Sure, let's write the fractions [tex]\(\frac{5}{6}\)[/tex] and [tex]\(\frac{7}{10}\)[/tex] with a common denominator.
1. Identify the denominators of the two fractions:
- The first fraction has a denominator of 6.
- The second fraction has a denominator of 10.
2. Find the least common multiple (LCM) of the denominators:
- The LCM of 6 and 10 is 30.
3. Convert both fractions to have the common denominator (30):
- For [tex]\(\frac{5}{6}\)[/tex]:
- Calculate the factor needed to convert 6 to 30: [tex]\(\frac{30}{6} = 5\)[/tex].
- Multiply both the numerator and denominator by this factor:
[tex]\[
\frac{5 \times 5}{6 \times 5} = \frac{25}{30}
\][/tex]
- For [tex]\(\frac{7}{10}\)[/tex]:
- Calculate the factor needed to convert 10 to 30: [tex]\(\frac{30}{10} = 3\)[/tex].
- Multiply both the numerator and denominator by this factor:
[tex]\[
\frac{7 \times 3}{10 \times 3} = \frac{21}{30}
\][/tex]
4. State the equivalent fractions with the common denominator:
- [tex]\(\frac{5}{6}\)[/tex] becomes [tex]\(\frac{25}{30}\)[/tex].
- [tex]\(\frac{7}{10}\)[/tex] becomes [tex]\(\frac{21}{30}\)[/tex].
So, the fractions [tex]\(\frac{5}{6}\)[/tex] and [tex]\(\frac{7}{10}\)[/tex] written with a common denominator are [tex]\(\frac{25}{30}\)[/tex] and [tex]\(\frac{21}{30}\)[/tex].
