Question

1. find the lcd and the gcf for the word problem below. when the fraction is in its simplest form, select gcf = 1. shanika gained 3\frac{3}{7} pounds. sebastian gained 5\frac{1}{14} pounds. what was their total weight gain?

Explanation:

Step1: Identify the denominators

The fractions are $\frac{3}{7}$ and $\frac{1}{14}$. The denominators are 7 and 14.

Step2: Find the Least - Common Denominator (LCD)

Since 14 is a multiple of 7 (i.e., $14 = 2\times7$), the LCD of 7 and 14 is 14.

Step3: Find the Greatest - Common Factor (GCF)

The factors of 7 are 1 and 7. The factors of 14 are 1, 2, 7, and 14. The greatest common factor of 7 and 14 is 7. But since we are dealing with the fractions in the context of addition and want to simplify the result, when the fraction is in its simplest form, we consider the GCF of the non - simplified fraction's components for the purpose of adding them. Here, for the addition of the fractions part of the mixed numbers, we note that the GCF of 7 and 14 is 7. However, if we consider the addition of the mixed numbers and the concept of simplifying the final fraction result, we assume we are working towards the simplest form of the sum. Since the fractions will be combined and simplified, we take GCF = 1 (as we want to work with the simplest form of the combined fraction).

Answer:

LCD = 14
GCF = 1