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Proportions Proportions Section 6-1

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ProportionsProportions

Section 6-1

ratio – a comparison of 2 quantities

The ratio of a to b can be expressed as a:b or where b is not 0. b

A special ratio often found in nature and used by artists and architects is the golden ratio. It is approximately 1: 1.618.

The Fibonacci sequence is related to the golden ratio. Each term in the sequence is the sum of the 2 previous terms. (1,1,2,3,5,8,13,…)

Page 4: Proportions Section 6-1. ratio – a comparison of 2 quantities The ratio of a to b can be expressed as a:b or where b is not 0

proportion – an equation stating that 2 ratios are equal eg. =

The cross products of a proportion are equal. (The product of the means equals the product of the extremes.)

mean

extreme

Page 5: Proportions Section 6-1. ratio – a comparison of 2 quantities The ratio of a to b can be expressed as a:b or where b is not 0

Equality of Cross ProductsEquality of Cross Products

For any numbers a and c and any nonzero numbers b and d,

iff ad = bc.b

Page 6: Proportions Section 6-1. ratio – a comparison of 2 quantities The ratio of a to b can be expressed as a:b or where b is not 0

Joke TimeJoke Time

How do you catch a “unique” rabbit?

“Unique” up on him!

Page 7: Proportions Section 6-1. ratio – a comparison of 2 quantities The ratio of a to b can be expressed as a:b or where b is not 0

How do you catch a “tame” rabbit?

The “tame” way!

Unitary ratio, direct and inverse proportions

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