Fraction OperationsA fraction compares 2 numbers through division. Come conduct basic operations, store in mental that any kind of number except 0 split by chin is 1, and 1 times any number is itself. The is, , and 1 × 5 = 5. Thus, any number split or multiplied by a fraction equal to one will be itself. Because that example, and also .

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When multiplying fractions, the molecule (top numbers) room multiplied together and the denominators (bottom numbers) space multiplied together. Therefore . And also .

To division fractions, rewrite the difficulty as multiply by the mutual (multiplicative inverse) that the divisor. For this reason .

To include fractions that have actually the same, or a common, denominator, simply include the numerators, and use the usual denominator. The figure listed below illustrates why this is true.

However, fractions can not be included until they are written with a common denominator. The figure listed below shows why including fractions with different denominators is incorrect.

To correctly add ½ and ⅓, common denominator must very first be found. Usually, the least usual multiple of the platform (also dubbed the least typical denominator) is the best choice for the typical denominator. In the instance below, the least typical multiple the the 2 denominators—2 and 3—is 6, therefore the least typical denominator is 6. To convert the fractions, multiply ½ through (which is indistinguishable to 1) to gain . Similarly, multiply ⅓ through (which is tantamount to 1) to obtain .



So , or

To version this trouble visually, divide a rectangle right into halves horizontally, then right into thirds vertically, developing six equal parts (see the number below). Shade one-half in color to show ½, and also then shade one-third in gray to show ⅓. Since, together the figure shows, the top left square has been shaded twice, it must be "carried" (see arrow). Now 5 of six squares are shaded; therefore, .

Subtraction of fractions is comparable to addition, in the the fractions gift subtracted must have actually a typical denominator. Therefore .

see likewise Fraction.

Stanislaus Noel Ting

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