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Ratios & Proportions

59 cards · 🇺🇸 English

Ratios, proportions, rates and how to solve for unknowns.

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Ratio in mathematics

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  1. 1Ratio in mathematics
    A ratio shows how many times one number contains another. It compares two quantities by division.
  2. 2the ratio 8:6
    For every 8 units of the first quantity, there are 6 units of the second quantity (equivalent to 4:3)
  3. 3Proportion
    A statement expressing the equality of two ratios, written as A:B = C:D or A:B∷C:D
  4. 4How can a ratio be expressed?
    As 'A to B', A:B, a fraction A/B, or a decimal fraction
  5. 5Antecedent in a ratio
    The first term (A) in a ratio A:B
  6. 6Consequent in a ratio
    The second term (B) in a ratio A:B
  7. 7In the proportion A:B = C:D, what are the extremes?
    A and D are called the extremes of the proportion
  8. 8In the proportion A:B = C:D, what are the means?
    B and C are called the means of the proportion
  9. 9Continued proportion
    The equality of three or more ratios, such as A:B = C:D = E:F
  10. 10Simplify the ratio 40:60
    Divide both terms by their greatest common factor (20): 40:60 = 2:3
  11. 11A ratio to be in simplest form
    The ratio has integers for both quantities and cannot be reduced further using integers
  12. 12Ratio one minute to 40 seconds in simplest form
    60 seconds : 40 seconds = 3:2
  13. 13If a bowl has 8 oranges and 6 lemons, what is the ratio of oranges to total fruit?
    8:14, which simplifies to 4:7
  14. 14Express the ratio 4:5 in the form 1:x
    1:1.25 (divide both sides by 4)
  15. 15Express the ratio 4:5 in the form x:1
    0.8:1 (divide both sides by 5)
  16. 16Verbal equivalent of 40:60∷2:3
    40 is to 60 as 2 is to 3
  17. 17If orange juice concentrate is diluted in ratio 1:4, what fraction is concentrate?
    1/5 of the total liquid (1 part concentrate, 4 parts water, 5 parts total)
  18. 18In a mixture with ratio 5:9:4:2, what percentage is the first component?
    25% (5 parts out of 20 total parts)
  19. 19Direct proportionality
    Two variables are directly proportional if y = kx, where k is a positive constant
  20. 20What symbol is used to denote proportionality?
    ∝ (or sometimes ~), as in y ∝ x
  21. 21Proportionality constant in y = kx
    k, also called the constant of variation or constant of proportionality
  22. 22How can direct proportionality be viewed graphically?
    As a linear equation with y-intercept of 0 and slope k > 0, corresponding to linear growth
  23. 23Example of direct proportionality in physics
    Distance traveled is directly proportional to time at constant speed (speed is the proportionality constant)
  24. 24Relationship between a circle's circumference and diameter
    Circumference is directly proportional to diameter, with proportionality constant π
  25. 25Inverse proportionality
    Two variables are inversely proportional if xy = k (constant), or y = k/x
  26. 26Graph of inverse proportionality
    A rectangular hyperbola that never crosses either axis
  27. 27In inverse proportion, what happens when one variable increases?
    The other variable decreases (in contrast to direct proportion where both increase or decrease together)
  28. 28Example of inverse proportionality
    For constant distance, travel time is inversely proportional to speed: s × t = d
  29. 29Aspect ratio of standard-definition television
    4:3, meaning width is 4/3 of the height (or 1.33:1)
  30. 30Aspect ratio of modern widescreen TVs
    16:9, or approximately 1.78:1

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