Question

1. choose the lcd and the gcf for the equation below. when the fraction is in its simplest form, select gcf = 1.

5\frac{2}{5}+\left(-4\frac{3}{10}\
ight)
lcd =
gcf =

Explanation:

Step1: Find the LCD of denominators

The denominators are 5 and 10. Prime - factorize: 5 = 5, 10=2×5. The LCD is the product of the highest - power prime factors involved, so LCD = 10.

Step2: Find the GCF of numerators and denominators

The mixed - numbers are \(5\frac{2}{5}=\frac{5\times5 + 2}{5}=\frac{27}{5}\) and \(-4\frac{3}{10}=\frac{-4\times10 + 3}{10}=\frac{- 43}{10}\). Since the fraction is in its simplest form as per the problem condition, the GCF of the numerators and denominators of the resulting fraction (after addition) is 1.

Answer:

LCD = 10
GCF = 1