Answer :
To convert [tex]\(-1.64\)[/tex] into a mixed number in simplest form, follow these steps:
1. Identify the integer part: The integer part of [tex]\(-1.64\)[/tex] is [tex]\(-1\)[/tex].
2. Separate the decimal part:
- The decimal part is [tex]\(-0.64\)[/tex] because [tex]\(-1.64 - (-1) = -0.64\)[/tex].
3. Convert the decimal part to a fraction:
- Consider the decimal part [tex]\(-0.64\)[/tex]. First, ignore the negative sign and convert [tex]\(0.64\)[/tex] to a fraction.
- [tex]\(0.64\)[/tex] is equivalent to [tex]\(\frac{64}{100}\)[/tex].
4. Simplify the fraction:
- Find the greatest common divisor (GCD) of 64 and 100, which is 4.
- Simplify [tex]\(\frac{64}{100}\)[/tex] by dividing both the numerator and the denominator by 4:
[tex]\[
\frac{64 \div 4}{100 \div 4} = \frac{16}{25}
\][/tex]
5. Reintroduce the negative sign:
- Since we started with a negative decimal, [tex]\(-0.64\)[/tex] as a fraction is [tex]\(-\frac{16}{25}\)[/tex].
6. Combine the integer part and the fraction:
- The mixed number is [tex]\(-1 \frac{16}{25}\)[/tex].
Therefore, [tex]\(-1.64\)[/tex] as a mixed number in simplest form is [tex]\(-1 \frac{16}{25}\)[/tex].
1. Identify the integer part: The integer part of [tex]\(-1.64\)[/tex] is [tex]\(-1\)[/tex].
2. Separate the decimal part:
- The decimal part is [tex]\(-0.64\)[/tex] because [tex]\(-1.64 - (-1) = -0.64\)[/tex].
3. Convert the decimal part to a fraction:
- Consider the decimal part [tex]\(-0.64\)[/tex]. First, ignore the negative sign and convert [tex]\(0.64\)[/tex] to a fraction.
- [tex]\(0.64\)[/tex] is equivalent to [tex]\(\frac{64}{100}\)[/tex].
4. Simplify the fraction:
- Find the greatest common divisor (GCD) of 64 and 100, which is 4.
- Simplify [tex]\(\frac{64}{100}\)[/tex] by dividing both the numerator and the denominator by 4:
[tex]\[
\frac{64 \div 4}{100 \div 4} = \frac{16}{25}
\][/tex]
5. Reintroduce the negative sign:
- Since we started with a negative decimal, [tex]\(-0.64\)[/tex] as a fraction is [tex]\(-\frac{16}{25}\)[/tex].
6. Combine the integer part and the fraction:
- The mixed number is [tex]\(-1 \frac{16}{25}\)[/tex].
Therefore, [tex]\(-1.64\)[/tex] as a mixed number in simplest form is [tex]\(-1 \frac{16}{25}\)[/tex].
