Drag each number to the correct location on the mixed number. Not all numbers will be used.

What is the fraction form of the following decimal expansion?
12.5 overline 18.

A. 500
B. 57
C. 259
D. 9
E. 110
F. 12
G. 50
( Use the lettered numbers for this ___. ____/____

User Icon for Bot GPT 4-o mini Bot GPT 4-o mini answered
1 month ago

To convert the decimal \( 12.5\overline{18} \) to a fraction, we can express it as follows:

Let:
\[ x = 12.5\overline{18} \]

**Step 1:** Break down \( x \):
\[ x = 12.5 + 0.0\overline{18} \]

Next, let's focus on the repeating decimal \( 0.0\overline{18} \).

**Step 2:** Set \( y = 0.0\overline{18} \):
\[ y = 0.0181818... \]

Multiply \( y \) by 100 (to shift the repeating part left of the decimal):
\[ 100y = 1.818181... \]

Now, we have:
\[ y = 0.0181818... \]
\[ 100y = 1.818181... \]

**Step 3:** Subtract the two equations:
\[ 100y - y = 1.818181... - 0.0181818... \]
\[ 99y = 1.8 \]

**Step 4:** Solve for \( y \):
\[ y = \frac{1.8}{99} = \frac{18}{990} = \frac{1}{55} \]

**Step 5:** Combining everything:
We have:
\[ x = 12.5 + \frac{1}{55} \]

**Step 6:** Convert \( 12.5 \) to a fraction:
\[ 12.5 = \frac{125}{10} = \frac{25}{2} \]

Now combine the two fractions:
\[ x = \frac{25}{2} + \frac{1}{55} \]

**Step 7:** Get a common denominator (for 2 and 55, it's 110):
Convert \( \frac{25}{2} \) to a fraction with a denominator of 110:
\[ \frac{25}{2} = \frac{25 \times 55}{2 \times 55} = \frac{1375}{110} \]

Convert \( \frac{1}{55} \) to a fraction with a denominator of 110:
\[ \frac{1}{55} = \frac{1 \times 2}{55 \times 2} = \frac{2}{110} \]

**Step 8:** Add the two fractions:
\[ x = \frac{1375}{110} + \frac{2}{110} = \frac{1377}{110} \]

So, the fraction form of \( 12.5\overline{18} \) is:
\[ \frac{1377}{110} \]

Now, based on the choices provided, you are looking for a mixed number expression, where:

The corresponding labels to use:
- A (500)
- B (57)
- C (259)
- D (9)
- E (110)
- F (12)
- G (50)

In the mixed number form, \( 1377 = 12 \times 110 + 57 \).

Thus, the answer would be:
\[ \frac{1377}{110} \text{ can be represented as } F \text{ (12)}/E \text{ (110)}. \]

So, the final answer is:
**Answer: F/E = 12/110**.

User Icon for UnicornSparkles UnicornSparkles answered
1 month ago

Not ____/_____ it’s ____. _____/______ 3 things

User Icon for Bot GPT 4-o mini Bot GPT 4-o mini answered
1 month ago

I apologize for the misunderstanding! Given that you're looking for the format with three components, the mixed number representation of \( 12.5\overline{18} \) can be expressed as:

**12 ____/____**

From our calculation, we have \( 12.5\overline{18} = \frac{1377}{110} \).

So we need to express this in the form:

\[ 12 \frac{57}{110} \]

Thus, using the lettered options from your provided list:

- The integer part (whole number) is represented by **F = 12**.
- The fraction part is represented by **B = 57** and **E = 110**.

So the final answer is:

**12 B/E = 12 57/110.**