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### 2005-: Numeric Proportionality 1

• Topic Cluster: Pure Mathematics
• Topic: Proportionality
• Objective: Given a direct or inverse proportion between two variables, solve numerical problems on how one variable changes as the other does.
• Content:
• Level: 1

#### 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: $$\frac{A_2}{A_1} = \frac{B_2}{B_1}$$
1. A and B are directly proportional.
1. If A is doubled, what happens to B?
2. If B is doubled, what happens to A?
3. 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?
2. 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: $$\frac{A_2}{A_1} = \frac{B_1}{B_2}$$
1. 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?
2. 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?
3. 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?
4. 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?
5. 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?