Question

set 2 solve fraction division problems
write and solve an equation to solve the problems. show your work.
1 a pumpkin weighs $7\frac{1}{2}$ pounds. an apple weighs $\frac{1}{3}$ pound. how many times the apples weight is the pumpkins weight?
2 a rectangle has an area of $\frac{9}{10}$ in.² and a width of $\frac{3}{4}$ in. what is its length?

Explanation:

Step1: Convert mixed number to improper fraction

The pumpkin's weight is \(7\frac{1}{2}=\frac{7\times2 + 1}{2}=\frac{15}{2}\) pounds. Let \(x\) be the number of times the apple's weight is the pumpkin's weight. The equation is \(\frac{1}{3}x=\frac{15}{2}\).

Step2: Solve for \(x\)

Using the rule \(x = \frac{15}{2}\div\frac{1}{3}\). When dividing by a fraction, we multiply by its reciprocal. So \(x=\frac{15}{2}\times\frac{3}{1}=\frac{45}{2}=22.5\).

For the rectangle problem:

Step1: Use the area formula \(A = lw\) (where \(A\) is area, \(l\) is length, \(w\) is width)

We know \(A=\frac{9}{10}\) and \(w = \frac{3}{4}\). The equation for length \(l\) is \(l=\frac{9}{10}\div\frac{3}{4}\).

Step2: Divide the fractions

Multiply by the reciprocal: \(l=\frac{9}{10}\times\frac{4}{3}\). Simplify: \(\frac{9\times4}{10\times3}=\frac{36}{30}=\frac{6}{5} = 1.2\) inches.

Answer:

1. The pumpkin's weight is \(22.5\) times the apple's weight.
2. The length of the rectangle is \(\frac{6}{5}\) (or \(1.2\)) inches.