Ratio: a recipe that survives every scale

Where we are on the map

A fraction measures one quantity; a ratio compares two quantities in a stated order.

Begin with a familiar image

If a drink uses two parts juice to three parts water, doubling the recipe must change both amounts together.

Precise meaning

Order matters in a:b. After matching units, multiplying or dividing both terms by the same factor preserves the ratio.

The lesson’s support signal

meaning → model → calculation → check → explain in your own words

state the order → align units → find one part → scale both quantities together

Worked example

2:3 = 4:6 because both terms were multiplied by 2. Cross-products confirm it: 2 × 6 = 3 × 4.

Example with a fading prompt

Change the numbers in the example and repeat the solution without copying its steps. Estimate first, calculate exactly, and check against the original condition.

Recall without a prompt

1. Define the main idea in one sentence.
2. Rebuild the support signal from memory.
3. Solve the example with different numbers and explain why every step is valid.

Find and correct the mistake

Changing only the first term from 2:3 to 4:3 does not preserve the recipe; both quantities need the same scale factor.

Transfer to a new setting

Apply the same relationship to something you can measure yourself. Name the quantities, units, and the boundary within which the model is valid. Check the answer by a second representation or an inverse operation.

Exercise

Required. Blue and white paint are mixed in a 3:5 ratio. Find each amount in 32 litres of mixture.

With your own data. Create one everyday example with the same structure and show it in words, a formula, and a check.

Optional. Seven days later, change the numbers and repeat without the support map.

Open perspective

Percent is a widely used ratio language built around one hundred parts.

Course contents