Question

1. choose the correct sum for each expression.
2. for a trip to the beach, kelly drove for \\(\frac{5}{6}\\) hour and joshua drove for \\(\frac{2}{5}\\) hour.

a. estimate how much longer kelly drove than joshua. explain how you found your estimate.
\\(1 - \frac{1}{2} = \frac{1}{2}\\)
b. how much longer did kelly drive than joshua? find the exact amount.
\\(\frac{5}{6}\\)
\\(\frac{2}{5}\\)

Explanation:

Part A: Estimate the Difference

Step1: Analyze the fractions

Kelly drove for $\frac{5}{6}$ hour, which is close to 1 (since $\frac{5}{6} \approx 1$). Joshua drove for $\frac{2}{5}$ hour, which is close to $\frac{1}{2}$ (since $\frac{2}{5} = 0.4$, close to $0.5=\frac{1}{2}$).

Step2: Estimate the difference

Subtract the estimated values: $1 - \frac{1}{2} = \frac{1}{2}$. So we estimate Kelly drove about $\frac{1}{2}$ hour longer.

Step1: Find a common denominator

The denominators are 6 and 5. The least common denominator (LCD) of 6 and 5 is $6\times5 = 30$.

Step2: Rewrite the fractions

Rewrite $\frac{5}{6}$ and $\frac{2}{5}$ with denominator 30:
$\frac{5}{6}=\frac{5\times5}{6\times5}=\frac{25}{30}$
$\frac{2}{5}=\frac{2\times6}{5\times6}=\frac{12}{30}$

Step3: Subtract the fractions

Subtract the two fractions: $\frac{25}{30}-\frac{12}{30}=\frac{25 - 12}{30}=\frac{13}{30}$.

Answer:

The estimated difference is about $\frac{1}{2}$ hour. We estimated $\frac{5}{6}\approx1$ and $\frac{2}{5}\approx\frac{1}{2}$, then calculated $1 - \frac{1}{2}=\frac{1}{2}$.

Part B: Exact Difference