Ratio and Proportion: 20 flashcards
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1. What is a ratio $a:b$?
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A comparison of two quantities of the same kind, written in lowest terms.
2. Does order matter in a ratio? Give an example.
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Yes. $3:5 \neq 5:3$ — the order of terms changes the meaning.
3. What is a proportion?
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An equality of two ratios: $a:b :: c:d$.
4. State the fundamental rule of proportion.
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$a:b :: c:d \iff ad = bc$ (product of extremes = product of means).
5. In $a:b :: c:d$, which terms are the extremes and which are the means?
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Extremes: $a$ and $d$. Means: $b$ and $c$.
6. How do you find the missing fourth proportional in $x:b :: c:d$?
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$x = \dfrac{bc}{d}$.
7. What is direct proportion? Give its key relation.
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Both quantities increase or decrease together; $\dfrac{a}{b} = k$ (constant).
8. What is inverse proportion? Give its key relation.
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One quantity rises as the other falls; $ab = k$ (constant).
9. What is continued proportion?
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$a:b :: b:c$, which implies $b^2 = ac$.
10. What is the mean proportional between $a$ and $c$?
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$\sqrt{ac}$.
11. What is the third proportional to $a$ and $b$?
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$\dfrac{b^2}{a}$.
12. How do you split a total $T$ in ratio $a:b:c$?
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One part $= \dfrac{T}{a+b+c}$; multiply each term by this value.
13. If boys : girls $= 3:5$, what is boys : total?
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$3:8$.
14. How do you combine $a:b = 2:3$ and $b:c = 4:5$?
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Make the common term $b$ equal: $a:b:c = 8:12:15$.
15. What does a map scale like $1:50{,}000$ represent?
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A ratio of lengths — 1 unit on the map equals 50,000 units on the ground.
16. State the componendo rule.
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If $a:b = c:d$, then $(a+b):b = (c+d):d$.
17. State the dividendo rule.
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If $a:b = c:d$, then $(a-b):b = (c-d):d$.
18. State the componendo–dividendo rule.
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If $a:b = c:d$, then $\dfrac{a+b}{a-b} = \dfrac{c+d}{c-d}$.
19. Why must you convert units before forming a ratio (e.g., 3 kg : 400 g)?
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A ratio compares like quantities; convert to the same unit first: $3000:400 = 15:2$.
20. In men–days–work problems with fixed total work, which proportion applies?
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Inverse proportion — more men, fewer days.
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