Question

1. choose the lcd and the gcf for the equation below. when the fraction is in its simplest form, select gcf = 1. 2\frac{1}{2}+3\frac{1}{8} lcd = gcf =

Explanation:

Step1: Find the LCD of denominators

The denominators are 2 and 8. Since 8 is a multiple of 2 (8 = 2×4), the least - common denominator (LCD) of 2 and 8 is 8.

Step2: Find the GCF of numerators and denominators

The mixed - numbers are \(2\frac{1}{2}=\frac{5}{2}\) and \(3\frac{1}{8}=\frac{25}{8}\). The factors of 2 are 1, 2; the factors of 8 are 1, 2, 4, 8; the factors of 5 are 1, 5; the factors of 25 are 1, 5, 25. The greatest common factor (GCF) of all non - 1 numbers involved in the fractions (\(2,8,5,25\)) considering the whole problem context and since the fractions are in a relatively simple form, GCF = 1.

Answer:

LCD = 8
GCF = 1