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Math  /  Numbers & Operations

QuestionMayumi rides her bike around a park. Each lap around the park is 23\frac{2}{3} mi. Mayumi rides a total of 3 mi .
How many laps around the park does Mayumi ride? Write your answer as a whole number of laps, plus a fraction of a lap. You can use the model to help.
Mayumi rides whole laps, plus ? of a lap. \begin{tabular}{|c|c|c|c|} \hline \multicolumn{3}{|c|}{⋅⋯\cdot \cdots} & xx \\ \hline 7 & 8 & 9 & xx \\ \hline 4 & 5 & 6 & - \\ \hline 1 & 2 & 3 & - \\ \hline 0 & & -1 & □\square \\ \hline \end{tabular} Sign out Dec 3 71.54

Studdy Solution

STEP 1

1. Each lap around the park is 23\frac{2}{3} miles.
2. Mayumi rides a total of 3 miles.
3. We need to determine how many whole laps and what fraction of a lap Mayumi rides.

STEP 2

1. Calculate the total number of laps Mayumi rides.
2. Determine the number of whole laps.
3. Determine the fractional part of the lap.

STEP 3

Calculate the total number of laps by dividing the total distance by the distance per lap.
Total laps=3 miles23 miles per lap\text{Total laps} = \frac{3 \text{ miles}}{\frac{2}{3} \text{ miles per lap}}

STEP 4

Simplify the division by multiplying by the reciprocal.
Total laps=3×32=92=4.5\text{Total laps} = 3 \times \frac{3}{2} = \frac{9}{2} = 4.5

STEP 5

Determine the number of whole laps by taking the integer part of the total laps.
Whole laps=⌊4.5⌋=4\text{Whole laps} = \lfloor 4.5 \rfloor = 4

STEP 6

Determine the fractional part of the lap by subtracting the whole laps from the total laps.
Fractional part=4.5−4=0.5\text{Fractional part} = 4.5 - 4 = 0.5
Mayumi rides 4 whole laps, plus 12\frac{1}{2} of a lap.
4 whole laps, plus 12 of a lap\boxed{4 \text{ whole laps, plus } \frac{1}{2} \text{ of a lap}}

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