How to bring to a common denominator?
In order to add or subtract fractions, they must first be reduced to a common denominator. How to do it? To find the lowest common denominator for fractions, you must perform the following steps.
The scheme to bring to a common denominator
- It is necessary to determine which will be the least common multiple of the denominators of fractions. If you are dealing with a mixed or integer number, then you must first turn it into a fraction, and only then determine the least common multiple. To turn an integer into a fraction, you need to write the number itself in the numerator, and the number in the denominator. For example, the number 5 in the form of a fraction would look like this: 5/1. To turn a mixed number into a fraction, you need to multiply an integer by the denominator and add the numerator to it. Example: 8 whole and 3/5 as a fraction = 8x5 + 3/5 = 43/5.
- After that, it is necessary to find an additional factor, which is determined by dividing the NOZ by the denominator of each fraction.
- The last step is to multiply the fraction by an additional factor.
It is important to remember that the reduction to a common denominator is necessary not only for addition or subtraction. To compare several fractions with different denominators, it is also necessary to first bring each of them to a common denominator.
Reduction of fractions to a common denominator
In order to understand how to bring a fraction to a common denominator, it is necessary to understand some properties of fractions. So, an important property used to reduce to the NOZ is the equality of fractions. In other words, if the numerator and denominator of a fraction are multiplied by a number, the result is a fraction equal to the previous one. As an example, we give the following example. In order to bring the fractions 5/9 and 5/6 to the lowest common denominator, you need to perform the following steps:
- We first find the least common multiple of the denominators. In this case, for the numbers 9 and 6, the NOC will be equal to 18.
- We determine the additional factors for each of the fractions. This is done as follows. We divide the LCM by the denominator of each fraction, resulting in 18: 9 = 2, and 18: 6 = 3. These numbers will be additional factors.
- We give two fractions to NOZ.Multiplying the fraction by the number, you need to multiply both the numerator and the denominator. Fraction 5/9 can be multiplied by an additional factor of 2, with the result that a fraction equal to this one is obtained - 10/18. We do the same with the second fraction: we multiply 5/6 by 3, with the result that we get 15/18.
As you can see from the above example, both fractions were reduced to the lowest common denominator. To finally understand how to find a common denominator, it is necessary to master another property of fractions. It lies in the fact that the numerator and denominator of the fraction can be reduced by the same number, which is called the common divisor. For example, the fraction 12/30 can be reduced to 2/5, if you divide it by a common divisor - the number 6.