Understanding Percentages in Mathematics
"Learn the basics of percentages in mathematics, including definitions, conversions, and calculations for fractions, decimals, and ratios. Find out how to convert fractions to percentages and vice versa, and understand the relationship between percentages and fractions. Explore the concepts of percentages as quantities and how to express them in corresponding units effectively."
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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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