Abstract inverse proportion | Maths | Quizalize & Oak National Academy

Starter quiz

Two variables are ______ proportional if there is a constant multiplicative relationship between one variable and the reciprocal of the other.

jointly

directly

inversely ✓

promisingly

uncommonly
Pair up the reciprocals with the following numbers.

3

⇔

$\frac{1}{3}$ ✓

5

⇔

$\frac{1}{5}$ ✓

$\frac{3}{2}$

⇔

$\frac{2}{3}$ ✓

2

⇔

$\frac{1}{2}$ ✓

12

⇔

$\frac{1}{12}$ ✓

$\frac{5}{9}$

⇔

$\frac{9}{5}$ ✓
What is the single multiplier that connects 9 to 54?

'6' ✓
What is the single multiplier that connects 15 to 10?

$\frac{3}{2}$

$\frac{2}{3}$ ✓

$\frac{9}{5}$

$\frac{15}{10}$
What is the single multiplier that connects 24 to 9.6?

$\frac{24}{9.6}$

$\frac{9.6}{24}$

$\frac{5}{2}$

$\frac{2}{5}$ ✓

$\frac{2}{3}$
$y\propto \sqrt{x}$ , when $x=64, y=6$ . Work out the value of $y$ when $x=400$ .

'15' ✓

Exit quiz

Match the equations with the correct proportions.

$y\propto\frac{1}{x^2}$

⇔

$y=\frac{3}{x^2}$ ✓

$y\propto\frac{1}{\sqrt{x}}$

⇔

$y=\frac{10}{\sqrt{x}}$ ✓

$y\propto\frac{1}{\sqrt[3]{x}}$

⇔

$y=\frac{3}{4\sqrt[3]{x}}$ ✓

$y\propto\frac{1}{x}$

⇔

$y=\frac{\sqrt{2}}{x}$ ✓

$y\propto x^2$

⇔

$y= 9x^2$ ✓

$y\propto \sqrt{x}$

⇔

$y= 5\sqrt{x}$ ✓
Which of the following are examples of inverse proportion?

Converting euros to dollars or vice versa

The hours you work and the salary received

The taps to fill a water bucket and the time it takes to fill the bucket ✓

The number of robots to complete a job and the time to complete the job ✓
$<Math>p\propto \frac{1}{q}</Math>, match the correct values for A, B and C.$

$p\propto \frac{1}{q}$ , match the correct values for A, B and C.

A

⇔

20 ✓

B

⇔

1000 ✓

C

⇔

62.5 ✓
It takes 10 workers 6 hours to build a wall. They all work at the same rate. Firstly, all workers build for 2 hours, then 6 workers leave. How many hours will it take the 4 workers to finish the wall?

'10' ✓
$y\propto \frac{1}{\sqrt{x}}$ , when $x=25, y=16$ . Work out the value of $y$ when $x=400$ .

'4' ✓
$y\propto \frac{1}{\sqrt[3]{x}}$ , when $x=125, y=0.15$ . Work out the value of $y$ when $x=0.008$ .

'3.75' ✓

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Lesson Details

Key learning points

Inverse proportion equations are of the form y = k ÷ x^n
k is the constant of proportionality.
To find k, you can use a pair of values.

Common misconception

For all direct and inverse proportions, the multiplicative relationship is with x and y.

The multiplicative relationship whether direct or inverse can be shown as y and x^n. Show a ratio table of y and 1/x^2 and a table of y and 1/x. The inverse multiplicative relationship is seen with y and 1/x^2 and not with 1/x.

Keywords

Inversely proportional - Two variables are inversely proportional if there is a constant multiplicative relationship between one variable and the reciprocal of the other.