Question

comparing walks
deon walked \\(\frac{2}{3}\\) as far as miguel. evelyn walked \\(1\frac{1}{2}\\) times as far as miguel. miguel walked 24 city blocks.

how can you determine how far deon and evelyn walked?

when we do math, we ask ourselves questions to make sense of the problem.

what do i know about the problem?

• three students walked different distances.

what dont i know?

• how far each student walked
• who walked the shortest distance
• who walked the longest distance

Explanation:

Identify the given values

We identify the known quantities.

• Miguel's distance: \(24\) blocks
• Deon's distance: \(\frac{2}{3}\) of Miguel's distance
• Evelyn's distance: \(1\frac{1}{2}\) times Miguel's distance

Calculate Deon's distance

Using the Fraction Arithmetic knowledge point

$$ \text{Deon's distance} = 24 \times \frac{2}{3} = \frac{48}{3} = 16 \text{ blocks} $$

Calculate Evelyn's distance

Using the Fraction Arithmetic knowledge point

$$ \text{Evelyn's distance} = 24 \times 1\frac{1}{2} = 24 \times \frac{3}{2} = 12 \times 3 = 36 \text{ blocks} $$

Formulate the final explanation

We summarize the required steps.

• Multiply Miguel's distance by \(\frac{2}{3}\) for Deon.
• Multiply Miguel's distance by \(1\frac{1}{2}\) for Evelyn.

Answer:

To determine how far Deon and Evelyn walked, you multiply Miguel's distance (24 blocks) by each of their respective fractional comparison factors:

• Deon's distance: Multiply Miguel's distance by \(\frac{2}{3}\):

$$24 \times \frac{2}{3} = 16\text{ blocks}$$

• Evelyn's distance: Multiply Miguel's distance by \(1\frac{1}{2}\) (or \(\frac{3}{2}\)):

$$24 \times \frac{3}{2} = 36\text{ blocks}$$