Question

Javier is making a special fertilizer for his garden. The ingredients are mixed in the ratios shown below. • 3} 8of the fertilizer is cottonseed. • 1} 4of the fertilizer is phosphate. • 1} 4of the fertilizer is wood ash. • 1} 8of the fertilizer is limestone.

Answer 1

To find out the total ratio of the ingredients that Javier is using for his special fertilizer, we need to add up all the fractions to ensure they equal 1 (or the whole amount of fertilizer).

1. **Cottonseed**: \( \frac{3}{8} \)
2. **Phosphate**: \( \frac{1}{4} \)
3. **Wood Ash**: \( \frac{1}{4} \)
4. **Limestone**: \( \frac{1}{8} \)

First, let’s convert \( \frac{1}{4} \) to eighths to make it easier to add the fractions:

\[
\frac{1}{4} = \frac{2}{8}
\]

Now we can rewrite the fractions to combine them:

- Cottonseed: \( \frac{3}{8} \)
- Phosphate: \( \frac{2}{8} \)
- Wood Ash: \( \frac{2}{8} \)
- Limestone: \( \frac{1}{8} \)

Now, adding them together:

\[
\frac{3}{8} + \frac{2}{8} + \frac{2}{8} + \frac{1}{8} = \frac{3 + 2 + 2 + 1}{8} = \frac{8}{8} = 1
\]

The total equals 1, meaning that the proportions are correct and all ingredients are accounted for in the mix.

Thus, the special fertilizer consists of:
- **Cottonseed**: \( \frac{3}{8} \)
- **Phosphate**: \( \frac{1}{4} \) (or \( \frac{2}{8} \))
- **Wood Ash**: \( \frac{1}{4} \) (or \( \frac{2}{8} \))
- **Limestone**: \( \frac{1}{8} \)

Javier's fertilizer is mixed in these specified ratios.