Abstract direct proportion | Maths | Quizalize & Oak National Academy

Starter quiz

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

'constant' ✓
Which of the following is an example of inverse proportion?

The number of cans of drink and the number of boxes bought

The time taken to fill a lorry and the number of people packing the lorry ✓

The number of metres run and the number of kilometres run

The number of euros exchanged and the number of dollars

The amount of flour needed and the number of biscuits being made
Which of the following is an equation representing inverse proportion?

$y={{{5}\over{x}}-1}$

$y={{{x}\over{5}}}$

$y={{{5}\over{x}}}$ ✓

$y={{{5}\over{x}}+1}$
A graph representing inverse proportion will appear in how many quadrants when plotted on a pair of axes?

'2' ✓
The smaller the dividend, the ______ to the origin the graph will be.

'closer' ✓
Which of the following is the graph of $y={{{3.5}\over{x}}}$ ?

Exit quiz

Any non-zero number multiplied by its reciprocal is equal to ______.

$-1$

0

1 ✓

2
Which of the following tables show direct proportion?

a ✓

b ✓

c

d ✓
Match the numbers to their reciprocals.

5

⇔

$1\over5$ ✓

$2\over5$

⇔

$5\over2$ ✓

$1\over2$

⇔

2 ✓

$3\over4$

⇔

$4\over3$ ✓

$1\over4$

⇔

4 ✓
Decide which of the following would share a directly proportional relationship.

The time taken to mow a lawn and the size of the lawn ✓

The time taken to run a 5 k race and the speed at which its run

The number of metres of ribbon bought and the cost of the ribbon ✓

The cost of hiring a coach and the cost per person
$h$ is directly proportional to $g$ . When $g$ = 12, $h$ = 7.2. Find $h$ when $g$ = 28.

'16.8' ✓
$g$ is directly proportional to $h$ . When $g$ = 17, $h$ = 93.5. Find $g$ when $h$ = 45.1.

'8.2' ✓

Worksheet

Loading worksheet ...

Presentation

Loading presentation ...

Video

Lesson Details

Key learning points

Direct proportion equations are of the form y = kx
k is the constant of proportionality and it is also the gradient of the graph.
To find the gradient, k, you can use a set of coordinates (pair of values).

Common misconception

We use the term 'multiplicative relationship' when talking about direct proportion. Pupils may need reminding that division is equivalent to multiplying by the reciprocal.

Allow opportunities to explore division of a number and multiplication of its reciprocal. Remind pupils that any non-zero number multiplied by its reciprocal is equal to 1.

Keywords

Direct proportion - Two variables are in direct proportion if they have a constant multiplicative relationship.
Reciprocal - The reciprocal is the multiplicative inverse of any non-zero number. Any non-zero number multiplied by its reciprocal is equal to 1.