How do you add fractions with different denominators? This is a common question among students learning basic mathematics. Adding fractions with different denominators can seem daunting at first, but with the right approach, it becomes a straightforward process. In this article, we will explore the steps involved in adding fractions with different denominators and provide some practical examples to help you master this skill.
Adding fractions with different denominators requires a few key steps. First, you need to find a common denominator, which is a number that both denominators can be divided by evenly. Once you have a common denominator, you can convert each fraction to an equivalent fraction with the common denominator. Finally, you can add the numerators of the equivalent fractions and place the sum over the common denominator to get your final answer.
To find a common denominator, you can use the least common multiple (LCM) of the two denominators. The LCM is the smallest number that is a multiple of both denominators. For example, if you are adding the fractions 1/3 and 1/4, you would find the LCM of 3 and 4, which is 12. This means that both 3 and 4 are factors of 12, so you can use 12 as the common denominator for the two fractions.
Once you have the common denominator, you need to convert each fraction to an equivalent fraction with that denominator. To do this, you can multiply the numerator and denominator of each fraction by a number that will make the denominator equal to the common denominator. For example, to convert 1/3 to an equivalent fraction with a denominator of 12, you would multiply both the numerator and denominator by 4 (since 3 x 4 = 12). This gives you 4/12.
Now that both fractions have the same denominator, you can add the numerators and place the sum over the common denominator. Using our previous example, you would add 4/12 and 3/12 to get 7/12. This is your final answer.
Let’s look at another example to illustrate this process. Suppose you want to add the fractions 2/5 and 3/10. First, you find the LCM of 5 and 10, which is 10. Then, you convert 2/5 to an equivalent fraction with a denominator of 10 by multiplying both the numerator and denominator by 2 (since 5 x 2 = 10). This gives you 4/10. Now, you can add 4/10 and 3/10 to get 7/10, which is your final answer.
In conclusion, adding fractions with different denominators involves finding a common denominator, converting each fraction to an equivalent fraction with that denominator, and then adding the numerators. By following these steps, you can easily add fractions with different denominators and improve your math skills. Practice with various examples will help you become more proficient in this area.
