Question

proportions with complex fractions practice ws
4 5 potatoes weigh $4\frac{1}{2}$ pounds. how many potatoes weigh 13 pounds?
set up proportion
solve proportion

Explanation:

Step1: Convert mixed number to improper fraction

First, convert \(4\frac{1}{3}\) to an improper fraction. \(4\frac{1}{3}=\frac{4\times3 + 1}{3}=\frac{13}{3}\) pounds.
We set up a proportion: let \(x\) be the number of potatoes that weigh 13 pounds. The proportion is \(\frac{5}{\frac{13}{3}}=\frac{x}{13}\) (since the ratio of potatoes to weight should be constant).

Step2: Cross - multiply to solve for \(x\)

Cross - multiplying gives us \(\frac{13}{3}x=5\times13\).
Simplify the right - hand side: \(5\times13 = 65\), so we have \(\frac{13}{3}x=65\).
To solve for \(x\), multiply both sides by the reciprocal of \(\frac{13}{3}\), which is \(\frac{3}{13}\).
\(x = 65\times\frac{3}{13}\).
Since \(65\div13 = 5\), then \(x=5\times3=15\).

Answer:

15