Which option shows the following fractions written with a common denominator?

[tex]\[ \frac{5}{6} \text{ and } \frac{7}{10} \][/tex]

A. [tex]\(\frac{25}{30}\)[/tex] and [tex]\(\frac{21}{30}\)[/tex]

B. [tex]\(\frac{50}{60}\)[/tex] and [tex]\(\frac{42}{60}\)[/tex]

C. [tex]\(\frac{5}{60}\)[/tex] and [tex]\(\frac{7}{60}\)[/tex]

D. [tex]\(\frac{30}{36}\)[/tex] and [tex]\(\frac{35}{36}\)[/tex]



Answer :

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].