# Mathematics Review

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This web page provides a review of the mathematical concepts you will apply in this course.

### Fractions and Percentages %

Fractions are a part of every-day life and they are also used in science. A fraction with the same numerator (number on top) as another but with a smaller denominator (number on bottom) is a larger number. For example 1/2 is bigger than 1/3 which is bigger than 1/4, etc. That is because if you divide 1 by 2, you get 0.5 but 1 divided by 3 is only 0.333 and 1 divided by 4 is only 0.25. The fraction 3/5 (=0.6) is bigger than 3/6 (=0.5) which is bigger than 3/7 (=0.4286).

Fractions are sometimes expressed as a percent. To express a fraction as a percentage, find the decimal form and multiply by 100. The percent symbol ``%'' simply means ``divide by 100.'' For example 1/2 = 0.5 = 0.5× 100% = 50%; 3/5 = 0.6 = 0.6× 100% = 60%. Some examples on converting percentages to fractions or decimals: 5.8% = 5.8/100 = 0.058; 0.02% = 0.02/100 = 0.0002; the Sun is 90% hydrogen means that 90 out of every 100 atoms in the Sun is hydrogen.

### ``Times'' and ``Factor of''

Several homework questions ask you to find some quantity and find out how many ``times'' smaller or larger it is than something else, e.g., star A is ____times larger than star B. This means star A = a × star B, and you must find the number a. Another example: A gallon is equivalent to 4 quarts. This means that 1 gallon is 4 times bigger than 1 quart since 1 gallon = 4 × 1 quart, or (1 gallon)/(1 quart) = 4/1. This also means that 1 quart is 4 times smaller than 1 gallon since 1 quart = 1/4 × (1 gallon), or (1 quart)/(1 gallon) = 1/4. Notice when ``times bigger'' is used and when ``times smaller'' is used.

The use of the phrase ``factor of'' is very similar to the use of ``times''. For example, 1 quart is a factor of 4 smaller than 1 gallon, or 1 gallon is a factor of 4 bigger than 1 quart.

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last updated: 08 August 2001