Ratios and Equivalent Ratios

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What is a ratio?

Back

A ratio is a comparison of two quantities by division, showing how many times one value contains or is contained within the other.

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How do you write a ratio?

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Ratios can be written in three ways: using a colon (e.g., 3:2), as a fraction (e.g., 3/2), or with the word 'to' (e.g., 3 to 2).

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What are equivalent ratios?

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Equivalent ratios are ratios that express the same relationship between two quantities, even if the numbers are different (e.g., 1:2 and 2:4).

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How can you find equivalent ratios using multiplication?

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To find equivalent ratios using multiplication, multiply both terms of the ratio by the same non-zero number (e.g., for 2:3, multiplying by 2 gives 4:6).

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How can you find equivalent ratios using division?

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To find equivalent ratios using division, divide both terms of the ratio by the same non-zero number (e.g., for 4:6, dividing by 2 gives 2:3).

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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 quantities are expressed in their lowest terms, meaning they have no common factors other than 1 (e.g., 4:8 simplifies to 1:2).

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If the ratio of apples to oranges is 3:5, how many oranges are there if there are 9 apples?

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There are 15 oranges. (Using the ratio 3:5, if 3 parts represent 9 apples, then 5 parts represent 15 oranges.)

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What is the relationship between ratios and fractions?

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Ratios can be expressed as fractions, where the first quantity is the numerator and the second quantity is the denominator (e.g., the ratio 3:4 can be written as 3/4).

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How do you solve for an unknown in a ratio?

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To solve for an unknown in a ratio, set up a proportion and cross-multiply to find the missing value.

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What is a proportion?

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A proportion is an equation that states that two ratios are equal (e.g., 1:2 = 2:4).