math · 28 minutes · Official OETT Aligned
Ratios & Proportions
Keep a mixture or comparison in the same balance
What to know
- ratio: a comparison of amounts
- price or amount for one item
- scaling both amounts equally
- keeping labels in order
A ratio tells you how two amounts go together, such as concentrate and water.
The core rule
Label both amounts. If you multiply one by a number, multiply the other by that same number.
A ratio of 2 parts concentrate to 5 parts water means the order matters. To use 8 parts concentrate, multiply 2 by 4. Multiply the water by 4 too: 5 × 4 = 20 parts. This keeps the mixture the same strength.
Worked examples
Example 1: easy
2 parts concentrate to 5 water means 8 parts needs 20 water.
- Match concentrate to concentrate: 8 ÷ 2 = scale factor 4.
- Apply 4 to water: 5 × 4 = 20 parts water.
Multiply both parts of the mixture by the same number.
Example 2: medium
Three filters for $18 gives a $6 unit rate.
- Divide total cost by filter count: $18 ÷ 3 filters.
- The unit rate is $6 per filter; 3 × $6 checks back to $18.
Price per filter means the cost of one filter.
Example 3: hard
A 4:7 mix totaling 55 uses 20 and 35 parts.
- Total ratio parts are 4 + 7 = 11, so each part is 55 ÷ 11 = 5.
- Scale each term: 4 × 5 = 20 and 7 × 5 = 35; 20 + 35 = 55.
Find one part first, then multiply to get each amount.
Common mistakes
You can reverse a ratio without changing its meaning.
Keep the labels in order. Two parts concentrate to five water is not the same as five concentrate to two water.
Put it into practice
Use guided explanations, check your answers, and try a new variation.