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THE MAGIC OF NATURE POEM WRITTEN BY SAFALYA PAL

THE MAGIC OF NATURE THE MAGIC OF NATURE OUR WONDER DOES GROW THE SECRETS OF NATURE ARE NOT FOR THE HUMANS TO KNOW THE MAGIC OF NATURE IS FOR ALL TO SEE IT IS ALL AROUND YOU AND ALL AROUND ME THE BEUTIFUL SCENIC VIEW EVERYTHING SEEMS AWESOME AND NEW LOOKING AT THE AWESOME SIGHT YOU FEEL SO TRANQUIL AND DELIGHT THINK HOW THE LUSH FORESTS ALWAYS REMAIN GREEN THINK WHY THE WATER DOESN’T ACCOMPLISH THINK HOW THE NORTHERN LIGHTS ESTABLISH THINK FROM WHERE DO WE GET NATURAL THINGS WE GET ALL THESE FROM THE NATURE AND THOSE ARE POSSIBLE FOR NATURE’S MAGIC! THE NATURAL BEAUTY OF NATURE HAS SO MUCH TO SAY, THE BEAUTIFUL CROSSROADS AND LONG WAY, THE NATURE HAS ITS CHARM, KEEP IT SAFE AND DO NOT HARM, THE NATURE WILL KEEP US UNSAFE, IF WE DON'T KEEP IT SAFE!                                               - SAFALYA PAL
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Ratio and Proportion, NCERT NOTES, Class 6


Ratio and Proportion

Ratio 

  • Ratio is the comparison of a quantity concerning another quantity.
  • It is denoted by ":".
  • Two quantities can be compared only if they are in the same unit.
  • Example: Father's age is 75 years and daughter's age is 25
                    years.
                    Ratio of father's age to daughter's age
                    = Father′s AgeDaughter′s Age= 3 1=3:1

Golden ratio

Two quantities are in golden ratio, if their ratio is same as the ratio of their sum to larger of the two quantities.

  • If two numbers a and b are in golden ratio, then a+ba=ab.
  • It is approximately equal to 1.618.

Difference between fractions and ratios

  •  A fraction describes a part of a whole and its denominator represents the total number of parts.
    Example: 13 means one part out of 3 parts.
  • A ratio is a comparison of two different quantities. 
    Example : In a society, 10 people like driving, 20 people like
                     swimming and total number of people in the society
                     is30.
                     Ratio of number of people liking driving to the total
                     number of people = 10:30
                     Ratio of number of people liking swimming to the
                     several people liking driving are 20:10.

Same ratio in different situations

  • Ratios can remain the same in different situations.
  • Example: Weight of JoeWeight of James=50100=1:2
                    Number of girlsNumber of boys=50100=1:2
                    Here, both the above ratios are equal.

Comparing quantities using ratios

  • Quantities can be compared using ratios.
  • Example: Joe worked for 8 hours and James worked for
                    2 hours. How many times are Joe's working hours is of James' working hours?
    Solution: Working hours of Joe = 8 hours
                   Working hours of Sheela = 2 hours
                   The ratio of working hours of Joe to Sheela =82=4
                   Therefore, Joe works four times more than James.

Equivalent Ratios

When the given ratios are equal, then these ratios are called as equivalent ratios.

  • Equivalent ratios can be obtained by multiplying and dividing the numerator and denominator with same number.
  • Example: Ratios 10:30 (=1:3) and 11:33 (=1:3) are equivalent ratios. 

Unitary Method

The method in which first we find the value of one unit and then the value of required number of units is known as Unitary Method.

  • Example: Cost of two shirts in a shop is Rs.200. What will be the cost of 5 shirts in the shop?
    Solution : Cost of 2 shirts =Rs.200 
                    Cost of 1 shirt =2002=Rs. 100
                    Cost of 5 shirts =(2002)×5=100×5=Rs.500

Proportions

If two ratios are equal, then they are said to be in proportion.

  • Symbol "::" or "=" is used to equate the two ratios.
  • Example: Ratios 2:3 and 6:9 are proportional.
                    ⇒ 2:3 :: 6:9 or 2:3 = 6:9

Uses of ratios and proportions

  • Example: Suppose a man travelled 80 km in 2 hours, how
                    much time will he take to travel 40 km?
    Solution: If x is the required time, then proportion is
                   80:2::40:x.
                   ⇒ 802=40x
                   ⇒  80x=80
                   ⇒ x=1 hour
                   So, the man takes one hour to complete 40km.
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