Question

1. cashews how many $1\frac{1}{4}$-pound packages can you make with $7\frac{1}{2}$ pounds of cashews? (section 2.4)

Explanation:

Step1: Convert mixed numbers to improper fractions

First, convert \(1\frac{1}{4}\) to an improper fraction. \(1\frac{1}{4}=\frac{1\times4 + 1}{4}=\frac{5}{4}\). Then, convert \(7\frac{1}{2}\) to an improper fraction. \(7\frac{1}{2}=\frac{7\times2+ 1}{2}=\frac{15}{2}\).

Step2: Divide the total amount by the package amount

To find the number of packages, we divide the total pounds of cashews by the pounds per package. So we calculate \(\frac{15}{2}\div\frac{5}{4}\). When dividing fractions, we multiply by the reciprocal, so \(\frac{15}{2}\times\frac{4}{5}\).

Step3: Simplify the multiplication

Simplify the fractions before multiplying. The 15 and 5 can be simplified: \(15\div5 = 3\), \(5\div5 = 1\). The 4 and 2 can be simplified: \(4\div2 = 2\), \(2\div2 = 1\). So now we have \(3\times2 = 6\).

Answer:

6