![]() For instance, the square root of two over the square root of five is considered a complex fraction: In this way 2 1/ 3 can be changed into 7/ 3.Ĭomplex fractions, used in higher mathematics, do not consist of natural numbers. Any mixed fraction can be changed into an improper fraction by multiplying the whole number by the denominator, adding the result to the numerator, and placing the total over the original denominator. Thus all improper fractions are equal to, or larger than, one.Ī mixed fraction, also called a mixed number, consists of a whole number and a fraction, such as 2 1/ 3. In improper fractions, the numerator is equal to, or larger than, the denominator, as 4/ 4 or 6/ 5. Therefore the value of a proper fraction is always less than one. A proper fraction has a numerator smaller than the denominator, such as 3/ 4. There are four kinds of common fractions: proper, improper, mixed, and complex. Not all common fractions, however, can be changed into such precise decimals: 2/ 3 as a decimal is an endless series of sixes to the right of the decimal point. In this way, 3/ 4 can be changed into the decimal 0.75. To change a common fraction into a decimal, one must divide the numerator by the denominator. Thus, 0.85 becomes the common fraction 85/ 100. This means that it is simple to change a decimal fraction into a common fraction by putting the proper denominator under the number to the right of the decimal point. But in decimals, the unwritten denominator is always 10, or some power of 10 such as 100, 1,000, 10,000, and so on. In common fractions, any number may be a denominator. As examples, the decimal 0.075 is read as “seventy-five thousandths,” and the fraction 0.3852 as “three thousand, eight hundred fifty-two ten-thousandths.” If there is only one figure to the right of the decimal point, the fraction is always read as “tenths.” If there are two figures, the fraction is read as “hundredths,” and if there are three, it is read as “thousandths.” In other words, decimal fractions follow the same progression as do whole numbers, where the first digit is in the “tens” column, the second in the “hundreds,” and so forth (see Arithmetic). Sometimes referred to simply as “decimals,” all decimal fractions consist of one or more numbers preceded by a dot called the decimal point: 0.4, for example, is read as four-tenths. When a baker makes a cake, he may use two cups of sugar for every three cups of flour: The ratio is two to three, and it may be expressed as a fraction, 2/ 3.ĭecimal fractions are so called because they are based on the decimal, or base-ten, numbering system (see Numeration Systems and Numbers). For example, the fraction 1/ 2 expresses the ratio of one to two: The relationship of one to two is that one is half of two. What is being expressed in a common fraction is not only a quantity but also a ratio: the relationship of one quantity to another. Any number except zero can be either a denominator or a numerator. In reading a common fraction, the numerator is stated first. In a common fraction, the number below the line is the denominator, and the number above the line is the numerator. These would usually be read as “point four” and “point zero seven.” They express the same amounts. The same numbers, when appearing as decimal fractions, would be 0.4 and 0.07. Common fractions are written as 4/ 10 or 7/ 100: four over ten and seven over one hundred. All fractions are written using the same symbols used to write whole numbers, but the symbols are used in a different way. The only difference between the two is in how they are written. In everyday mathematics there are two types of fractions, common and decimal. Measurements with fractions can often be more precise: it is more exact to say “four and one-tenth gallons” than “a little more than four gallons.” Types of Fractions Fractions are very helpful because they make possible measurements in other than whole numbers such as 1, 2, or 5. One inch is one twelve part, or one-twelfth, of a foot. Each of these segments can be expressed as a fraction. Miles are divided into feet and kilometers into meters. Days are divided into 24 hours and years into 12 months. It has long been convenient and customary to divide things into segments. These pieces are called fractions, from the same Latin word ( fractus, meaning “broken”) that fracture comes from.Īll fractions represent parts of a whole. No matter how the change is made, the dollar is broken up-“fractured”-into several pieces. Be sure to reduce.įor the following 10 problems, convert each complex decimal to a fraction.There are many ways to make change for a dollar: two half-dollars, four quarters, ten dimes, 20 nickels, or 100 pennies. Converting A Complex Decimal to a Fractionįor the following 20 problems, convert each decimal fraction to a proper fraction or a mixed number.Converting an Ordinary Decimal to a Fraction.
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