Percentages: Basic Concepts and Conversions
Percentages
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Introduction
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Definition and basic mathematics of percentage
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All students
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Basic mathematics of percentages:
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Definition
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Fractions as percentages and vice versa
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Fractions as decimals and vice versa
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Percentages as quantities, and quantities as
percentages
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A percentage in a number or ratio expressed as a
fraction with a denominator of 100
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The value/ratio of the percentage is expressed by
the numerator
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Percentages are dimensionless numbers – they
have no unit of measurement
•
Percentages relating to specified units of measure
must always be expressed in corresponding units:
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To convert a fraction to a percentage, use a
proportional set:
Convert
7
/
8
to a percentage
transpose and solve
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To convert a percentage to a fraction, just reduce it
to its simplest form:
Convert 17.5% to a fraction:
÷ 4 =
÷ 4 =
÷ 25 =
÷ 25 =
X 10 =
X 10 =
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To convert a percentage to a decimal, simply divide
it by 100:
Convert 1.25% to a decimal:
2, 1
2, 1
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To convert a decimal to a percentage, simply multiply
it by 100:
Convert 0.9875 to a percentage:
1, 2
1, 2
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What is 35% of 120? (as a percentage)
What is 15% of 7.5? (as a decimal)
÷ 5 = 7
÷ 5 = 2 ÷2=1
12÷2= 6
reduce
reduce
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What percentage of 150 is 48? (as a proportional set)
What percentage of 600 is 105? (as a decimal)
÷ 3 = 16
reduce
÷ 50 = 2
÷ 50 = 3 ÷3 = 1
reduce
X 100 =
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Basic mathematics of percentages:
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Definition
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Fractions as percentages, and vice versa
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Percentages as decimals, and vice versa
•
Percentages as quantities, and vice versa
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Questions?
Introduction to percentages, including definitions and basic mathematical operations. Learn how to convert between fractions, decimals, and percentages, along with practical examples. Discover the fundamental principles behind percentages and gain insights into their role in various math problems and real-world applications.
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Presentation Transcript
Percentages www.kent.ac.uk/student-learning-advisory-service
Percentages Percentages Introduction Definition and basic mathematics of percentage All students
Percentage Percentage Basic mathematics of percentages: Definition Fractions as percentages and vice versa Fractions as decimals and vice versa Percentages as quantities, and quantities as percentages
Percentages Percentages A percentage in a number or ratio expressed as a fraction with a denominator of 100 The value/ratio of the percentage is expressed by the numerator Percentages are dimensionless numbers they have no unit of measurement Percentages relating to specified units of measure must always be expressed in corresponding units: ?? ??????? 100 ??????? 100 100??
Fractions as percentages Fractions as percentages To convert a fraction to a percentage, use a proportional set: transpose and solve transpose and solve 3 5= ? ? =3 100 100 = 60% 5 Convert 7/8 to a percentage 7 8= ? ? =7 100 100 = 87.5% 8
Percentages as fractions Percentages as fractions To convert a percentage to a fraction, just reduce it to its simplest form: 4 = 4 = 32 100 8 32% = = 4 = 4 = 25 Convert 17.5% to a fraction: 25 = 25 = X 10 = X 10 = X 10 = X 10 = =17.5 100 175 1000 7 17.5% = = 25 = 25 = 40
Percentages as decimals Percentages as decimals To convert a percentage to a decimal, simply divide it by 100: =12.0 100 2, 1 2, 1 =0.12 12% = 0.12 1 2, 1 2, 1 Convert 1.25% to a decimal: =1.25 100 =0.0125 1.25% = 0.0125 1
Decimals as percentages Decimals as percentages To convert a decimal to a percentage, simply multiply it by 100: =1.15 1.00 1, 2 1, 2 1, 2 1, 2 =115 100 = 115% 1.15 Convert 0.9875 to a percentage: =0.9875 =98.75 100 = 98.75% 0.9875 1
A percentage of a quantity A percentage of a quantity What is 35% of 120? (as a percentage) 12 12 2= 6 2= 6 reduce reduce 5 = 7 5 = 7 35 100 120 =35 120 100 5 = 2 5 = 2 2=1 reduce reduce =7 6 = 42 1 2=1 What is 15% of 7.5? (as a decimal) 0.15 7.5 = 1.125
A quantity as a percentage A quantity as a percentage What percentage of 150 is 48? (as a proportional set) 3 = 16 3 = 16 50 = 2 50 = 2 reduce reduce 48 150= 100 =48 100 ? = 32% 150 50 = 3 50 = 3 3 = 1 reduce reduce 3 = 1 What percentage of 600 is 105? (as a decimal) 105 600 = 0.175 = 17.5% X 100 = X 100 =
Percentage Percentage Basic mathematics of percentages: Definition Fractions as percentages, and vice versa Percentages as decimals, and vice versa Percentages as quantities, and vice versa
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