Answer :
Alright, let's convert the mixed decimal 157.43 into a mixed number and reduce it to the lowest terms.
### Step-by-Step Solution:
1. Separate the Mixed Decimal:
- The integer part of the mixed decimal is 157.
- The decimal part of the mixed decimal is 0.43.
2. Convert the Decimal Part to a Fraction:
- We need to convert 0.43 into a fraction. Since 0.43 = [tex]\(\frac{43}{100}\)[/tex], it is already in fractional form.
3. Form the Mixed Number:
- Combine the integer part and the fractional part to create the mixed number. This gives us [tex]\(157 \frac{43}{100}\)[/tex].
4. Reduce the Fraction to Lowest Terms:
- The fraction [tex]\(\frac{43}{100}\)[/tex] is already in its simplest form since 43 is a prime number and doesn't have any common factors with 100 other than 1.
Thus, the mixed number in its lowest terms is [tex]\(157 \frac{43}{100}\)[/tex].
### Selecting the Correct Option:
Comparing the mixed number we formed with the provided options:
- [tex]\(158 \frac{45}{100}\)[/tex] is not the correct option.
- [tex]\(157 \frac{43}{100}\)[/tex] matches exactly with our result.
- [tex]\(156 \frac{42}{100}\)[/tex] is not the correct option.
- [tex]\(157 \frac{44}{100}\)[/tex] is not the correct option.
Therefore, the correct answer is [tex]\(157 \frac{43}{100}\)[/tex], which is the second option. Hence, the correct answer is:
[tex]\[
\boxed{2}
\][/tex]
### Step-by-Step Solution:
1. Separate the Mixed Decimal:
- The integer part of the mixed decimal is 157.
- The decimal part of the mixed decimal is 0.43.
2. Convert the Decimal Part to a Fraction:
- We need to convert 0.43 into a fraction. Since 0.43 = [tex]\(\frac{43}{100}\)[/tex], it is already in fractional form.
3. Form the Mixed Number:
- Combine the integer part and the fractional part to create the mixed number. This gives us [tex]\(157 \frac{43}{100}\)[/tex].
4. Reduce the Fraction to Lowest Terms:
- The fraction [tex]\(\frac{43}{100}\)[/tex] is already in its simplest form since 43 is a prime number and doesn't have any common factors with 100 other than 1.
Thus, the mixed number in its lowest terms is [tex]\(157 \frac{43}{100}\)[/tex].
### Selecting the Correct Option:
Comparing the mixed number we formed with the provided options:
- [tex]\(158 \frac{45}{100}\)[/tex] is not the correct option.
- [tex]\(157 \frac{43}{100}\)[/tex] matches exactly with our result.
- [tex]\(156 \frac{42}{100}\)[/tex] is not the correct option.
- [tex]\(157 \frac{44}{100}\)[/tex] is not the correct option.
Therefore, the correct answer is [tex]\(157 \frac{43}{100}\)[/tex], which is the second option. Hence, the correct answer is:
[tex]\[
\boxed{2}
\][/tex]
