# What method do you prefer to use when adding or subtracting fractions and mixed numbers? For example, do you find common denominators first, convert fractions into decimals and then back into fractions, or simplify fractions first and then add or subtract them?

Explain why you prefer to use this method.

Give at least one example of using this method.

As you learn new strategies throughout the unit, you may change which method you prefer to use. If that happens, explain why you changed your preferred method.

Be sure to comment on at least two classmates’ comments as well.

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## The method used for hundreds of years

1. get rid of those useless mixed numbers and simply fractions if possible
2. find a common denominator
3. change your fractions to ones having that new denominator
5. Simplify your fractions to lowest terms

all done!

e.g. 4 1/3 + 3/7 - 6/4
= 13/3 + 3/7 - 3/2 , your LCD is 42
= 182/42 + 18/42 - 63/42
= 137/42

changing it to decimals and then doing the calculation, and finally going
back to fractions is not a good idea.
In my example, 3/7 would not have given you an exact decimal,
and right away you have lost accuracy.
I would only consider doing that if the fractions are easily converted to
decimals, e.g. 2/5, 1/4 etc

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## When adding or subtracting fractions and mixed numbers, there are multiple methods you can use. The method I prefer is finding common denominators first, as it simplifies the process and allows for straightforward addition or subtraction.

Here's why I prefer this method:
1. Efficiency: Finding common denominators allows you to directly add or subtract the numerators, which simplifies the calculation. It avoids the need to convert fractions into decimals and back into fractions, which can be time-consuming.
2. Accuracy: By finding common denominators, you are working with fractions that have the same base, making it easier to ensure accuracy in your calculations.
3. Convenience: When dealing with mixed numbers, finding a common denominator makes it simpler to handle the whole numbers and the fractions separately.

Here's an example of using the common denominator method:
Suppose we have to add 2/3 and 5/8.

Step 1: Find the least common denominator (LCD) of the fractions 3 and 8. In this case, the LCD is 24.

Step 2: Adjust the fractions to have the same denominator of 24.
2/3 becomes 16/24 (multiply the numerator and denominator by 8)
5/8 remains 5/8 since the denominator is already 8.

Now we have the fractions 16/24 and 5/24 with the same denominator.

Step 3: Add the numerators and keep the same denominator.
16/24 + 5/24 = 21/24

Step 4: Simplify the fraction if necessary. In this case, we can simplify 21/24 to 7/8.

Therefore, 2/3 + 5/8 = 7/8 using the common denominator method.

As you learn new strategies, you may change your preferred method based on personal preference or the specific requirements of the problem at hand. It's important to choose a method that you feel comfortable with and ensures accuracy in your calculations.

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