Direct & Inverse Proportion Flashcards

All 10 cards in this deck

What are the steps to scale a recipe up or down for a different number of items?

e.g. a recipe for 16 flapjacks uses 120 g butter — how much butter for 24 flapjacks?

1. Divide the new number by the old to get the multiplier: $24 \div 16 = 1.5$
2. Multiply every ingredient by that multiplier: $120 \times 1.5 = 180$ g butter

What are the steps of the unitary method for finding the cost of a different quantity?

e.g. 5 kg of apples cost £4 — what do 7 kg cost, and is a £5 budget enough?

1. Divide to find the cost of one unit: $4 \div 5 = £0.80$
2. Multiply by the new quantity: $0.80 \times 7 = £5.60$
3. Compare with the budget: £5 is not enough

What are the steps to solve an inverse proportion problem?

e.g. 5 identical pumps fill a tank in 14 hours — how long would 4 pumps take?

1. Multiply to find the total work: $5 \times 14 = 70$ pump-hours
2. Divide by the new number: $70 \div 4 = 17.5$ hours
   Fewer pumps means more time.

What do the equations $y = kx$ and $y = \dfrac{k}{x}$ each tell you?

e.g. $H = \dfrac{72}{n}$

$y = kx$: $y$ is directly proportional to $x$; $y = \dfrac{k}{x}$: $y$ is inversely proportional to $x$ ($k$ is the constant of proportionality).
e.g. $H = \dfrac{72}{n}$, so when $n = 6$, $H = 72 \div 6 = 12$

What does a graph of two quantities in direct proportion look like, and how do you read a value from it?

e.g. a graph of cost against weight of potatoes — find the cost of 7 kg

A straight line through the origin; go up from 7 on the weight axis to the line, then across to read the cost off the cost axis.

True or false? Two quantities are in direct proportion if one gets bigger whenever the other gets bigger.

False. They are in direct proportion only if the ratio between them stays the same (equal ratios), i.e. one divided by the other is always the same number.

How can you tell from a graph whether two quantities are in direct proportion or inverse proportion?

Direct: a straight line through the origin.
Inverse: a curve sloping downwards, getting closer to both axes but never touching them.

True or false? Any straight line graph shows that two quantities are in direct proportion.

False.
The line must also pass through the origin $(0,0)$.

On a direct proportion graph, what does the value read off at 1 on the horizontal axis tell you?

e.g. a graph of cost against weight of potatoes

The amount for one unit, which you can multiply up for any quantity.
e.g. the cost of 1 kg of potatoes.

What are the steps to use a direct proportion graph to find a value beyond the end of the graph?

e.g. a cost-against-weight graph stops at 5 kg — find the cost of 20 kg

1. Read off the largest value you can: 5 kg costs £4.
2. See how many times bigger: $20 \div 5 = 4$.
3. Multiply: $4 \times £4 = £16$.