Direct Proportion
If \(A\) is directly proportional to \(B\)...

then if \(B\) is multipled by a number,
\(A\) is multiplied by the same number.

and \(B\) is divided by a number,
\(A\) is divided by the the same number.

and \(A\) and \(B\) can be represetned by the equation:
\( \frac{A_2}{A_1} = \frac{B_2}{B_1} \)

A and B are directly proportional.

If A is doubled, what happens to B?

If B is doubled, what happens to A?

A has a value of 40. B has a value of 30.
The value of A increases to 160.
What is the new value of B?

C and D are directly proportional.
C has a value of 6 and D has a value of 0.01.
If C is decreased to 3, what is the new value of D?
Inverse Proportion
If \(A\) is inversely proportional to \(B\)...

then if \(B\) is multipled by a number,
\(A\) is divided by that number.

and \(B\) is divided by a number,
\(A\) is multiplied by that number.

and \(A\) and \(B\) can be represetned by the equation:
\( \frac{A_2}{A_1} = \frac{B_1}{B_2} \)

E and F are inversely proportional.
When E has a value of 5, F has a value of 11.
When E is increased to 15, what is the new value of F?

G and H are inversely proportional.
When G has a value of one million, H has a value of 6.
When G is decreased to 500,000, what is the new value of H?

I and J are directly proportional.
When I has a value of 4000, J has a value of 0.0002.
When I is increased to 16000, what is the new value of J?

K and L are inversely proportional.
When K has a value of \( 8 \cdot 10^{10} \),
L has a value of 4 million.
If the value of L is increased to 8 million,
what is the new value of K?

M and N are directly proportional.
When M has a value of \( 3 \cdot 10^4 \),
N has a value of \( 6 \cdot 10^{8} \).
When M is increased to \( 3 \cdot 10^6 \),
what is the new value of N?
Add and Subtract?
Proportionality only gives you information about division and multiplication,
it does not give you any information about addition or subtraction.