Answer :
To rename the fractions [tex]\(\frac{5}{6}\)[/tex] and [tex]\(\frac{14}{15}\)[/tex] using the least common denominator, follow these steps:
1. Find the Least Common Denominator (LCD):
- The denominators are 6 and 15. To find the least common denominator, we need the least common multiple (LCM) of these numbers.
- The multiples of 6 are [tex]\(6, 12, 18, 24, 30, \ldots\)[/tex].
- The multiples of 15 are [tex]\(15, 30, 45, 60, \ldots\)[/tex].
- The smallest common multiple is 30, so the LCD is 30.
2. Rename [tex]\(\frac{5}{6}\)[/tex] using the LCD:
- We want to express [tex]\(\frac{5}{6}\)[/tex] with 30 as the denominator.
- To change the denominator from 6 to 30, multiply both the numerator and the denominator by 5 (because [tex]\(6 \times 5 = 30\)[/tex]).
- [tex]\(\frac{5}{6} = \frac{5 \times 5}{6 \times 5} = \frac{25}{30}\)[/tex].
3. Rename [tex]\(\frac{14}{15}\)[/tex] using the LCD:
- We want to express [tex]\(\frac{14}{15}\)[/tex] with 30 as the denominator.
- To change the denominator from 15 to 30, multiply both the numerator and the denominator by 2 (because [tex]\(15 \times 2 = 30\)[/tex]).
- [tex]\(\frac{14}{15} = \frac{14 \times 2}{15 \times 2} = \frac{28}{30}\)[/tex].
Now, the fraction [tex]\(\frac{5}{6}\)[/tex] is renamed as [tex]\(\frac{25}{30}\)[/tex], and [tex]\(\frac{14}{15}\)[/tex] is renamed as [tex]\(\frac{28}{30}\)[/tex].
1. Find the Least Common Denominator (LCD):
- The denominators are 6 and 15. To find the least common denominator, we need the least common multiple (LCM) of these numbers.
- The multiples of 6 are [tex]\(6, 12, 18, 24, 30, \ldots\)[/tex].
- The multiples of 15 are [tex]\(15, 30, 45, 60, \ldots\)[/tex].
- The smallest common multiple is 30, so the LCD is 30.
2. Rename [tex]\(\frac{5}{6}\)[/tex] using the LCD:
- We want to express [tex]\(\frac{5}{6}\)[/tex] with 30 as the denominator.
- To change the denominator from 6 to 30, multiply both the numerator and the denominator by 5 (because [tex]\(6 \times 5 = 30\)[/tex]).
- [tex]\(\frac{5}{6} = \frac{5 \times 5}{6 \times 5} = \frac{25}{30}\)[/tex].
3. Rename [tex]\(\frac{14}{15}\)[/tex] using the LCD:
- We want to express [tex]\(\frac{14}{15}\)[/tex] with 30 as the denominator.
- To change the denominator from 15 to 30, multiply both the numerator and the denominator by 2 (because [tex]\(15 \times 2 = 30\)[/tex]).
- [tex]\(\frac{14}{15} = \frac{14 \times 2}{15 \times 2} = \frac{28}{30}\)[/tex].
Now, the fraction [tex]\(\frac{5}{6}\)[/tex] is renamed as [tex]\(\frac{25}{30}\)[/tex], and [tex]\(\frac{14}{15}\)[/tex] is renamed as [tex]\(\frac{28}{30}\)[/tex].
