Unit 1 · Essential SkillsE1 · Ratios · Ground Ops

Ratios & Proportions

Read ratios in the right order, scale them, and split a total into proportional parts.

29 min
Unlocks: Fuel Mixer
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7 steps · about 29 minutes

Start with the warm-up.

Start

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Warm-up

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Key terms

Ratio: An ordered comparison of two quantities.
Proportion: An equation stating that two ratios are equal.
Scale factor: The multiplier connecting corresponding quantities.

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Take a shot before the lesson. Write one relationship from the stem, even if you do not finish.

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The big idea

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See the structure

A ratio compares quantities in a stated order. $3:5$ means 3 units of the first quantity for every 5 units of the second; it is not automatically part to whole.

Key idea

Name quantities before calculating

Write what each number measures. A correct calculation with the wrong quantity or unit still misses the question.

Build a reliable method

To split a total in the ratio $a:b$ , count $a+b$ equal shares. One share is the total divided by $a+b$ , then multiply by the requested number of shares.

Explore in Desmos

Split one total into ratio shares

A 35-cup mix has oats:raisins

3:4

. Read 5 cups per part, 15 cups of oats, and 20 cups of raisins. Check that the two shares add to 35.

The calculator is live: change anything and see what happens.

Split one total into ratio shares

Degree mode

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Stretch to a 36

A proportion is an equality of two ratios. Keep corresponding quantities in matching positions, then cross-multiply or graph both sides.

Trap

A believable answer to the wrong question

The choices often include a correct intermediate number. Before selecting it, reread the highlighted ask and check the unit, sign, and domain.

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Skip check · 2 questions

Already know this? Get both right on the first try and you can skip the worked examples.

Worked example

Example 1: Split a total by all ratio parts

Problem

Trail mix has oats:raisins

3:4

and 35 cups total. How many cups are oats?

The whole contains

3+4=7

equal parts, so one part is

35/7=5

Which ratio setup uses every part of the whole?

Oats use 3 parts:

3(5)=15

cups.

Which calculation checks the ratio and total?

Worked example

Example 2: Scale a recipe rather than split a total

Problem

A drink uses 2 cups concentrate for every 5 cups water. How much concentrate pairs with 20 cups water?

Water scales by

20/5=4

Which ratio setup uses every part of the whole?

Apply the same factor to concentrate:

2(4)=8

cups.

Which calculation checks the ratio and total?

Faded example · you finish it

Example 3: Complete the setup and result

Problem

How many liters are in the 5-part share of a 72-liter blend mixed in the ratio

5:3

Choose the setup that follows the stated relationship.

Choose the resulting value.

Desmos way

Check every share of a ratio split

For a 72-liter blend in the ratio

5:3

, type 72/(5+3). Read 9 liters per ratio part.

Type 72/(5+3)*5 and 72/(5+3)*3. Read 45 and 27; their sum is 72 and

45:27

reduces to

5:3

Check every share of a ratio split

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Where did it go wrong?

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Optional · 4 questions · Hardest levelChallenge set: the kind of question that decides a 36

These are last-ten-questions hard. Take your time, use Desmos when it helps, and expect to miss some: that's where the learning is.