Addition, subtraction, multiplication and division of fractions

To add fractions having the same denominator (like fractions) add their numerators and write the sum over the common denominator (do not add the denominators). Reduce the Resulting fraction to lowest terms.

To add fractions having different denominators (unlike fractions) the fractions must be changed¹ to equivalent fractions which have the same or a common denominator. The least number which will be a common denominator, for example, of 2/3 and 3/5 is 15. 15 is the least common denominator, or lowest common denominator of 2/3 and 3/5. The least common denominator is sometimes denoted by the letters L.C.D.

To subtract fractions having the same denominator subtract the numerators and write the difference over the common denominator (do not subtract denominators).

To subtract fractions having different denominators first change the fractions to equivalent fractions having a common denominator. To subtract the fractions when they have a common denominator, subtract the numerators and write the difference over the denominator.

To multiply a mixed number and a fraction: 1) reduce the fraction to its lowest terms; 2) change the mixed number to an improper fraction; 3) multiply the two numerators to obtain the numerator of the answer; 4) multiply the denominators to obtain the denominator of the answer; 5) reduce the fraction obtained when possible. Reduction can be done by dividing a numerator and denominator by the same number. The numbers that are divided are crossed out, and the quotients are written as the new numerator and the new denominator.

To divide a whole number by a fraction, multiply the whole number by the denominator of the fraction and divide the result by the numerator of the fraction.

Note:

¹ must be changed - должны быть превращены.