Arrange the rational numbers - 13 20 , 6 15 , 7 12 , - 9 10 and 3 5 in the descending order.

Given rational numbers are - 13 20 , 6 15 , 7 12 , - 9 10 and 3 5 To arrange the rational numbers in descending order make their denominators equals to L.C.M of the denominators of all rational numbers. So, L.C.M of 20 , 15 , 12 , 10 , 5 = 60 So, make the denominators of each rational numbers equal to 60 by multiplying and dividing with constant number. Multiply and divide the fraction with 3 ⇒ - 13 20 × 3 3 = - 39 60 Multiply and divide the fraction with 4 ⇒ 6 15 × 4 4 = 24 60 Multiply and divide the fraction with 5 ⇒ 7 12 × 5 5 = 35 60 Multiply and divide the fraction with 6 ⇒ - 9 10 × 6 6 = - 54 60 Multiply and divide the fraction with 12 ⇒ 3 5 × 12 12 = 36 60 Descending order means arranging the numbers from larger to smaller values. Now compare the numerators of all the rational numbers obtained, 36 60 > 35 60 > 24 60 > - 39 50 > - 54 60 So, the descending order of the rational numbers are 36 60 , 35 60 , 24 60 , - 39 50 , - 54 60

The angles of a pentagon are in the ratio 2 : 4 : 2 : 1 : 1 . The angles add up to 540 ° . What is the size of each angle?

Given, ratio of all angles of a pentagon are 2 : 4 : 2 : 1 : 1 Let the angles be 2 x , 4 x , 2 x , x , x Given, sum of angles in a pentagon is 540 ° ⇒ 2 x + 4 x + 2 x + x + x = 540 ° ⇒ 10 x = 540 ° ⇒ x = 540 ° 10 ⇒ x = 54 ° So, the angles are ⇒ 2 54 ° = 108 ° ⇒ 4 54 ° = 216 ° Hence, the measure of angles of a pentagon are 108 ° , 216 ° , 108 ° , 54 ° , 54 ° .