1. Ordering rational numbers

2. Rational numbers
A rational number is a number that can be expressed in the form
where p and q are integers and q ≠ 0.
Numerator
Denominator
For example are rational numbers
NOTE:
A rational number is said to be in standard form if its
denominator is positive and the numerator and
denominator have no common factor other than 1.
If a rational number is not in the standard form, then it can
be reduced to the standard form.

3. Integers - Recap Left - Numbers smaller Right - Numbers larger
When we move towards the right on the number line, the numbers become larger.
When we move towards the left on the number line, the numbers become smaller.
Ascending order: Arranging from smaller to greater number
Descending order: Arranging from greater to smaller number

4. Least Common Multiple(Recap)
Least Common Multiple (LCM) is the smallest Number that can divide 2
numbers without leaving a reminder
LCM can be found by Prime Factorization method.
Example: Find the LCM of 20 and 28.
The LCM of 20 , 28 = 2 X 2 X 5 X 7
= 140
Find if the two numbers are commonly divisible by 2,3,5,7,11,13,17

5. Answer: -15 < -10 < -9 < -6 < -5
Example 1: Arrange the rational numbers in the ascending order
Solution:
Step 1: In the given rational numbers, denominators
are same
Denominators are same
Step 2: Arrange the numerator numbers from
smaller to the bigger
-15 < -10 < -9 < -6 < -5
Step 3: Thus, arranging the Rational numbers
Note: Numbers on left are smaller than numbers on right
Answer:

6. Answer: 8 > 4 > 0 > -2 > -6
Example 2: Arrange the rational numbers in the descending order
Solution:
Step 1: In the given rational numbers, denominators are
same
Denominators are same
Step 2: Arrange the numerator numbers from
bigger to smaller
8 > 4 > 0 > -2 > -6
Step 3: Thus, arranging the Rational numbers
Note: Numbers on left are greater than numbers on right
Answer:

7. Example 3: Arrange the rational numbers in the ascending order
Solution:
Step 1 – Easy to arrange if Denominators are same
Lets make denominators same using LCM Method 3
LCM (3,9,3) = 3 x 3 = 9
x 3
x 1
x 3
Step 2 – Rewrite fractions with denominator of 9
x 1
x 3
x 3
Step 3 – Arrange the numerator numbers from smallest to biggest
-12 < -3 < -2
Step 4 - Thus, arranging the Rational numbers
Note: Numbers on left are smaller than numbers on right
Answer:

8. Example 4: Arrange the rational numbers in the descending order
Solution:
LCM (3,9,3)
= 3 x 3 = 9 3
Step 1 – Easy to arrange if Denominators are same
Lets make denominators same using LCM Method
Step 2 – Rewrite fractions with denominator of 9
x 3
x 1
x 1
x 3
x 1
x 1
x 3
x 3
Step 3 – Arrange the numerator numbers from biggest to smallest
12 > 0 > -5 > -6
Step 4 - Thus, arranging the Rational numbers
Note: Numbers on left are greater than numbers on right
Answer:

9. Try these 1. Arrange the rational numbers in the ascending order
2. Arrange the rational numbers in the descending order
3. Arrange the rational numbers in the ascending order