75 parts per million (ppm), means that the proportion is 75/1,000,000. Whether common fractions or decimal fractions are used is often a matter of taste and context. Common fractions are used most often when the denominator is relatively small. By mental calculation, it is easier to multiply 16 by 3/16 than to do the same calculation using the fraction's decimal equivalent (0.1875). And it is more accurate to multiply 15 by 1/3, for example, than it is to multiply 15 by any decimal approximation of one third. Monetary values are commonly expressed as decimal fractions with denominator 100, i.e., with two decimals, for example $3.75. However, as noted above, in pre-decimal British currency, shillings and pence were often given the form (but not the meaning) of a fraction, as, for example, "3/6" (read "three and six") meaning 3 shillings and 6 pence, and having no relationship to the fraction 3/6. Mixed numbers A mixed numeral (also called a mixed fraction or mixed number) is a traditional denotation of the sum of a non-zero integer and a proper fraction (having the same sign). It is used primarily in measurement: inches, for example. Scientific measurements almost invariably use decimal notation rather than mixed numbers. The sum can be implied without the use of a visible operator such as the appropriate "+". For example, in referring to two entire cakes and three quarters of another cake, the numerals denoting the integer part and the fractional part of the cakes can be written next to each other as instead of the unambiguous notation Negative mixed numerals, as in , are treated like Any such sum of a whole plus a part can be converted to an improper fraction by applying the rules of adding unlike quantities. This tradition is, formally, in conflict with the notation in algebra where adjacent symbols, without an explicit infix operator, denote a product. In the expression , the "understood" operation is multiplication. If is replaced by, for example, the fraction , the "understood" multiplication needs to be replaced by explicit multiplication, to avoid the appearance of a mixed number. When multiplication is intended, may be written as or or An improper fraction can be converted to a mixed number as follows: Using Euclidean division (division with remainder), divide the numerator by the denominator. In the example, , divide 11 by 4. 11 ÷ 4 = 2 remainder 3. The