Proportional Reasoning

Proportional Reasoning

Proportional Reasoning

• As a directly proportional variable increases the answer will increase by same factor.

• As an indirectly proportional variable increases the answer will decrease by the same factor.

• If a variable is squared the answer will increase by factor squared.

• If a variable is inversely proportional to the square of a variable the answer will decrease by square of factor.

Example a= F/m

• If F is doubled a will double

• If F is tripled a will triple

• If m is doubled, a will be halved.

• if m is halved, a will be doubled

Example a = F/m

• ?a = 4F/m ?=4

• ?a = 3F/m ?=3

• ?a = F/2m ? = 1/2

• ?a = F/4m ? = 1/4

• ?a = F/(1/2m) ? = 2

• ? a = F/(1/4m) ? = 4

• ?a = 4F/2m ?=4/2 ?=2

Example F = mv²/r

• ?F = 2mv²/r ? = 2

• ?F = m(2v)²/r ? = 4

• ?F = m(3v)²/r ? = 9

• ?F = 2m(2v)²/r ? = 8

• ?F = 2m(3v)²/r ? = 18

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Example G = m/r²

• ?G = m/(2r)² ?=1/4

• ?G = m/(3r)² ?= 9

• ?G = m/(4r)² ?=16

• ?G = m/(1/2r)² ? = 1/4

• ?G = m/(1/3r)^{2 ?} = 1/9

• ?G = 2m/(1/2r)² ?=8

• ?G = 2m/(5r)² ? =4/25

Multiple Choice

Equation is F = ma

What happens if I double mass?

• ? = 2

• ? = 1/2

Multiple Choice

F = mv²/r What happens to F if I double v?

• ? = 0

• ? = 1/2

• ? = 2

• ? = 4

Multiple Choice

The equation is a = F/m What happens if I double m?

• ? = 4

• ? = 2

• ? = 1/2

• ? = 1/4

Multiple Choice

The equation is G = m/r² What happens when I double m?

• ? = 2

• ? = 4

• ?= 1/2

• ? = 1/4

Multiple Choice

The equation is G = m/r²

^{What happens when r is doubled?}

• ? = 4

• ? = 2

• ? = 1/2

• ? = 1/4

Multiple Choice

The equation is G = m/r²

^{What happens when I halve r?}

• ? = 1/4

• ? = 1/2

• ? = 2

• ? = 4

Multiple Choice

The equation is F = ma

What happens if I triple m and double a?

• ? = 2/3

• ? = 3/2

• ? = 6

• ? = 12