Equivalent Ratios

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What is an equivalent ratio?

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An equivalent ratio is a ratio that expresses the same relationship between two quantities, even if the numbers are different. For example, the ratios 1:2 and 2:4 are equivalent.

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How do you find an equivalent ratio using division?

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To find an equivalent ratio using division, divide both terms of the ratio by the same non-zero number. For example, for the ratio 15:30, dividing both terms by 15 gives the equivalent ratio 1:2.

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What is the simplest form of a ratio?

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The simplest form of a ratio is when the two numbers are reduced to their smallest whole number values while maintaining the same relationship. For example, the ratio 8:12 can be simplified to 2:3.

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How can you determine if two ratios are equivalent?

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Two ratios are equivalent if their cross products are equal. For example, for the ratios a:b and c:d, they are equivalent if a*d = b*c.

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What is the relationship between the ratios 14:18 and 7:9?

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The ratios 14:18 and 7:9 are equivalent because both can be simplified to the same ratio by dividing by their greatest common divisor.

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What is the ratio of 45:9 in simplest form?

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The ratio 45:9 simplifies to 5:1.

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If a ratio is 4:1, what does this mean in terms of parts?

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A ratio of 4:1 means that for every 4 parts of one quantity, there is 1 part of another quantity.

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How do you create an equivalent ratio by multiplication?

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To create an equivalent ratio by multiplication, multiply both terms of the ratio by the same non-zero number. For example, multiplying the ratio 2:3 by 2 gives the equivalent ratio 4:6.

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What is the equivalent ratio of 2:7 when both terms are multiplied by 7?

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The equivalent ratio of 2:7 when both terms are multiplied by 7 is 14:49.

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Can ratios be expressed in different forms?

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Yes, ratios can be expressed in different forms, such as fractions, decimals, or percentages, while still representing the same relationship.