Question

1. find the lcd and the gcf for the word problem below. when the fraction is in its simplest form, select gcf = 1. the office coffee pot started out having 9\frac{1}{2} quarts of coffee. at the end of the day, there were 4\frac{4}{5} quarts left. how many quarts of coffee were consumed during the day? lcd = gcf =

Explanation:

Step1: Convert mixed - numbers to improper fractions

$9\frac{1}{2}=\frac{9\times2 + 1}{2}=\frac{19}{2}$ and $4\frac{4}{5}=\frac{4\times5+4}{5}=\frac{24}{5}$

Step2: Find the LCD of 2 and 5

The denominators are 2 and 5. Since 2 and 5 are prime numbers, the least - common denominator (LCD) is their product. So, $LCD = 2\times5=10$.

Step3: Find the GCF of the numerators and denominators in the context of the problem

The numerators are 19 and 24, and the denominators are 2 and 5. The numbers 19, 24, 2, and 5 have no common factors other than 1. So, $GCF = 1$.

Answer:

LCD = 10
GCF = 1