Setting up and solving ratio and proportion problems, including unit rates and scale factors, for middle school math.
34 cards · basic cards · AI-written, checked twice. Edit anything.
- What is a ratio?
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A comparison of two quantities using division.- Write three ways to express the ratio of 3 to 5.
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3:5, 3/5, or 'three to five'.- What are equivalent ratios?
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Ratios that represent the same comparison, like 2:3 and 4:6.- To simplify a ratio, what do you do?
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Divide both numbers by their greatest common factor (GCF).- Simplify the ratio 8:12.
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2:3 (divide both by 4, the GCF).- What is a unit rate?
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A ratio that compares a quantity to one unit of another quantity.- If 5 apples cost 10 dollars, what is the unit rate?
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2 dollars per apple (divide 10 by 5).- If you travel 150 miles in 3 hours, what is your unit rate?
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50 miles per hour.- What is a proportion?
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An equation that states two ratios are equal.- What is cross multiplication?
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A method for solving proportions: multiply the numerator of each fraction by the denominator of the other.- Solve: 3/5 = x/10. Find x.
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x = 6 (cross multiply: 3 times 10 = 5 times x, so 30 = 5x).- Solve: 2/3 = 8/x. Find x.
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x = 12 (cross multiply: 2 times x = 3 times 8, so 2x = 24).- What is a scale factor?
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A multiplier that describes how much a figure is enlarged or reduced.- If a scale factor is 3, how does the figure change?
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The figure is enlarged; all dimensions are multiplied by 3.- If a scale factor is 1/2, how does the figure change?
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The figure is reduced; all dimensions are multiplied by 1/2.
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