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Answer :
To rename the fractions [tex]\(\frac{5}{6}\)[/tex] and [tex]\(\frac{14}{15}\)[/tex] using the least common denominator, we'll follow these steps:
1. Identify the Denominators: The denominators we have are 6 and 15.
2. Finding the Least Common Denominator (LCD):
- The least common denominator is the smallest number that both 6 and 15 can divide evenly. To find this, we determine the least common multiple (LCM) of the denominators.
- List the multiples of 6: 6, 12, 18, 24, 30, ...
- List the multiples of 15: 15, 30, 45, ...
- The smallest common multiple is 30. So, the LCD is 30.
3. Renaming the Fractions:
- For [tex]\(\frac{5}{6}\)[/tex]:
- Multiply the numerator and the denominator by the same number to get a new denominator of 30.
- Determine what to multiply 6 by to get 30: [tex]\( \frac{30}{6} = 5 \)[/tex].
- Multiply both the numerator and denominator by 5:
[tex]\[
\frac{5}{6} = \frac{5 \times 5}{6 \times 5} = \frac{25}{30}
\][/tex]
- For [tex]\(\frac{14}{15}\)[/tex]:
- Determine what to multiply 15 by to get 30: [tex]\( \frac{30}{15} = 2 \)[/tex].
- Multiply both the numerator and denominator by 2:
[tex]\[
\frac{14}{15} = \frac{14 \times 2}{15 \times 2} = \frac{28}{30}
\][/tex]
4. Final Answer:
- [tex]\(\frac{5}{6} = \frac{25}{30}\)[/tex]
- [tex]\(\frac{14}{15} = \frac{28}{30}\)[/tex]
These fractions now have the same denominator, 30, making them easier to compare or perform operations on.
1. Identify the Denominators: The denominators we have are 6 and 15.
2. Finding the Least Common Denominator (LCD):
- The least common denominator is the smallest number that both 6 and 15 can divide evenly. To find this, we determine the least common multiple (LCM) of the denominators.
- List the multiples of 6: 6, 12, 18, 24, 30, ...
- List the multiples of 15: 15, 30, 45, ...
- The smallest common multiple is 30. So, the LCD is 30.
3. Renaming the Fractions:
- For [tex]\(\frac{5}{6}\)[/tex]:
- Multiply the numerator and the denominator by the same number to get a new denominator of 30.
- Determine what to multiply 6 by to get 30: [tex]\( \frac{30}{6} = 5 \)[/tex].
- Multiply both the numerator and denominator by 5:
[tex]\[
\frac{5}{6} = \frac{5 \times 5}{6 \times 5} = \frac{25}{30}
\][/tex]
- For [tex]\(\frac{14}{15}\)[/tex]:
- Determine what to multiply 15 by to get 30: [tex]\( \frac{30}{15} = 2 \)[/tex].
- Multiply both the numerator and denominator by 2:
[tex]\[
\frac{14}{15} = \frac{14 \times 2}{15 \times 2} = \frac{28}{30}
\][/tex]
4. Final Answer:
- [tex]\(\frac{5}{6} = \frac{25}{30}\)[/tex]
- [tex]\(\frac{14}{15} = \frac{28}{30}\)[/tex]
These fractions now have the same denominator, 30, making them easier to compare or perform operations on.
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