Let's interpret the given problem and develop a step-by-step solution to understand the ratio of Hallie's donation to Mattie's donation.
1. Identify the quantities given:
- Hallie donated 3 pairs of blue jeans.
- Mattie donated 6 pairs of blue jeans.
2. Understand what is being asked:
- We need to find the ratio of Hallie's donation to Mattie's donation of blue jeans.
3. Set up the ratio:
- A ratio compares two quantities by division. Therefore, the ratio of Hallie's donation to Mattie's donation is calculated as:
[tex]\[
\text{Ratio} = \frac{\text{Hallie's donation}}{\text{Mattie's donation}}
\][/tex]
- Substituting the given values:
[tex]\[
\text{Ratio} = \frac{3}{6}
\][/tex]
4. Simplify the ratio:
- To simplify the ratio, we divide both the numerator and the denominator by their greatest common divisor (GCD). In this case, the GCD of 3 and 6 is 3.
- Simplifying the fraction:
[tex]\[
\frac{3 \div 3}{6 \div 3} = \frac{1}{2}
\][/tex]
5. Interpret the simplified ratio:
- The simplified ratio is [tex]\( \frac{1}{2} \)[/tex].
- This means that for every pair of blue jeans that Hallie donates, Mattie donates 2 pairs of blue jeans.
6. Convert the ratio to the desired format if necessary:
- Ratios can be written in several formats: as a fraction ([tex]\( \frac{1}{2} \)[/tex]), using a colon (1:2), or in word form (1 to 2).
Therefore, the ratio representing Hallie's donation to Mattie's donation is [tex]\( \frac{1}{2} \)[/tex], or 1:2, or 1 to 2.
Answer:
The correct ratio from the provided options is [tex]\(\boxed{0.5}\)[/tex] which matches the simplified ratio of Hallie's donation to Mattie's donation.
