Write -12.405 as a mixed number in simplest form.
Understand the Problem
The question is asking to convert the decimal number -12.405 into its mixed number form in the simplest way, which involves separating the whole number and fractional part.
Answer
$$ -12 \frac{81}{200} $$
Answer for screen readers
$$ -12 \frac{81}{200} $$
Steps to Solve
- Identify the Whole Number and Fractional Part
The number is $-12.405$. The whole number part is $-13$ (since we round down for negative numbers) and the fractional part is $0.405$.
- Convert the Fractional Part to a Fraction
To convert $0.405$ into a fraction, recognize that $0.405$ is equal to $\frac{405}{1000}$.
- Simplify the Fraction
Next, simplify $\frac{405}{1000}$. Find the greatest common divisor (GCD) of $405$ and $1000$, which is $5$.
So, we divide the numerator and denominator by $5$: $$ \frac{405 \div 5}{1000 \div 5} = \frac{81}{200} $$
- Combine the Whole Number and the Fraction
Now, we combine the whole number and the fraction to write $-12.405$ as a mixed number: $$ -12.405 = -13 + \frac{81}{200} $$
This can be expressed as: $$ -12 \frac{81}{200} $$
$$ -12 \frac{81}{200} $$
More Information
The mixed number represents the decimal $-12.405$ in a format that includes both a whole and a fractional part. This is particularly useful in contexts where mixed numbers are preferred, such as cooking measurements or certain mathematical applications.
Tips
- Not recognizing that for negative numbers, the whole part should be rounded down (more negative).
- Failing to simplify the fractional part correctly.
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