How would I describe a step-by-step procedure for adding two fractions with different denominators?
The first thing you need to do is make the denominators the same. You do this by finding their lowest common multiple. We'll use this as an example:
(2/3)+(3/8)
The first multiple of eight that three can evenly divide into is 24. So, we change each denominator to 24, also multiplying each numerator by the number we had to multiply the denominator by to reach 24 (I hope that made sense, I can't think of a better way to articulate it). We end up with:
(16/24)+(9/24)
Add the numerators; the denominator remains the same:
25/24
1 1/24
To describe a step-by-step procedure for adding two fractions with different denominators, follow these steps:
Step 1: Find the lowest common multiple (LCM) of the denominators.
- To find the LCM, list the multiples of both denominators and find the smallest one that is common to both.
Step 2: Rewrite each fraction with the new common denominator.
- Multiply the numerator and denominator of each fraction by the same factor necessary to make the denominator equal to the LCM obtained in Step 1.
Step 3: Add the numerators and keep the denominator the same.
- Add the numerators of the fractions obtained in Step 2. The denominator remains the same.
Step 4: Simplify the fraction, if necessary.
- If the numerator and denominator have a common factor, divide both by that factor to simplify the fraction.
Step 5: If applicable, convert the improper fraction to a mixed number.
- If the numerator is greater than or equal to the denominator, divide the numerator by the denominator to find the whole number part. The remainder becomes the numerator of the proper fraction part.
For example, let's use the fractions (2/3) + (3/8):
Step 1: The LCM of 3 and 8 is 24.
Step 2: Rewrite the fractions:
- (2/3) becomes (16/24) since 24 divided by 3 is 8, and multiplying the numerator 2 by 8 gives 16.
- (3/8) becomes (9/24) since 24 divided by 8 is 3, and multiplying the numerator 3 by 3 gives 9.
Step 3: Add the numerators while keeping the denominator:
- (16/24) + (9/24) = 25/24
Step 4: Since the fraction 25/24 cannot be simplified further, we move to step 5.
Step 5: Convert the improper fraction to a mixed number:
- 25 divided by 24 is equal to 1 with a remainder of 1. So the final result is 1 1/24.
To describe a step-by-step procedure for adding two fractions with different denominators, here's what you would do:
1. Identify the denominators of the fractions you want to add.
2. Find the lowest common multiple (LCM) of the two denominators. This is the smallest number that both denominators can evenly divide into.
3. Rewrite each fraction so that the denominator matches the LCM.
4. To do this, multiply the numerator and denominator of each fraction by the same number that was used to find the LCM. This is done to keep the value of the fraction the same while changing the denominator.
5. After rewriting both fractions with the new denominators, add the numerators together while keeping the denominator the same.
6. Simplify the fraction, if possible, by reducing it to its simplest form. This may involve dividing both the numerator and the denominator by their greatest common factor.
7. If the numerator is larger than or equal to the denominator, convert the improper fraction to a mixed number.
By following these steps, you should be able to accurately add two fractions with different denominators.