common denominator
In mathematics, a common denominator refers to a shared multiple of the denominators of two or more fractions
In mathematics, a common denominator refers to a shared multiple of the denominators of two or more fractions. It is crucial when performing operations on fractions, such as addition or subtraction.
To find a common denominator, you need to identify the least common multiple (LCM) of the denominators. The LCM is the smallest positive integer that is divisible by each denominator without leaving a remainder.
Let’s work through an example to illustrate the concept:
Consider the fractions 1/3 and 2/5. To find a common denominator, we need to determine the LCM of 3 and 5.
First, let’s find the multiples of each denominator:
Multiples of 3: 3, 6, 9, 12, 15, 18, …
Multiples of 5: 5, 10, 15, 20, 25, 30, …
From the multiples listed above, we can see that 15 is the smallest number that appears in both lists. Therefore, the common denominator for 1/3 and 2/5 is 15.
To convert the fractions to have a common denominator of 15, we multiply the numerator and denominator of each fraction by the appropriate value. For 1/3, we multiply numerator and denominator by 5, and for 2/5, we multiply numerator and denominator by 3.
1/3 * 5/5 = 5/15
2/5 * 3/3 = 6/15
Now that both fractions have the common denominator 15, we can easily perform operations on them. For example, if we wish to add them:
5/15 + 6/15 = (5 + 6)/15 = 11/15
In conclusion, a common denominator is a shared multiple of the denominators of two or more fractions. It is found by determining the least common multiple (LCM) of the denominators. The common denominator allows us to perform arithmetic operations on fractions.
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