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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 Geometric Mean – the number x that satisfies . . Ex: a x for two positive numbers a and b. x 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: 12 gallons 3gallons 16quarts 2 gallons Step 2 – Simplify 4 2 12 3 Cross Product Step 1 – Multiply the numerators with the denominators of the opposite side: Step 2 – Simlify 6 x 7 14 x 5 33 11 9 27 x 12 1 35 100 x Geometric Mean a x or more directly using x ab x b Example: Find the geometric mean of 4 and 16 This can be solved using the proportion 8 16 x 1 10 Additional Properties of Proportions (short cuts) You can turn the proportion upside down! a c b d If , then . b d a c The denominator and numerator on opposite sides can be swapped! a c a b If , then . b d c d The denominators can be added to both sides! a c ab cd If , then . b d b d