Question: Homework 5-1: Ratios, Rates, Unit Rates
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Ratios
2. Hiroshi has $4$ engines and $18$ box cars. Determine the ratio of engines to box cars. Write the simplified ratio three different ways as indicated below.
Fraction: ____ ____ to ____ ____:____
1. **State the problem:** Determine the ratio of engines to box cars for Hiroshi who has $4$ engines and $18$ box cars.
2. **Write the ratio as a fraction:** The ratio of engines to box cars is $$\frac{4}{18}$$.
3. **Simplify the fraction:** Find the greatest common divisor (GCD) of $4$ and $18$, which is $2$.
4. **Divide numerator and denominator by the GCD:**
$$\frac{\cancel{4}^2}{\cancel{18}^9} = \frac{2}{9}$$
5. **Write the simplified ratio in three forms:**
- Fraction form: $$\frac{2}{9}$$
- "to" form: $2$ to $9$
- Colon form: $2:9$
6. **Explanation:** This means for every $2$ engines, there are $9$ box cars, which is the simplest ratio expressing the relationship between engines and box cars.
**Final answer:**
Fraction: $$\frac{2}{9}$$ $2$ to $9$ $2:9$