Question

10.1 13. there are 4 people on the middle - school relay team. each of them runs \\(\frac{1}{3}\\) mile. what is the total distance that the team runs? explain how you found your answer.
10.2 14. rory uses buttons for a project. of the buttons, \\(\frac{1}{2}\\) of them are round. of the round buttons, \\(\frac{2}{3}\\) have holes. what fraction of the buttons that rory uses are round with holes? explain your answer using the representation.
10.5 15. mrs. mishler uses carpet squares to cover the floor. one carpet square measures \\(1\frac{1}{2}\\) feet by \\(1\frac{1}{2}\\) feet. if mrs. mishler uses 15 carpet squares, what is the total area of the floor? show your work.

Explanation:

Problem 13

Step1: Define total distance formula

Total distance = Number of runners × Distance per runner

Step2: Substitute values and calculate

$$4 \times \frac{1}{3} = \frac{4}{3}$$

Problem 14

Step1: Identify target fraction

Multiply fraction of round buttons by fraction of round buttons with holes

Step2: Calculate the product

$$\frac{1}{2} \times \frac{2}{3} = \frac{2}{6} = \frac{1}{3}$$
(The diagram shows half the total buttons as round, then 2/3 of that half is shaded, representing the round buttons with holes, which equals 1/3 of the total.)

Problem 15

Step1: Calculate area of one carpet square

$$1\frac{1}{2} \times 1\frac{1}{2} = \frac{3}{2} \times \frac{3}{2} = \frac{9}{4}$$

Step2: Find total floor area

Total area = Number of squares × Area per square
$$15 \times \frac{9}{4} = \frac{135}{4}$$

Step3: Convert to mixed number (optional)

$$\frac{135}{4} = 33\frac{3}{4}$$

Answer:

1. $\frac{4}{3}$ miles (or $1\frac{1}{3}$ miles)
2. $\frac{1}{3}$
3. $\frac{135}{4}$ square feet (or $33\frac{3}{4}$ square feet)