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 because they both represent the same proportion.

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How do you simplify a ratio?

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To simplify a ratio, divide both terms of the ratio by their greatest common divisor (GCD). For example, to simplify the ratio 20:25, divide both numbers by 5 to get 4:5.

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What is the relationship between ratios and fractions?

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Ratios can be expressed as fractions. For example, the ratio 4:5 can be written as the fraction 4/5, which represents the same relationship between the two quantities.

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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, to check if 3:5 and 6:10 are equivalent, calculate 3*10 and 5*6. Since both products equal 30, the ratios are equivalent.

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What is the formula for finding equivalent ratios?

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To find equivalent ratios, multiply or divide 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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If a recipe calls for 4 cups of sugar for every 5 cups of flour, what is the ratio of sugar to flour?

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The ratio of sugar to flour is 4:5.

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How do you find the total number of items in a ratio problem?

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To find the total number of items in a ratio problem, add the parts of the ratio together and then use that sum to find the total based on the given quantities.

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What is the GCD and how is it used in simplifying ratios?

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The GCD, or greatest common divisor, is the largest number that divides two or more numbers without leaving a remainder. It is used to simplify ratios by dividing both terms of the ratio by the GCD.

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What is the significance of the order of terms in a ratio?

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The order of terms in a ratio is significant because it indicates the relationship between the two quantities. For example, the ratio 4:5 is not the same as 5:4.

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How can you express a ratio in different forms?

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A ratio can be expressed in different forms, such as a fraction, a decimal, or a percentage. For example, the ratio 1:4 can be expressed as 1/4 or 0.25.