Percentage: Basic Concepts and Conversions

• A free mathematics foundation batch is starting on the Rankers Gurukul YouTube channel.
• The batch aims to cover math from beginner to advanced levels.
• The course helps students who are economically weak and cannot afford paid courses.
• The first topic is Percentage, starting with basic concepts and conversions.
• Percentage is important for all exams and vital for other arithmetic chapters.
• Aaditya Ranjan has cleared several SSC exams with high scores, including 227/200 in CGLE Mains.
• He aims to provide experiential learning to help students clear exams.

What is Percentage?

• "Percent" means "per 100," indicating a value out of 100.
• Example: 10% represents 10 out of 100.

Converting Percentages and Fractions

• To convert a percentage to a fraction, divide by 100.
• To convert a fraction to a percentage, multiply by 100.
• This conversion is essential for solving percentage problems.

Percentage to Fraction Conversion

• To convert 10% to a fraction: 10/100 = 1/10
• To convert 20% to a fraction: 20/100 = 1/5
• To convert 12.5% to a fraction: 12.5/100 = 1/8

Fraction to Percentage Conversion

• If one person's share in a family of four is calculated as a percentage: (1/4) * 100 = 25%
• Convert 1/3 to a percentage: (1/3) * 100 = 33 1/3%
• Fraction-to-percentage conversion involves multiplying the fraction by 100 and adding a percentage sign.

Important Fractions and Their Percentage Equivalents

• 1/1 = 100%
• 1/2 = 50%
• 1/3 = 33 1/3%
• 1/4 = 25%
• 1/5 = 20%
• 1/6 = 16 2/3% or 16.66%
• 1/7 = 14 2/7%
• 1/8 = 12.5% or 12 1/2%
• 1/9 = 11 1/9%
• 1/10 = 10%
• 1/11 = 9 1/11%
• 1/12 = 8 1/3%
• 1/13 = 7 9/13%
• 1/14 = 7 1/7%
• 1/15 = 6 2/3%
• 1/16 = 6 1/4% or 6.25%
• 1/17 = 5 15/17%
• 1/18 = 5 5/9%
• 1/19 = 5 5/19%
• 1/20 = 5%
• 1/25 = 4%
• Memorizing these fractions is crucial for quick problem-solving.

Converting Fractions Where Numerator is Larger than Denominator

• When the numerator is greater than the denominator by one:
  • 9/8 = 1 + 1/8 = 100% + 12.5% = 112.5%
• 17/8 = 2 + 1/8 = 200% + 12.5% = 212.5%
• 65/8 = 8 + 1/8= 800% + 12.5% = 812.5%
• You can convert to a mixed fraction, and then add the percentage values.
• 41/8 = 5 + 1/8 = 500% + 12.5% = 512.5%

Converting Fractions Where Numerator is Smaller than Denominator by One

• For 7/8: 1 - 1/8 = 100% - 12.5% = 87.5%
• For 15/8: 2 - 1/8 = 200% - 12.5% = 187.5%
• 23/8 = 3 - 1/8 = 300% - 12.5% = 287.5%

Adjusting Improper Fractions in Percentages:

• 56 9/7 % can be written as 56 + (9/7)
• 9/7 = 1 2/7
• 56+ 1 2/7 = 57 2/7 %

Examples of Improper Fraction Adjustments:

• 73 15/13 = 74 2/13 %
• 41 32/7 = 45 4/7 %

Finding percentage of any number

• Example: Find 111% of 500:
• Step 1: 100% of 500 is 500.
• Step 2: 10% of 500 is 50.
• Step 3: 1% of 500 is 5.
• Step 4: Add up 500 + 50 + 5 = 555
• Find 111% of 468
• Step 1: 100% of 468 is 468.
• Step 2: 10% of 468 is 46.8.
• Step 3: 1% of 468 is 4.68.
• Step 4: Add up 468 + 46.8 + 4.68 = 519.48

Using A% of B equals B% of A to simplify problems

• The rule is: A% of B = B% of A
• Use A% of B = B% of A. If asked to find 800% of 777= 777% of 800
• Evaluate 7/8 x 800 = 700
• To find 64.28% of 259, consider 64.28% as 50% + 14.28 - 50%-is 1/2 and evaluate 1/2 + 1/7= 9/14 x 259= 166.5= 37%

Metric System Conversions

• Conversion: 1 millimeter (mm) to centimeters (cm):
  • 1 mm = 1/10 cm = 0.1 cm
• 1 millimeter to decimeters
  • 1/100 = 0.01 Decimeters
• Metric system, to millimeter to dekameters must divide by 10000
• 1 Kilometer (km) to meter (m)
  • 1 km = 1000m
• To find 80 meters of 5 kilometer is 80mm/5000mm X 100= 1.6%
• To find 8% of 5 Liters in ML= 8/100 x 5L X 1000mL =400mL

Changing any number to percentage

• Conversion of 2.4 to percentage needs multiplication by 100, resulting in 240%.
• Always do decimal and division when finding the values of percentage
• Difference between 0.9 and 0.009 is 0.891

Use previous information to find the answer

• For 49% of x is y. It can be said that y% of 50 would be 24.5%
• 25% of half of x= 2.5 x 30% X 1/4= is 50%