Card 1 of 8
MediumStudy card 1
Prompt
Why does ratio order matter?
Answer
a:b compares a to b; reversing it creates the reciprocal relationship.
MathProblem-Solving & Data Analysis
Flashcards
Ratios and Rates Flashcards
Recall proportional reasoning, unit rates, conversions, and ratio traps.
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Session progress0 of 8 studied
Card 1 of 8. Answer hidden.
Card 2 of 8
EasyStudy card 2
Prompt
What is a unit rate?
Answer
A rate expressed per one unit of the denominator quantity.
Card 3 of 8
MediumStudy card 3
Prompt
When are two ratios proportional?
Answer
When their cross products are equal, assuming denominators are nonzero.
Proportion test
\[\frac{a}{b}=\frac{c}{d}\iff ad=bc\]
Card 4 of 8
MediumStudy card 4
Prompt
If every length is multiplied by k, what is the linear scale factor?
Answer
k; corresponding lengths and other linear measures multiply by k.
Card 5 of 8
MediumStudy card 5
Prompt
How does dimensional analysis prevent conversion errors?
Answer
Write units as factors so unwanted units cancel and the desired unit remains.
Card 6 of 8
MediumStudy card 6
Prompt
What is density?
Answer
Mass per unit volume.
Density
\[\rho=\frac{m}{V}\]
Card 7 of 8
MediumStudy card 7
Prompt
What signals that you used a reciprocal rate?
Answer
Your final units are reversed from the units requested.
Card 8 of 8
HardStudy card 8
Prompt
What is the additive ratio trap?
Answer
Adding the same amount to both parts does not generally preserve a ratio; proportional scaling multiplies both parts.
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