Question

How can knowing the GCF and LCM help you when you add, subtract, and multiply fractions?

Answer 1

Explanation:

The LCM, or least common multiple, is the smallest number that two other numbers can divide evenly into. The LCM is the basis of the LCD, or least common denominator, which is used while adding and subtracting fractions.

When adding or subtracting fractions, we must have a common denominator. In order to avoid simplifying more than necessary, it is helpful to use the least common denominator, or LCD. This is basically the LCM of the denominators.

The GCF, or greatest common factor, is what we use to simplify fractions. When we finish adding, subtracting or multiplying fractions, we often have a fraction that needs simplified. In order to do this, we want to divide the numerator and denominator by a common factor. However, using small factors results in more work; it is much easier to use the largest factor that will evenly divide into both numbers, or the GCF.

Answer 2

When you add fractions, the denominators must be the same, so you may have to generate equivalent fractions by using the lowest common multiple of all the denominators. For subtraction of fractions, you use the same method. When multiplying fractions, you can only multiply the numerators together, and the denominators together.