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. In the fraction 34, 3 is the numerator and 4 is the denomi-nator. In any fraction, the numerator is being divided by the denominator. So in the previous example, 3 is being divided by 4.• A mixed numberis an integer together with a fraction, such as235. The integer is the integral part, and the fraction is the fractional part.• An improper fractionis one in which the numerator is equal to or greater than the denominator, such as 196, 254, or 1010.In a fraction problem, the whole quantity is 1, which can be expressed by a fraction in which the numerator and denominator are the same number. For example, if a problem involves 18of a quantity, the whole quantity is 88, or 1.Rules to Know: Fractions and Mixed NumbersIf you understand the rules outlined in this section, you’ll be able to solve any arithmetic problem that involves fractions and mixed numbers. Study the rules and example problems, and be sure that you understand each rule before moving on to the practice exercises.
228PART V: Arithmetic AbilityMaster the™ Civil Service ExamsConverting Mixed Numbers and Improper FractionsTo solve fraction problems, it’s often helpful to convert mixed numbers to improper fractions. To do so, follow these three steps:10. Multiply the denominator of the fraction by the integer.11. Add the numerator to this product.12. Place this sum over the denominator.Change 347to an improper fraction using these steps:• 7 (denominator) × 3 (integer) = 21• 21 (product) + 4 (numerator) = 25• The answer is 257.To convert an improper fraction to a mixed number, reverse the process and follow these two steps:1. Divide the numerator by the denominator. The quotient, disregarding the remainder, is the integral part of the mixed number.2. Place the remainder, if any, over the denominator. This is the fractional part of the mixed number.Change 3613to a mixed number using these steps:• 36 (numerator) ÷ 13 (denominator) = 2 with a remainder of 10• The answer is 21013.Reducing FractionsThe numerator and denominator of a fraction can be changed by dividing both by the same number, without affecting the value of the fraction. This process is called reducing the fraction. A fraction that has been reduced as much as possible is said to be in lowest terms.For example, the value of the fraction 312is not altered if both the numerator and denominator are divided by 3, resulting in 14. Likewise, if 630is reduced to lowest terms (by dividing both the numerator and denominator by 6), the result is 15.Finding the Least Common DenominatorFractions can’t be added or subtracted unless the denominators are all the same. To convert all frac-tions to have the same denominator, you must first find the least common denominator. The least common denominator (LCD) is the lowest number that can be divided evenly by all the given denominators. If no two of the given denominators can be divided by the same number, the LCD is the product of all the denominators.
Chapter 15: Fractions and Decimals229
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Physics, Federal government of the United States, Civil service, United States civil service