thirds of one quarter. Thus two thirds times three quarters is six twelfths. A short cut for multiplying fractions is called "cancellation". Effectively the answer is reduced to lowest terms during multiplication. For example: A two is a common factor in both the numerator of the left fraction and the denominator of the right and is divided out of both. Three is a common factor of the left denominator and right numerator and is divided out of both. Multiplying a fraction by a whole number Since a whole number can be rewritten as itself divided by 1, normal fraction multiplication rules can still apply. This method works because the fraction 6/1 means six equal parts, each one of which is a whole. Multiplying mixed numbers When multiplying mixed numbers, it is considered preferable to convert the mixed number into an improper fraction. For example: In other words, is the same as , making 11 quarters in total (because 2 cakes, each split into quarters makes 8 quarters total) and 33 quarters is , since 8 cakes, each made of quarters, is 32 quarters in total. Division To divide a fraction by a whole number, you may either divide the numerator by the number, if it goes evenly into the numerator, or multiply the denominator by the number. For example, equals and also equals , which reduces to . To divide a number by a fraction, multiply that number by the reciprocal of that fraction. Thus, . Converting between decimals and fractions To change a common fraction to a decimal, do a long division of the decimal representations of the numerator by the denominator (this is idiomatically also phrased as "divide the denominator into the numerator"), and round the answer to the desired accuracy. For example, to change to a decimal, divide by (" into "), to obtain . To change to a decimal, divide by (" into "), and stop when the desired accuracy is obtained, e.g., at decimals with . The fraction can be written exactly with two decimal digits, while the fraction cannot be written exactly as a decimal with a finite number of digits. To change a decimal to a fraction, write in the denominator a followed by as many zeroes as there are digits to the right of the decimal point, and write in the numerator all the digits of the original decimal, just omitting the