Mathematical: Ratios and Proportional Relationships Flashcards
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Read the first 7 Mathematical: Ratios and Proportional Relationships flashcards as text
The graph of a proportional relationship is a straight line that must always pass through which point?
Answer: The origin (0, 0)
A proportional relationship has the equation y = kx, so when x = 0, y = 0, meaning it always passes through the origin.
A train travels 240 miles in 4 hours. How long will it take the same train to travel 360 miles at the same speed?
Answer: 6 hours
Speed = 240 ÷ 4 = 60 mph; time = 360 ÷ 60 = 6 hours.
In a survey, 45 out of 60 students preferred science over art. What percentage of students preferred science?
Answer: 75%
45 ÷ 60 = 0.75 = 75%.
A price increased from $40 to $50. What is the percent increase?
Answer: 25%
($50 minus $40) ÷ $40 = $10 ÷ $40 = 0.25 = 25%.
What is the constant of proportionality in the equation y = 7x?
Answer: 7
In y = kx, k is the constant of proportionality; here k = 7.
A car uses 5 gallons of gas to travel 150 miles. How many miles can it travel on 8 gallons at the same rate?
Answer: 240 miles
The rate is 150 ÷ 5 = 30 miles per gallon; 8 × 30 = 240 miles.
Two ratios form a proportion when which condition is true?
Answer: Their cross products are equal
Two ratios a/b = c/d form a proportion when the cross products ad = bc are equal.