Direct and Inverse Proportion

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Direct and Inverse Proportion

This video is from Mannel's Maths Music.

Level 1 Example

If $a$ varies directly with $b$ and $a=24$ when $b=8$ find $a$ when $b=9$

$$a \propto b$$ $$a = kb$$

Where $k$ is some constant. If $a=24$ when $b=8$ then

$$24 = 8k$$ $$k = 3$$

so the equation is

$$a = 3b$$

If $b = 9$ then

$$a = 3 \times 9 = 27$$

Level 2 Example

If $a$ is inversely proportional to $b$ and $a=4$ when $b=6$ find $a$ when $b=8$

$$a \propto \frac{1}{b}$$ $$a = \frac{k}{b}$$

Where $k$ is some constant. If $a=4$ when $b=6$ then

$$4 = \frac{k}{6}$$ $$k = 24$$

so the equation is

$$a = \frac{24}{b}$$

If $b = 8$ then

$$a = 24 \div 8 = 3$$

Level 3 Example

If $a$ is directly proportional to the square of $b$ and $a=24$ when $b=2$ find $a$ when $b=3$

$$a \propto b^2$$ $$a = kb^2$$

Where $k$ is some constant. If $a=24$ when $b=2$ then

$$24 = 2^2 \times k$$ $$k = 6$$

so the equation is

$$a = 6b^2$$

If $b = 3$ then

$$a = 6 \times 3^2 = 54$$

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1. If \(a\) is inversely proportional to \(b\) and \(a=2\) when \(b=12\) find \(a\) when \(b=4\)
and find \(b\) when \(a=8\)
2. If \(c\) is inversely proportional to \(d\) and \(c=3\) when \(d=30\) find \(c\) when \(d=6\)
and find \(d\) when \(c=5\)
3. If \(e\) is inversely proportional to \(f\) and \(e=4\) when \(f=35\) find \(e\) when \(f=7\)
and find \(f\) when \(e=5\)
4. If \(g\) is inversely proportional to \(h\) and \(g=5\) when \(h=48\) find \(g\) when \(h=0.8\)
and find \(h\) when \(g=0.6\)
5. A teacher shared some cherries between a group of pupils on the playground. There were six pupils in the group and they got four cherries each. How many cherries would they have got each if there were eight pupils in the group?
6. A fish pond can be filled in ten hours by three identical hose pipes. How many hours would it take to fill the pond by five identical hose pipes?
7. The volume V of a given mass of gas varies inversely as the pressure P. When V = 10m³, P = 100 Nm^-2. Find the volume in cubic metres when the pressure is 250 Nm^-2.
8. Click or tap on the graph which could represent inverse proportion. A B C D E

Direct and Inverse Proportion

A self-marking exercise in three levels on solving direct and inverse variation problems.

Level 1 Level 2 Level 3 Unitary Method Description Help Exam-Style More Ratio

Instructions

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Answers

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Description of Levels

Direct and Inverse Proportion

Level 1 Example

Level 2 Example

Level 3 Example