Ratios and Proportions

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What is a ratio?
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A ratio is a comparison of two quantities by division.
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How can a ratio be expressed?
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A ratio can be expressed in three ways: using the colon (a:b), as a fraction (a/b), or in words (a to b).
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What is a proportion?
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A proportion is an equation that states that two ratios are equal.
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If the ratio of apples to oranges is 3:4, how many apples are there if there are 8 oranges?
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There are 6 apples because 3/4 = x/8, so x=6.
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How do you solve a proportion like 2/3 = x/9?
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Cross-multiply to get 2×9 = 3x, then solve for x to get x = 6.
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What is the concept of equivalent ratios?
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Equivalent ratios are different ratios that represent the same relationship.
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How can you create an equivalent ratio to 5:10?
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By multiplying or dividing both terms by the same number. For example, multiply both by 2 to get 10:20.
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What is a real-life example of using ratios?
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Mixing paint colors in a specific ratio to achieve a desired shade.
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Describe the role of proportions in cooking recipes.
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Proportions are used to scale recipes up or down while maintaining the same ratio of ingredients.
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What are the four terms in a proportion called?
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First term, second term (antecedents), third term, and fourth term (consequents).
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How do you determine if two ratios form a proportion?
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Check if the cross products of the ratios are equal.
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What is an aspect of scaling in art that involves ratios?
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Aspect ratio in image resizing, where the ratio of width to height is maintained.
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How can errors in proportion affect real-world structures?
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Incorrect proportions can lead to structural failures, such as in architecture or engineering.
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What is the ratio of the sides of a triangle with sides measuring 3 cm, 4 cm, and 5 cm?
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The ratio is 3:4:5.
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How is understanding proportions useful in business?
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Proportions are used in financial analysis, such as calculating profit margins and cost ratios.
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