SAT Math For Dummies with Online Practice. Mark Zegarelli

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SAT Math For Dummies with Online Practice - Mark  Zegarelli


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      When a pair of fractions have different denominators, you need to get the denominators the same — that is, find a common denominator for both fractions. In some cases, you can do this by increasing the lesser denominator to the greater one. For example:

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      In other cases, you need to increase the denominators of both fractions. For example:

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      Multiplying and dividing fractions

      Multiplying and dividing fractions is often easier than adding or subtracting them, because you don’t need to find a common denominator.

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      In some cases, you can make multiplying fractions easier by canceling pairs of equivalent factors in the numerator and denominator. For example, when multiplying math and math, begin by canceling a factor of 4 in both the numerator and denominator:

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      Next, cancel a factor of 5:

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      Now when you multiply, the result is already the most simplified form of the answer:

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      To divide one fraction by another, change the division to multiplication using the mnemonic Keep-Change-Flip: Keep the first fraction as it is, Change the division sign to a multiplication sign, and Flip the second fraction to its reciprocal. For example:

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      As when multiplying fractions, you can sometimes make dividing fractions easier by canceling common factors in both the numerator and denominator. Be careful to cancel factors after changing the division to multiplication. For example, when dividing math by math, begin by using Keep-Change-Flip:

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      Now, cancel a common factor of 2 in both the numerator and denominator:

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      To complete the problem, multiply:

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      Connecting fractions and ratios

      Once you understand how fractions work, you can easily grasp the related concept of a ratio, which is a measurement of the relative sizes of two numbers. For example, if you know that a pet store has a math (or 1-to-3) ratio of dogs to cats, you know that the number of dogs is math the number of cats.

      Transforming a ratio to its related fraction in this way is often a good first step when answering SAT questions that involve ratios.

      I discuss ratios, plus the related concept of proportional equations, in Chapter 7.

      Review of decimals and percentages

      Like fractions and ratios, decimals and percentages are two common ways to represent rational numbers that aren’t integers. On the SAT, you’ll probably need to convert decimals to percentages, and vice versa. In this section, I review this relatively simple process.

      Converting decimals to percentages

      To change a decimal to a percentage, move the decimal point two places to the right and attach a percent sign. For example:

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      As you can see from the last example, after changing a decimal to a percentage, you can safely drop unnecessary leading zeros.

      In some cases, you may need to include one or more place-holding zeros in the percentage that you create. For example:

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