Question

1. elaine jogged \\(\frac{4}{5}\\) mile each day for 4 days. select all the expressions that tell how far elaine jogged in all. use drawings or number lines as needed. \\(\square\\) \\(4 \times \frac{4}{5}\\) \\(\square\\) \\(\frac{16}{5}\\) \\(\square\\) \\(3\frac{1}{5}\\) \\(\square\\) \\(4 \times \frac{1}{5}\\) \\(\square\\) \\(2\frac{1}{5}\\) 14. freddie skated \\(\frac{1}{2}\\) mile each day for 6 days. select all the equations that can be used to find \\(s\\), the total distance freddie skated. \\(\square\\) \\(s = \frac{1}{2} + \frac{1}{2} + \frac{1}{2} + \frac{1}{2} + \frac{1}{2} + \frac{1}{2}\\) \\(\square\\) \\(s = 6 \times \frac{1}{2}\\) \\(\square\\) \\(s = 6 + \frac{1}{2}\\) \\(\square\\) \\(s = 6 + 2 \times \frac{1}{2}\\) \\(\square\\) \\(s = 6 \times 2\\)

Explanation:

Problem 13 (Elaine's Jogging)

Step1: Understand the problem

Elaine jogs $\frac{4}{5}$ mile each day for 4 days. To find the total distance, we can use multiplication (repeated addition) or simplify the result.

Step2: Analyze each option

• Option 1: $4\times\frac{4}{5}$

This represents 4 days of jogging $\frac{4}{5}$ mile each day (repeated addition as multiplication). Correct.

• Option 2: $\frac{16}{5}$

Calculate $4\times\frac{4}{5}=\frac{16}{5}$. Correct.

• Option 3: $3\frac{1}{5}$

Convert $\frac{16}{5}$ to a mixed number: $\frac{16}{5}=3\frac{1}{5}$ (since $16\div5 = 3$ with remainder $1$). Correct.

• Option 4: $4\times\frac{1}{5}$

This equals $\frac{4}{5}$, which is not the total. Incorrect.

• Option 5: $2\frac{1}{5}$

$\frac{16}{5}=3\frac{1}{5}
eq2\frac{1}{5}$. Incorrect.

Problem 14 (Freddie's Skating)

Step1: Understand the problem

Freddie skates $\frac{1}{2}$ mile each day for 6 days. Let $s$ be the total distance.

Step2: Analyze each option

• Option 1: $s=\frac{1}{2}+\frac{1}{2}+\frac{1}{2}+\frac{1}{2}+\frac{1}{2}+\frac{1}{2}$

This is 6 additions of $\frac{1}{2}$ (repeated addition). Correct.

• Option 2: $s = 6\times\frac{1}{2}$

Multiplication represents repeated addition (6 days $\times\frac{1}{2}$ mile/day). Correct.

• Option 3: $s=6+\frac{1}{2}$

This adds 6 and $\frac{1}{2}$, not the total distance. Incorrect.

• Option 4: $s=6 + 2\times\frac{1}{2}$

Simplifies to $6 + 1=7$, which is not the total. Incorrect.

• Option 5: $s=6\times2$

This equals 12, but $6\times\frac{1}{2}=3
eq12$. Incorrect.

Answer:

(Problem 13):
$\boldsymbol{4\times\frac{4}{5}}$, $\boldsymbol{\frac{16}{5}}$, $\boldsymbol{3\frac{1}{5}}$