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Compare ratios

Comparison of ratios involves determining which of two relationships between quantities is greater, less, or equivalent by expressing them with a common comparison basis, such as equivalent ratios or unit rates. The reasoning applies to tables, double number lines, ratio notation, and fractions, while recognizing that comparing corresponding terms separately can give misleading results; this foundation supports proportional relationships, percent, rates, and later algebraic reasoning without extending to more advanced proportionality or abstract ratio proofs.

Detailed Explanation: Compare ratios

To compare two ratios, rewrite them so they use the same comparison basis. You can use equivalent ratios or find a unit rate.

Example: Which ratio is greater: 3:53:5 or 4:74:7?

Suppose these ratios describe red marbles to blue marbles:

  • 3:53:5 means 3 red marbles for every 5 blue marbles.
  • 4:74:7 means 4 red marbles for every 7 blue marbles.

Do not compare only the first numbers. Although 44 is greater than 33, the ratios have different second numbers. Instead, write the ratios as fractions:

35and47\frac{3}{5} \quad \text{and} \quad \frac{4}{7}

Find a common denominator. The least common denominator of 5 and 7 is 35:

35=2135\frac{3}{5}=\frac{21}{35}

and

47=2035\frac{4}{7}=\frac{20}{35}

Now compare:

2135>2035\frac{21}{35}>\frac{20}{35}

Therefore,

3:5 is greater than 4:7\boxed{3:5 \text{ is greater than } 4:7}

Both ratios now describe how many red marbles there are out of 35 blue-marble parts, so the comparison is fair.

Learn by doing: Compare ratios

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    Fraction Comparison - Problem Simplification - Mixed - Two Changed Denominators

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