When performing arithmetic operations with simple fractions, the question inevitably arises of how to add them or subtract them from one another, if the denominators contain different numbers? It is necessary to bring the fractions to some general form so that it is clear which parts of the whole number are added or subtracted. That is, it is necessary to bring the fractions to the lowest common denominator.
It is necessary
- - paper;
- - pen or pencil;
- - calculator.
Instructions
Step 1
Write out an example. Let's say you want to add the fractions 2 / a and 5 / b. Any numbers can be used instead of letters. See what is in the numerator and denominator of each fraction and if one of them or both can be canceled. It is advisable to do this in any case, regardless of whether the result of this action is the same denominators or not. For example, if you need to add 1/3 and 4/6, you need to reduce the second fraction. Remember the abbreviation rule. The numerator and denominator must be divided by the same number. In the given example, they are divided by 2. It turns out that 4/6 = 2/3, that is, it is necessary to add 2/3 to 1/3. The result is one.
Step 2
If the fractions do not cancel, or as a result of this action, different denominators are obtained, it is necessary to find a common one. Remember the property of a fraction, according to which its value does not change if the upper and lower parts are multiplied by the same number. This number is called the complementary factor. Find it for the fractions 2 / a and 5 / b. In this case, it is necessary to multiply the denominators, that is, the additional factor will be equal to a * b.
Step 3
Calculate by what number you need to multiply each of the fractions to get the same denominators. For the first fraction, this will be the number b, for the second, the number a. Thus, each fraction can be represented as 2 / a = 2b / ab; 5 / b = 5a / ab. In this case, you can already find the sum or difference of fractions. Sum m = 2b / ab + 5a / ab = (2b + 5a) / ab. In exactly the same way, the common denominator for three or more fractions is found.
Step 4
For computational convenience, fractions usually lead to the lowest common denominator. It is equal to the least common multiple of the numbers in the denominators of all data in the conditions of the problem of fractions. Remember how the least common multiple is calculated. It is the smallest number divisible by all of the original numbers. To do this, factor each number into prime factors. To calculate the least common multiple, you need to multiply them. Each prime factor must be taken as many times as it occurs in the number where there is most of it. For example, if you need to find the least common multiple of 10, 16, and 26, expand them as follows. 10 = 2 * 5.16 = 2 * 2 * 2 * 2.26 = 2 * 13. LCM = 5 * 2 * 2 * 2 * 2 * 13 = 1040. From this example, you can see that the prime factor 2 must be taken as many times as the number 16 is expanded.
