To rewrite the fractions [tex]\(\frac{1}{10}\)[/tex] and [tex]\(\frac{3}{14}\)[/tex] with the least common denominator, we need to follow these steps:
1. Identify the denominators:
The denominators of the given fractions are 10 and 14.
2. Find the Least Common Denominator (LCD):
To find the least common denominator of 10 and 14, we determine the smallest number that both 10 and 14 can evenly divide into. This involves finding the least common multiple (LCM) of the denominators.
3. Calculate the LCM of 10 and 14:
The LCM of 10 and 14 is 70, as 70 is the smallest number that both 10 and 14 divide into evenly.
4. Rewrite each fraction with the LCD:
- For [tex]\(\frac{1}{10}\)[/tex], convert it to a fraction with the denominator 70 by finding an equivalent fraction.
[tex]\[\frac{1}{10} = \frac{1 \times 7}{10 \times 7} = \frac{7}{70}\][/tex]
- For [tex]\(\frac{3}{14}\)[/tex], convert it to a fraction with the denominator 70 by finding an equivalent fraction.
[tex]\[\frac{3}{14} = \frac{3 \times 5}{14 \times 5} = \frac{15}{70}\][/tex]
Therefore, the fractions [tex]\(\frac{1}{10}\)[/tex] and [tex]\(\frac{3}{14}\)[/tex], when rewritten with the least common denominator 70, are [tex]\(\frac{7}{70}\)[/tex] and [tex]\(\frac{15}{70}\)[/tex] respectively.
So the correct answer is [tex]\(\frac{7}{70}\)[/tex] and [tex]\(\frac{15}{70}\)[/tex].
