Write, interpret, and compare ratios using words, symbols, tables, and diagrams.
Compare two ratios
Problem
Compare the red-to-blue ratios \(2:3\) and \(3:5\). State the ratio with more red marbles per blue marble, or state that the ratios are equal.
Big Picture
What this problem is really about
Both ratios describe red marbles per blue marble, so the comparison must hold the blue quantity constant. We’ll rewrite each ratio as a fraction, scale them to the same number of blue marbles, and compare the corresponding red counts. Cross products provide a quick independent check without comparing the sums of the terms.
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