Can anyone explain to me how to add fractions with different denominators? I can convert them to decimals, but i need to know how to add them. Anyone?
Sure! I would be happy to explain how to add fractions with different denominators.
To add fractions with different denominators, you first need to find a common denominator. A common denominator is a number that both denominators can evenly divide into.
Here's a step-by-step guide on how to proceed:
1. Find the Least Common Multiple (LCM) of the denominators. The LCM is the smallest number that the denominators can both divide into evenly. For example, if you have fractions with denominators 2 and 3, the LCM would be 6.
2. Convert the fractions so that they have the same denominator (the LCM you found in step 1). To do this, multiply the numerator and denominator of each fraction by the same value that will turn the original denominator into the LCM. For example, if you have 1/2 and 1/3, you would multiply the first fraction by 3/3 and the second fraction by 2/2.
3. Add the numerators of the fractions together since now they have the same denominator.
4. Simplify the resulting fraction, if necessary, by dividing both the numerator and the denominator by their greatest common divisor (GCD) to get the simplest form of the fraction.
5. Optionally, you can convert the fraction back to a decimal if needed.
Here's an example to illustrate this process:
Let's add 1/2 and 1/3.
Step 1: The LCM of 2 and 3 is 6.
Step 2: Convert the fractions to have the same denominator, which is 6:
1/2 = (1 × 3) / (2 × 3) = 3/6
1/3 = (1 × 2) / (3 × 2) = 2/6
Step 3: Add the numerators of the fractions: 3/6 + 2/6 = 5/6
Step 4: The fraction 5/6 is already in its simplest form, so no further simplification is needed.
So, the sum of 1/2 and 1/3 is 5/6.
Adding fractions with different denominators can be quite simple once you find a common denominator. Remember to simplify your answer if possible, and convert it to a decimal if needed.