Ratios, Proportions, and the Geometric Mean
Section 6.1-Ratios, Proportions, and the Geometric Mean
Vocab
Ratio – if a and b are two number quantities and b is not 0, then the ratio of a to b is: .
Proportion – an equation that states two are . Ex:
Geometric Mean – the number x that satisfies [pic] for two positive numbers a and b.
Simplifying Ratios
Step 1 – Take care of the units
|If the units are the same, eliminate them: |If the units are different, use a conversion factor: |
|[pic] |[pic] |
Step 2 – Simplify
|[pic] |[pic] |
Cross Product
Step 1 – Multiply the numerators with the denominators of the opposite side:
Step 2 – Simlify
|[pic] |[pic] |[pic] |[pic] |[pic] |
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Geometric Mean
This can be solved using the proportion [pic] or more directly using [pic]
Example: Find the geometric mean of 4 and 16
Additional Properties of Proportions (short cuts)
|You can turn the proportion upside down! |The denominator and numerator on opposite sides|The denominators can be added to both sides! |
|If [pic], then [pic]. |can be swapped! |If [pic], then [pic]. |
| |If [pic], then [pic]. | |
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