Group Activity:
Calculations with Percents

Introduction

Percentages are fractions out of 100. For a given set of items, the percentages of each subgroup of items add up to 100, just as all the fractions of a whole add up to 1. Decimals are also fractions. Decimals are fractions out of 10, 100, 1000, etc., depending on how many digits are recorded. Percents, fractions, and decimals are just different and equivalent ways of giving information about relative amounts of items compared to a whole.

You have done calculations with percents in your educational career but sometimes we need a refresher. The exercises below will provide you with an opportunity to quickly practice some essential calculations and concepts. Complete them in a small group.

Problems

Show your work for all the following calculations.

1. Fill in the table by doing some calculations:
   

   Coffee	Black Tea	Energy Drink	Sweet Colored Drink	Energy Shot
   Fractions out of 250
   50 ---- 250
   Decimals
   Percents
   Fractions out of 100
   20 ---- 100

2. Add up all of your percent values from that row of the table. What do you get?
   Why is this a way to double-check your work?
3. Add up all of your fraction values from that row of the table. What do you get?
   How is this related to the sum of all of the percent values?
4. According to some more made-up statistics, 45% of students say they do not get enough sleep.
   Out of 250, how many is this?
5. What about the rest of the students? How many say they do get enough sleep, out of 250?
   Calculate this in two ways:
   1. Calculation Method 1
   2. Calculation Method 2
6. Atoms of the same element come in different varieties called isotopes. They differ in their atomic mass number and in the number of neutrons in their nuclei. The relative abudance of an isotope is the percentage of atoms of an element that have a given atomic mass number. Percent abundances add up to 100% as all percentages do. Calculate the following:
   1. An element with two isotopes has a percent abundance for one of the isotopes of 25%. What is the percent abundance of the other isotope?
   2. Consider a sample of 500 atoms of an element. If 467 of them are one of the isotopes of the element, then what is the percent abundance of this isotope? Give an answer with two digits after the decimal in a number expressed as a percent.
   3. The percent abundance for an isotope of neon is 90.48%. Out of 10,000 atoms, how many atoms of neon are this particular isotope?
   4. An element has three isotopes. In an experiment it is found that out of 45,000 atoms:
      Isotope 1 makes up 4,500 atoms
      Isotope 2 makes up 4,950 atoms
      Isotope 3 makes up 35,550 atoms
      Calculate the percent abundances of the three isotopes.
7. For the element chlorine (Cl), fill in the missing blanks in this table.
   

   Isotope Symbol	Protons	Neutrons	Mass number	Percent abundance
   			35	75.78
   			37