Let's break down the conversion of these fractions step by step.
### Converting [tex]\(\frac{18}{12}\)[/tex] to a Mixed Number
1. The fraction [tex]\(\frac{18}{12}\)[/tex] can be simplified. Divide both the numerator and the denominator by their greatest common divisor (GCD), which is 6:
[tex]\[
\frac{18}{12} = \frac{18 \div 6}{12 \div 6} = \frac{3}{2}
\][/tex]
2. To convert [tex]\(\frac{3}{2}\)[/tex] to a mixed number, see how many times 2 fits into 3:
[tex]\[
3 \div 2 = 1 \text{ remainder } 1
\][/tex]
So, [tex]\(\frac{3}{2}\)[/tex] as a mixed number is:
[tex]\[
1 \frac{1}{2}
\][/tex]
### Converting [tex]\(1 \frac{7}{8}\)[/tex] to an Improper Fraction
1. A mixed number [tex]\(1 \frac{7}{8}\)[/tex] can be converted to an improper fraction by first converting the whole part into eighths and then adding the fractional part:
[tex]\[
1 = \frac{8}{8}
\][/tex]
2. Adding the fractional part:
[tex]\[
1 \frac{7}{8} = \frac{8}{8} + \frac{7}{8} = \frac{8 + 7}{8} = \frac{15}{8}
\][/tex]
Therefore, [tex]\(\frac{18}{12}\)[/tex] as a mixed number is [tex]\(1 \frac{1}{2}\)[/tex], and [tex]\(1 \frac{7}{8}\)[/tex] as an improper fraction is [tex]\(\frac{15}{8}\)[/tex].
Given these conversions, the correct answer is:
[tex]\[
\frac{18}{12}=1 \frac{1}{2} \text{ and } 1 \frac{7}{8}=\frac{15}{8}
\][/tex]
Which matches the following answer:
[tex]\[
\boxed{\frac{18}{12}=1 \frac{1}{2} \text{ and } 1 \frac{7}{8}=\frac{15}{8}}
\][/tex]
