Question

rochelle has 6 pounds of grass seed. she uses $1\frac{1}{3}$ pounds on the front yard and $1\frac{4}{9}$ pounds on the side yard. how many pounds are left? 5.ar.1.2
a $2\frac{7}{9}$ pounds
c $4\frac{2}{9}$ pounds
b $3\frac{2}{9}$ pounds
d $8\frac{2}{9}$ pounds

Explanation:

Step1: Convert mixed numbers to improper fractions

First, convert \(1\frac{1}{3}\) to an improper fraction. \(1\frac{1}{3}=\frac{1\times3 + 1}{3}=\frac{4}{3}\). Then convert \(1\frac{4}{9}\) to an improper fraction: \(1\frac{4}{9}=\frac{1\times9+4}{9}=\frac{13}{9}\). Also, write 6 as a fraction with denominator 9: \(6=\frac{54}{9}\), and \(\frac{4}{3}=\frac{12}{9}\) (by multiplying numerator and denominator by 3 to get a common denominator with \(\frac{13}{9}\)).

Step2: Calculate total used seed

Add the amounts used for front and side yard. Total used \(=\frac{12}{9}+\frac{13}{9}=\frac{12 + 13}{9}=\frac{25}{9}\).

Step3: Calculate remaining seed

Subtract total used from initial amount. Remaining \(=\frac{54}{9}-\frac{25}{9}=\frac{54 - 25}{9}=\frac{29}{9}\). Convert \(\frac{29}{9}\) back to a mixed number: \(3\frac{2}{9}\) (since \(29\div9 = 3\) with a remainder of \(2\)).

Answer:

B. \(3\frac{2}{9}\) pounds