 is 11/12.

5. Convert the rational number 24/36 into standard form.

= 24/36

= (24 ÷ 2)/(36 ÷ 2)

= 12/18

= (12 ÷ 2)/(18 ÷ 2)

= 6/9

= (6 ÷ 3)/(9 ÷ 3)

= 2/3   standard form of 24/36 is 2/3.  

6. Convert the rational number 72/84 into standard form.

= 72/84

= (72 ÷ 2)/(84 ÷ 2)

= 36/42

= (36 ÷ 2)/(42 ÷ 2)

= 18/21

= (18 ÷ 3)/(21 ÷ 3)

= 3/7

standard form of 72/84 is 3/7.

7. Convert the rational number 85/125 into standard form.

= 85/125

= (85 ÷ 5)/(125÷ 5)

= 17/25

standard form of 85/125 is 17/25.

8. Convert the rational number 20/24 into standard form.

= 20/24

= (20 ÷ 2)/(24 ÷ 2)

= 10/12

= (10 ÷ 2)/(12 ÷ 2)

= 5/6

standard form of 20/24 is 5/6.

9. Convert the rational number 128/224 into standard form.

= 128/224

= (128 ÷ 2)/(224 ÷ 2)

= 64/112

= (64 ÷ 2)/(112 ÷ 2)

= 32/56

= (32 ÷ 2)/(56 ÷ 2)

= 16/28

= (16 ÷ 2)/(28 ÷ 2)

= 8/14

= (8 ÷ 2)/(14 ÷ 2)

= 4/7

standard form of 128/224 is 4/7.