Adding Fractions with Unlike Denominators

Study Notes

Adding Fractions with Unlike Denominators

Common denominators are necessary to add fractions; bottom numbers must be the same.
Finding the least common multiple (LCM) of denominators helps in determining the common denominator.
Multiples of 9: 9, 18, 27, 36
Multiples of 3: 3, 6, 9; Common multiple found is 9, which is the LCM.
Example:
- For 4/9: Already has a denominator of 9, remains as 4/9.
- For 1/3: Convert by multiplying both numerator and denominator by 3 to get 3/9.
After renaming, add the numerators: 4 + 3 = 7; keep denominator as 9.
Final result: 7/9, which is already in simplest form (only common factor is 1).

Second Example

New problem: 3/10 + 2/6.
Multiples of 10: 10, 20, 30, 40.
Multiples of 6: 6, 12, 18, 24; extend to find common multiple which is 30.
Convert:
- For 3/10: Multiply numerator and denominator by 3 for equivalent 9/30.
- For 2/6: Multiply both by 5 to convert to 10/30.
Add the new fractions: 9 + 10 = 19; keep denominator as 30.
Final result: 19/30, also in simplest form (only common factor is 1).

Conclusion

Steps to add fractions:
- Find a common denominator (use LCM).
- Rename fractions with that common denominator.
- Add numerators and keep the common denominator.
- Simplify the result if possible.
Additional resources and links provided for further understanding of multiples and LCM.

Adding Fractions with Unlike Denominators

A common denominator is essential for adding fractions; both denominators need to be identical.
The least common multiple (LCM) of the denominators is used to establish the common denominator.
For fractions with denominators of 9 and 3, the LCM is 9, as multiples of 9 include 9, 18, 27, 36, and multiples of 3 include 3, 6, 9.
In the example of 4/9, no conversion is necessary since the denominator is already 9.
To convert 1/3 to a fraction with a denominator of 9, multiply both the numerator and denominator by 3, resulting in 3/9.
After renaming fractions, add the numerators: 4 + 3 = 7, while maintaining the denominator of 9.
The sum, 7/9, is in its simplest form with no common factors other than 1.

Second Example

In a new problem involving 3/10 and 2/6, establish a common denominator by finding the LCM.
Multiples of 10 include 10, 20, 30, and 40, while multiples of 6 are 6, 12, 18, and 24; the LCM here is 30.
For 3/10, convert it to 9/30 by multiplying both numerator and denominator by 3.
For 2/6, converting involves multiplying both parts by 5 to achieve 10/30.
Add the converted fractions by summing the numerators: 9 + 10 = 19, while keeping the denominator at 30.
The final result of 19/30 is also in the simplest form, as the only common factor is 1.

Conclusion

Steps for adding fractions with unlike denominators include:
- Determine a common denominator through the least common multiple (LCM).
- Rename each fraction using the identified common denominator.
- Add numerators while keeping the denominator the same.
- Simplify the final fraction if possible to its lowest terms.
Additional resources are available for further understanding of multiples and LCM concepts.

Description

This quiz focuses on the essential steps to add fractions with different denominators. It covers finding the least common multiple (LCM) of the denominators and converting the fractions accordingly. Test your understanding of how to effectively add fractions by making their denominators the same.