How do the GCF, divisibility and LCM connect to fractions
lets say you're doing addition
1/5 + 1/2
you can't add them directly until you find the common denominator. You can use LCM(lowest common multiple)
for these it is ten.
so
2/10 + 5/10 = your anwer
Thank you, Angel
The Greatest Common Factor (GCF), divisibility, and the Least Common Multiple (LCM) are all concepts that connect to fractions in different ways.
1. GCF and Fractions:
The GCF is the largest number that can divide two or more numbers evenly. When it comes to fractions, finding the GCF of the numerators and the denominators can simplify the fraction. By dividing both the numerator and the denominator of a fraction by their GCF, you can reduce the fraction to its simplest form.
For example, consider the fraction 12/24. The GCF of 12 and 24 is 12. By dividing both the numerator and denominator by 12, the fraction simplifies to 1/2.
2. Divisibility and Fractions:
Divisibility rules determine whether one number can be divided by another without leaving a remainder. When dealing with fractions, divisibility rules can help identify if a fraction is simplified or not.
For instance, if the numerator and denominator have a common factor other than 1, the fraction can be simplified further. Therefore, by applying the divisibility rules to the numerator and denominator, you can determine if the fraction can be further reduced.
3. LCM and Fractions:
The Least Common Multiple (LCM) is the smallest number that is divisible by two or more numbers. When working with fractions, the LCM plays a role in finding a common denominator for addition, subtraction, or comparison of fractions.
To add or subtract fractions, you need to have a common denominator. By finding the LCM of the denominators, you can determine the least common multiple for the fractions which allows for easier addition or subtraction.
For example, if you need to add 1/4 and 2/3, first find the LCM of 4 and 3, which is 12. Then, convert both fractions to have a denominator of 12 (1/4 = 3/12, and 2/3 = 8/12), making it possible to add them together: 3/12 + 8/12 = 11/12.
In summary, the GCF helps simplify fractions, divisibility rules assist in determining if fractions can be simplified further, and the LCM aids in finding a common denominator for adding or subtracting fractions. These concepts all connect to fractions, making it easier to manipulate and compare them.