Question

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?
12.518

259
12
57
50
110
500
9

Answer 1

To convert the decimal 12.518 into a mixed number, we can break it down into its whole number and fractional parts:

1. The whole number part is **12**.
2. The decimal part is **0.518**.

Now, we convert the decimal 0.518 into a fraction. Here’s how to do that:

1. The decimal has three digits after the decimal point (518), which means it is in the thousandths place.
2. We can express this as:
\[
0.518 = \frac{518}{1000}
\]

Next, we should simplify this fraction. We need to find the greatest common divisor (GCD) of 518 and 1000.

- The prime factorization of 518 is \(2 \times 259\).
- The prime factorization of 1000 is \(2^3 \times 5^3\).

The only common factor is **2**.

Now, we can simplify the fraction:
\[
\frac{518 \div 2}{1000 \div 2} = \frac{259}{500}
\]

Putting it all together, we can write the mixed number as:
\[
12.518 = 12 \frac{259}{500}
\]

Thus, the correct numbers to use are:
- Whole number part: **12**
- Fraction part: **259**
- Denominator of the fraction part: **500**

The numbers **57, 50, 110, and 9** are not used in this conversion.