Understanding Percentages: Basic Concepts and Conversions

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.

• Percentages
• Mathematics
• Fractions
• Decimals
• Conversions

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1. Percentages www.kent.ac.uk/student-learning-advisory-service

2. Percentages Percentages Introduction Definition and basic mathematics of percentage All students

3. 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

4. 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??

5. 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

6. 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

7. 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

8. 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

9. 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

10. 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 =

11. 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

12. To book a maths/stats appointment To book a maths/stats appointment www.kent.ac.uk/student-learning-advisory-service

13. Questions?