3. Four days last week Trey ran $$ 5 \frac{1}{4}, 3 \frac{1}{2}, 2 $$ and $$ 4 \frac{5}{6} $$ miles. What was his total mileage?

Question

UpStudy AI · Accepted Answer

The four runs are:
- $$ 5\frac{1}{4} $$
- $$ 3\frac{1}{2} $$
- $$ 2 $$
- $$ 4\frac{5}{6} $$

**Step 1. Convert to improper fractions:**

$$
5\frac{1}{4} = \frac{5 \times 4 + 1}{4} = \frac{21}{4}
$$

$$
3\frac{1}{2} = \frac{3 \times 2 + 1}{2} = \frac{7}{2}
$$

$$
2 = \frac{2}{1}
$$

$$
4\frac{5}{6} = \frac{4 \times 6 + 5}{6} = \frac{29}{6}
$$

**Step 2. Find a common denominator and convert all fractions:**

The denominators are $$4$$, $$2$$, $$1$$, and $$6$$. The least common denominator (LCD) is $$12$$.

$$
\frac{21}{4} = \frac{21 \times 3}{4 \times 3} = \frac{63}{12}
$$

$$
\frac{7}{2} = \frac{7 \times 6}{2 \times 6} = \frac{42}{12}
$$

$$
\frac{2}{1} = \frac{2 \times 12}{1 \times 12} = \frac{24}{12}
$$

$$
\frac{29}{6} = \frac{29 \times 2}{6 \times 2} = \frac{58}{12}
$$

**Step 3. Sum the distances:**

$$
\frac{63}{12} + \frac{42}{12} + \frac{24}{12} + \frac{58}{12} = \frac{63+42+24+58}{12} = \frac{187}{12}
$$

**Step 4. Convert the sum to a mixed number:**

Divide $$187$$ by $$12$$:
- $$12 \times 15 = 180$$
- Remainder: $$187 - 180 = 7$$

Thus,

$$
\frac{187}{12} = 15\frac{7}{12}
$$

Trey ran a total of $$ 15\frac{7}{12} $$ miles.
Trey ran a total of $$ 15\frac{7}{12} $$ miles.

3. Four days last week Trey ran \( 5 \frac{1}{4}, 3 \frac{1}{2}, 2 \) and \( 4 \frac{5}{6} \) miles. What was his total mileage?