Apply Problem Standard: 6.NS.B.3

🏃 Apply: Pine Ridge Trail Run

Jordan is training to run the 28.8-mile Pine Ridge Trail on the path shown below. Hydration and aid stations are placed along the path every 1.6 miles. How many aid station intervals are along the entire trail?

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The 2-Step Decimal Rule for Division:

Step A: Move the decimal in the divisor 1 place to the right until it is a whole number.
Step B: Move the decimal in the dividend 1 place to the right to match!

🔄 Decimal Movement Simulator Step-by-step decimal jump

Divisor (Outside)

1.6

⟌

Dividend (Inside)

28.8

Guided Solver

Work Through the Problem: 28.8 ÷ 1.6

1 Write the Division Expression

Divide the total trail distance by the distance between stations:

Expression: 28.8 ÷ 1.6

2 Move the Decimal in the Divisor One Place to the Right

Look at the divisor 1.6 (the outside number). Move the decimal 1 place to the right ($\times 10$) to make it a whole number:

1.6 ➔ New Whole-Number Divisor:

3 Move the Decimal in the Dividend One Place to the Right

Because you moved the divisor's decimal 1 place right, you must also move the dividend 28.8 (the inside number) 1 place to the right ($\times 10$):

28.8 ➔ New Dividend:

4 Divide and Solve: 288 ÷ 16

Now perform standard long division with your new whole-number problem:

Quotient:

288

Original Problem: $28.8 \div 1.6$

Step 2 (Move Divisor): $1.6 \xrightarrow{\times 10} \mathbf{16}$

Step 3 (Move Dividend): $28.8 \xrightarrow{\times 10} \mathbf{288}$

Step 4 (Divide): $288 \div 16 = \mathbf{18\text{ aid station intervals}}$

Pedagogical Rationale: Separating the divisor shift from the dividend shift teaches students why the change happens: the divisor *must* become a whole number first, and the dividend shifts *to maintain an equivalent ratio* ($\frac{28.8 \times 10}{1.6 \times 10} = \frac{288}{16}$).