Real-life Proportion and Inverse Proportion

Real-Life Proportion

Starter

Activity

Complete the proportion and inverse proportion sheet.

Real-Life Proportion

Worked

Example

3

203

1350

W = kr

4.06 = k x 27

k =

203

1350

W = x 5

W = x 125

W = 18.8 kg

Real-Life Inverse Proportion

10

Real-Life Inverse Proportion

The gravitational force between two objects is inversely proportionally to the square of the distance between the two objects. A comet orbits the earth in an elliptical orbit. At its closest distance the comet is 8.83 x 10 metres from the Sun, and the gravitational force between the comet and the Sun is 3.77 x 10 . Work out the gravitational force between the comet and the Sun at its greatest distance of 5.25 x 10 metres.

12

Activities

Worked

Example

11

10

The gravitational force between two objects is inversely proportionally to the square of the distance between the two objects. A comet orbits the earth in an elliptical orbit. At its closest distance the comet is 8.83 x 10 metres from the Sun, and the gravitational force between the comet and the Sun is 3.77 x 10 N. Work out the gravitational force between the comet and the Sun at its greatest distance of 5.25 x 10 metres.

12

2

34

F x d = 2.93942753 x 10

F = 293942753 x 10 / (5.25 x 10 )

F = 1.07 x 10

12

2

9

Key

Examples

Further Proportion Problems

3

Starter

3

1

8

T is inversely proportional to the square root of p .

(a) If p gets 4 times bigger, what is the effect on T?

Use T = 1 and p = 1 which gives: T x p = 1

If p = 4: T x 4 = 1 T x 8 = 1 T =

T is of what it was before.

(b) If T doubles, what is the effect on p?

If T = 2: 2 x p = 1 p = p = p = = 0.62996...

p is 0.63 times the size that it was before.

Worked

Example

1

8

T is inversely proportional to the square root of p .

(a) If p gets 4 times bigger, what is the effect on T?

(b) If T doubles, what is the effect on p?

3

1

4

3

1

4

1

2

Activity

Answers

(a) Yes (b) No (c) No (d) No (e) Yes

Activity

Real-life Proportion and Inverse Proportion

3

Complete the proportion and inverse proportion sheet.

3

5

6

(a) F = 10/x (b) F = 1 N (c) 0.5 metres

(a) V = 4.2r (b) 525 cm (c) 12.6 cm

0.015625

Make it 4 times longer.

(a) Light intensity is a quarter of before.

(b) Move the projector to 0.71 of the distance before.

(a) V = r h (b) V h (c) V r

T

1) a) direct b) I = 20T 2) a) Inverse b) L x W = 450

3) a) direct b) 3825 metres c) t = 2 n d) 45 cm

4) a) 32 b) 21 5) a) Inverse b) A x n = 360

6) a) 1250 b) 2 7) a) 6.25 b) 43.52

8) a) 8 b) 1.28 c) 1/8 d) 1/18

9) 24

10) a) F x w = 300069 b) 340.2 m c) 247.0 m

d) 648 kHz e) 1052.9 kHz

2

L.O. - Revisit practical problems involving proportion and Inverse proportion.

1

km