Sure! Let's rewrite the fractions [tex]\(\frac{3}{4}\)[/tex] and [tex]\(\frac{5}{16}\)[/tex] so that they both have a common denominator.
1. Identify the least common denominator (LCD):
To add or compare fractions, they must have the same denominator. We find the least common denominator (LCD) of the denominators 4 and 16. The LCD of 4 and 16 is 16.
2. Convert each fraction to have the LCD as the denominator:
- For [tex]\(\frac{3}{4}\)[/tex]:
- We need to convert 4 to 16.
- This can be done by multiplying both the numerator and the denominator of [tex]\(\frac{3}{4}\)[/tex] by 4 (because [tex]\(16 ÷ 4 = 4\)[/tex]).
- [tex]\(\frac{3}{4} \times \frac{4}{4} = \frac{3 \times 4}{4 \times 4} = \frac{12}{16}\)[/tex].
- For [tex]\(\frac{5}{16}\)[/tex]:
- The denominator is already 16, so no conversion is necessary.
- [tex]\(\frac{5}{16}\)[/tex] remains as [tex]\(\frac{5}{16}\)[/tex].
3. Write the two fractions with their common denominator:
The fractions [tex]\(\frac{3}{4}\)[/tex] and [tex]\(\frac{5}{16}\)[/tex] can be rewritten as [tex]\(\frac{12}{16}\)[/tex] and [tex]\(\frac{5}{16}\)[/tex] respectively.
Therefore, the correct answer is:
[tex]$\frac{12}{16} \text{ and } \frac{5}{16}$[/tex]
