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➤ When we compare the fractions by comparing their equivalent fractions whose denominator is 100, we say that we are comparing in percentage (per hundred).
"Percentages are numerators of fractions with denominator 100 and have been used in comparing results."
➧ Per cent is derived from Latin word ‘per centum’ meaning ‘per hundred’
➧ Per cent is represented by the symbol % and means hundredths too (1/100).
e.g., 1/100 = 1%, 5/100 = 5% , 21.5/100 = 21.5%
➧ So to compare quantities which are significant as a part (or fraction), we can use percentage.
➧ We can treat percentage as Equivalent fraction whose denominator is 100.
➧ Part/Whole = Percent/100
➧ Percent = Part/Whole ×100
➧ Parts always add to give 100.
(Q) If 65% of students in a class have a bicycle, what per cent of the student do not have bicycles ?
Ans: Students which do not have bicycles = (100−65)% = 35%
Converting Fraction to Percentage
➢ Get the equivalent fraction whose denominator is 100 by multiplying both numerator and denominator with same number.➢ Remove the 100 in denominator and express the number as percent.
→ Write as a percentage : 1/2, 1/7, 7/5
→ 1/2 = 1×50/2×50 = 50/100 = 50% ,
1/7 = 1×100/7×100 = 100/7×100 = 100/7 % = 142/7 %
7/5 = 7×20/5×20 = 140/100 = 140 %
➢ The percentages related to proper fractions are less than 100 whereas percentages related to improper fractions are more than 100.
➢ To find the percentage we can use this formula -
Percent = Part/Whole ×100
Converting Decimals to Percentage
➢ Convert the decimal into fraction➢ Multiply or divide both numerator and denominator with same number to get 100 in denominator.
➢ Remove the 100 in denominator and express the number as percent.
→ Write as a percentage : 0.65, 0.07, 4.57
→ 0.65 = 65/100 = 65% ,
0.07 = 7/100 = 7 %
4.57 = 457/100 = 457 %
Converting Percentage to Fraction or Decimals
➢ Remove the % and multiply the number by 1/100.→ Write as a fraction or decimal : 57%, 3.8%, 175%
→ 57% = 57/100 = 0.57
3.8 % = 3.8/100 = 0.038
175 % = 175/100 = 7/4 = 1.75
Converting Percentage to "How Many" (Part or Whole)
➤ Finding the part
1). Find: (a) 50% of 164 (b) 75% of 12 (c)121/2 % of 64Ans- (a) 50% of 164 = 50% ×164 = 50/100×64 = 1/2×64 =32
(b) 75% of 12 = 75% ×12 = 75/100×12 = 3/4×12 =3×3 = 9
(c)121/2 % of 64 = 25/2% ×64 = 25/2×100×64 = 1/8×64 =8
2). 8% children of a class of 25 like getting wet in the rain. How many children like getting wet in the rain.
Ans- Number of children like getting wet in the rain = 8% of 25 = 8/100 ×25 = 2
➤ Finding the whole
Let the whole be x1). 9 is 25% of what number?
2). 75% of what number is 15?
Ans-
1). Let, the number be x, then
25% of x = 9
⇒ 25/100× x = 9
⇒ 1/4× x = 9
⇒ x = 9×4 = 36
∴ 9 is 25% of 36.
1). Let, the number be x, then
75% of x = 15
⇒ 75/100× x = 15
⇒ 3/4× x = 15
⇒ x = 15×4/3 = 20
∴ 15 is 75% of 20 .
Ratio to Percents
➢ In case of ratio of quantities, we get the whole (total of all parts) by adding all of them.➢ Percent of individual quantity can then be found by taking it as the part of the whole.
➢ To find the percentage we can use this formula -
Percent = Part/Whole ×100
Q) In a salad, ratio carrot to radish is 2:1. What is the percentage of both in that mixture?
A) Total of all part (whole) = 2 + 1 = 3
Percentage of carrot = 2/3×100 = 2/3× 100 = 200/3% = 662/3%
Percentage of carrot = 1/3×100 = 1/3× 100 = 100/3% = 331/3%
Q) If angles of a triangle are in the ratio 2 : 3 : 4. Find the value of each angle and its percentage.
A) Total of all part (whole) = 2 +3 +4 = 9
Sum of angles of triangle = 180°
First angle = 2/9 of 180° = 2/9×180° = 40°
First angle percentage = 2/9×100 = 200/9 % =222/9 %
Second angle = 3/9 of 180° = 3/9×180° = 60°
Second angle percentage = 3/9×100 = 300/9 % =331/3 %
Third angle = 4/9 of 180° = 4/9×180° = 80°
Third angle percentage = 4/9×100 = 400/9 % =444/9 %
Increase or Decrease as Percent
Amount of Change/Original Amount or Base = Percent of change/100
➧ Percent of change = Amount of Change/Original Amount or Base ×100
➧ Percentage increase = Increase in Amount/Original Amount or Base ×100
➧ Percentage decrease = Decrease in Amount/Original Amount or Base ×100
Q1). Find Percentage of increase or decrease:
a) Price of shirt decreased from Rs 80 to Rs 60.
b) Marks in a test increased from 20 to 30.
Q2). My father says, in his childhood petrol was Re 1 a litre. It is Rs 52 per litre today. By what Percentage has the price gone up?
A1). a) Decrease in price of shirt = Rs 80 − Rs 60 = Rs 20
Percentage decrease in price of shirt = 20/80×100% = 25%.
b) Increase in marks in a test = 30 − 20 = 10
Percentage increase in marks in a test = 10/30×100% = 100/3% = 331/3%
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