Ratios and rates: keep the comparison in order.
A ratio compares quantities. A rate compares quantities with different units. Writing the units and the order keeps the comparison meaningful.
Reviewed · Official ASVAB scope and calculator guidance. Examples are original AptiStep material.
A ratio has an order
A paint mixture uses 2 cups of blue for every 3 cups of white. Blue:white is 2:3, while white:blue is 3:2. Neither ratio is wrong, but they answer different questions. The total mixture contains 5 parts, so blue is 2/5 of the mixture, not 2/3.
A unit rate compares to one
If 4 identical packs cost $18, the unit price is $18 ÷ 4 = $4.50 per pack. To compare another offer, convert that offer to the same unit. A lower total price is not necessarily a lower unit price if the pack sizes differ.
Check that the rate can stay constant
A proportional calculation assumes the same rate. If a problem adds a fixed fee or changes the rate after a threshold, simply scaling the first total will not work. For example, a $5 delivery fee plus $3 per item costs $11 for two items, but four items cost $17, not $22.
Try a unit-rate question
A machine fills 84 bottles in 7 minutes at a constant rate. How many bottles does it fill in 5 minutes?
Show the solution
The rate is 84 ÷ 7 = 12 bottles per minute. In 5 minutes it fills 12 × 5 = 60 bottles. Five minutes is less than seven, so the answer should be less than 84.
Four fresh questions
Try each example before opening its answer. Then explain the step you used in your own words.
Blue and white tiles are in a ratio of 3:2. There are 25 tiles. How many are blue?
Show answer and reasoning
15 tiles
The whole contains 3 + 2 = 5 ratio parts. Each part is 25 ÷ 5 = 5 tiles. Blue uses three parts: 3 × 5 = 15.
Four pounds of rice cost $10. At the same unit price, how much do seven pounds cost?
Show answer and reasoning
$17.50
One pound costs 10 ÷ 4 = $2.50. Seven pounds cost 7 × $2.50 = $17.50. The rate has units of dollars per pound.
A mix has 2 cups of concentrate for every 7 cups of water. How much water goes with 6 cups of concentrate?
Show answer and reasoning
21 cups
Concentrate scales from 2 to 6, a factor of 3. Apply that factor to water: 7 × 3 = 21 cups. Preserve the order of the ratio.
A printer makes 84 labels in 6 minutes at a steady rate. How many labels does it make in 5 minutes?
Show answer and reasoning
70 labels
Find the unit rate: 84 ÷ 6 = 14 labels per minute. Multiply by 5 minutes to get 70 labels. Less time should produce fewer than 84 labels.
Can you explain the method without looking?
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