Ordering rational numbers

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Presentation transcript:

Ordering rational numbers

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.

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

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 2 20 28 2 10 14 5 7 Find if the two numbers are commonly divisible by 2,3,5,7,11,13,17

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:

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:

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 9 3 1 3 1 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:

Example 4: Arrange the rational numbers in the descending order Solution: LCM (3,9,3) = 3 x 3 = 9 3 9 3 3 1 3 1 1 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:

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