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PEAZIT Aha card

Direct proportion: find the value for one unit

In direct proportion, y/x is constant. Find the price per item, then multiply by the new quantity.

Identical notebooks with no bulk discount: the unit price stays fixed.

Expression	Meaning
3 → 45	Three notebooks cost 45 currency units.
1 → 15	Divide 45 by three.
5 → 75	Five items cost 5 × 15.

One worked example

3 → 45Three notebooks cost 45 currency units.
1 → 15Divide 45 by three.
5 → 75Five items cost 5 × 15.

Watch out: A fixed fee or bulk discount breaks direct proportion. It is not enough that both quantities increase.

Goal, prerequisites and card origin

What you will learn: Solve a problem where multiplying quantity multiplies price equally.

What you need first: Division and multiplication.

An original PEAZIT working card. Independent expert review and effectiveness testing have not yet taken place. · v1

Show connections

In direct proportion, y/x is constant. Find the price per item, then multiply by the new quantity.

Without JavaScript, write your answer elsewhere before opening the solution.4 identical notebooks cost 60 currency units with no discounts. What do 7 cost?

Solution — open after your own attempt

105 One notebook costs 60/4 = 15 units. Seven cost 7 × 15 = 105.

A question for your next return: 6 kg of the same apples cost 150 units. What do 2.5 kg cost at the same unit price?

Solution — open after your own attempt

62.5 1 kg costs 25 units; 2.5 × 25 = 62.5.

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