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Answer :
To rename [tex]\(\frac{5}{6}\)[/tex] and [tex]\(\frac{14}{15}\)[/tex] using the least common denominator (LCD), follow these steps:
1. Find the Least Common Denominator (LCD):
The denominators we have are 6 and 15. To find the LCD, we need the smallest number that both 6 and 15 can divide into evenly. The LCD of 6 and 15 is 30.
2. Adjust the fractions to have the LCD as the new denominator:
- For [tex]\(\frac{5}{6}\)[/tex]:
- Determine what factor you need to multiply 6 by to get 30: [tex]\(30 \div 6 = 5\)[/tex].
- Multiply both the numerator and the denominator of [tex]\(\frac{5}{6}\)[/tex] by this factor: [tex]\(\frac{5 \times 5}{6 \times 5} = \frac{25}{30}\)[/tex].
- For [tex]\(\frac{14}{15}\)[/tex]:
- Determine what factor you need to multiply 15 by to get 30: [tex]\(30 \div 15 = 2\)[/tex].
- Multiply both the numerator and the denominator of [tex]\(\frac{14}{15}\)[/tex] by this factor: [tex]\(\frac{14 \times 2}{15 \times 2} = \frac{28}{30}\)[/tex].
So, the renamed fractions with the least common denominator are:
[tex]\[
\frac{5}{6} = \frac{25}{30} \quad \text{and} \quad \frac{14}{15} = \frac{28}{30}
\][/tex]
These steps ensure that both fractions now have the same denominator, making it easier to compare or combine them.
1. Find the Least Common Denominator (LCD):
The denominators we have are 6 and 15. To find the LCD, we need the smallest number that both 6 and 15 can divide into evenly. The LCD of 6 and 15 is 30.
2. Adjust the fractions to have the LCD as the new denominator:
- For [tex]\(\frac{5}{6}\)[/tex]:
- Determine what factor you need to multiply 6 by to get 30: [tex]\(30 \div 6 = 5\)[/tex].
- Multiply both the numerator and the denominator of [tex]\(\frac{5}{6}\)[/tex] by this factor: [tex]\(\frac{5 \times 5}{6 \times 5} = \frac{25}{30}\)[/tex].
- For [tex]\(\frac{14}{15}\)[/tex]:
- Determine what factor you need to multiply 15 by to get 30: [tex]\(30 \div 15 = 2\)[/tex].
- Multiply both the numerator and the denominator of [tex]\(\frac{14}{15}\)[/tex] by this factor: [tex]\(\frac{14 \times 2}{15 \times 2} = \frac{28}{30}\)[/tex].
So, the renamed fractions with the least common denominator are:
[tex]\[
\frac{5}{6} = \frac{25}{30} \quad \text{and} \quad \frac{14}{15} = \frac{28}{30}
\][/tex]
These steps ensure that both fractions now have the same denominator, making it easier to compare or combine them.
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