A fraction is a mathematical expression that states the ratio between two numbers. The adjective common in the term common fraction means that both numbers involved are integers, or whole numbers. The common fraction ¾ can be thought of as the whole number 3 being compared to the whole number 4 in some way or another. A common fraction is generally written with the two numbers separated by a diagonal or horizontal line, as ¾. The number above the line is the numerator of the fraction, and the number below the line, the denominator of the fraction. The diagonal or horizontal line separating the numerator and denominator is mathematically equivalent to the division sign (÷) or the ratio sign (:).

The fraction "3 compared to 4," or ¾, can be interpreted in many ways. At a beginning level, one can imagine a whole object—such as a pie—divided into four parts. The common fraction ¾, in this instance, refers to 3 parts out of 4. The 4 in the fraction "¾, of a pie" refers to the total number of parts into which the pie is divided. The 3 refers to the number of pieces being considered. Thus, ¾ means 3 of the 4 pieces cut from one whole pie.

Another way of interpreting fractions is to think of the denominator as a number of whole parts and the numerators as some selection of those parts. In this case, ¾ could refer to a set of 4 pies, 3 of which are being considered. In this case, ¾ means "3 pies out of a complete set of 4 pies."

Yet a third way of thinking about a fraction is as a division problem. The common fraction ¾ also means the number 3 divided by the number 4. Treating a common fraction as a division problem results in the formation of another kind of fraction, a decimal fraction. A decimal fraction is a fraction whose denominator is 10, 100, 1,000, or some other multiple of 10.

Dividing 3 by 4 results in 0.75. The number 0.75 is a decimal fraction because it can be thought of as a fraction whose denominator is 100. That is, 0.75 also can be expressed as the common fraction

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Denominator:
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The bottom number in a fraction; the number of parts into which the
whole has been divided.

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Equivalent fractions:
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Two or more fractions with different numerators and denominators but
the same numerical value.

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Improper fraction:
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A fraction in which the numerator is greater than the denominator.

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Numerator:
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The top number in a fraction; that part of a fraction that tells how
many parts of the whole are being dealt with.

Fractions are numbers that can be manipulated according to the same rules as those used for whole numbers, such as addition, subtraction, multiplication, and division. Fractions are of immense use in mathematics and physics (the science of matter and energy) and in the application of these studies to modern technology. They are used in everyday life as well, for instance when baking a cake or selecting a nut to screw into a bolt.

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