Sure, let's solve this question step-by-step.
### Converting [tex]\(\frac{18}{12}\)[/tex] to a Mixed Number
1. Divide the numerator by the denominator:
Divide [tex]\(18\)[/tex] by [tex]\(12\)[/tex]:
[tex]\[
18 \div 12 = 1 \quad \text{(quotient)}
\][/tex]
2. Find the remainder:
Calculate the remainder of [tex]\(18\)[/tex] divided by [tex]\(12\)[/tex]:
[tex]\[
18 \mod 12 = 6
\][/tex]
3. Form the mixed number:
So, the mixed number is:
[tex]\[
18 \div 12 = 1 \quad \text{with remainder} \quad 6
\][/tex]
This gives us:
[tex]\[
1 \frac{6}{12}
\][/tex]
4. Simplify the fraction:
Simplify [tex]\(\frac{6}{12}\)[/tex] to its lowest terms:
[tex]\[
\frac{6}{12} = \frac{1}{2}
\][/tex]
Hence, [tex]\(\frac{18}{12}\)[/tex] as a mixed number is:
[tex]\[
1 \frac{1}{2}
\][/tex]
### Converting [tex]\(1 \frac{7}{8}\)[/tex] to an Improper Fraction
1. Multiply the whole number part by the fraction's denominator:
Multiply [tex]\(1\)[/tex] by [tex]\(8\)[/tex]:
[tex]\[
1 \times 8 = 8
\][/tex]
2. Add the numerator of the fraction:
Add [tex]\(7\)[/tex] to the result:
[tex]\[
8 + 7 = 15
\][/tex]
3. Form the improper fraction:
The numerator is the result from above ([tex]\(15\)[/tex]), and the denominator remains the same ([tex]\(8\)[/tex]):
[tex]\[
\frac{15}{8}
\][/tex]
### Final Results
So, [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]
Therefore, the following shows the correct transformations:
[tex]\[
\frac{18}{12} = 1 \frac{1}{2} \quad \text{and} \quad 1 \frac{7}{8} = \frac{15}{8}
\][/tex]
