Get the answers you need at Westonci.ca, where our expert community is dedicated to providing you with accurate information. Discover the answers you need from a community of experts ready to help you with their knowledge and experience in various fields. Our platform provides a seamless experience for finding reliable answers from a network of experienced professionals.
Sagot :
To find the Least Common Denominator (LCD) for the fractions [tex]\(\frac{7}{10}\)[/tex] and [tex]\(\frac{5}{6}\)[/tex] and express each fraction using this common denominator, we'll proceed step-by-step.
### Step 1: Identify the Denominators
First, identify the denominators of the given fractions:
- The denominators are [tex]\(10\)[/tex] and [tex]\(6\)[/tex].
### Step 2: Calculate the Least Common Denominator (LCD)
To find the LCD of the two denominators, we need to determine the smallest number that both [tex]\(10\)[/tex] and [tex]\(6\)[/tex] can divide without a remainder. The Least Common Denominator is:
[tex]\[ \text{LCD}(10, 6) = 30 \][/tex]
### Step 3: Convert Each Fraction to Use the LCD
Next, we convert each fraction to an equivalent fraction with the common denominator [tex]\(30\)[/tex].
#### Converting [tex]\(\frac{7}{10}\)[/tex]:
To convert [tex]\(\frac{7}{10}\)[/tex], multiply both the numerator and the denominator by the same number to get [tex]\(30\)[/tex] in the denominator:
[tex]\[ \frac{7}{10} = \frac{7 \times 3}{10 \times 3} = \frac{21}{30} \][/tex]
#### Converting [tex]\(\frac{5}{6}\)[/tex]:
Similarly, convert [tex]\(\frac{5}{6}\)[/tex] by multiplying the numerator and the denominator to get [tex]\(30\)[/tex] in the denominator:
[tex]\[ \frac{5}{6} = \frac{5 \times 5}{6 \times 5} = \frac{25}{30} \][/tex]
### Final Equivalents:
Thus, the fractions [tex]\(\frac{7}{10}\)[/tex] and [tex]\(\frac{5}{6}\)[/tex] expressed with the Least Common Denominator [tex]\(30\)[/tex] are:
[tex]\[ \frac{7}{10} = \frac{21}{30} \][/tex]
[tex]\[ \frac{5}{6} = \frac{25}{30} \][/tex]
### Related Conversions for Given Fractions:
Given the additional fractions to be converted to a common denominator, follow similar steps.
#### Converting [tex]\(\frac{7}{30}, \frac{5}{30}\)[/tex]:
These fractions already have a common denominator of [tex]\(30\)[/tex] and are:
[tex]\[ \frac{7}{30} \quad \text{and} \quad \frac{5}{30} \][/tex]
#### Converting [tex]\(\frac{42}{60}, \frac{30}{60}\)[/tex]:
These fractions already have a common denominator of [tex]\(60\)[/tex] and are:
[tex]\[ \frac{42}{60} \quad \text{and} \quad \frac{30}{60} \][/tex]
#### Converting [tex]\(\frac{42}{60}, \frac{50}{60}\)[/tex]:
These fractions already have a common denominator of [tex]\(60\)[/tex] and are:
[tex]\[ \frac{42}{60} \quad \text{and} \quad \frac{50}{60} \][/tex]
Therefore, the results of these conversions are:
1. The Least Common Denominator is [tex]\(30\)[/tex].
2. The fractions [tex]\(\frac{7}{10}\)[/tex] and [tex]\(\frac{5}{6}\)[/tex] expressed with the Least Common Denominator are:
[tex]\[ \frac{7}{10} = \frac{21}{30} \][/tex]
[tex]\[ \frac{5}{6} = \frac{25}{30} \][/tex]
The provided fractions have been confirmed as:
[tex]\[ \frac{7}{30}, \frac{5}{30}, \frac{21}{30}, \frac{25}{30}, \frac{42}{60}, \frac{30}{60}, \frac{42}{60}, \frac{50}{60} \][/tex]
These results are consistent with the original question and the given solution.
### Step 1: Identify the Denominators
First, identify the denominators of the given fractions:
- The denominators are [tex]\(10\)[/tex] and [tex]\(6\)[/tex].
### Step 2: Calculate the Least Common Denominator (LCD)
To find the LCD of the two denominators, we need to determine the smallest number that both [tex]\(10\)[/tex] and [tex]\(6\)[/tex] can divide without a remainder. The Least Common Denominator is:
[tex]\[ \text{LCD}(10, 6) = 30 \][/tex]
### Step 3: Convert Each Fraction to Use the LCD
Next, we convert each fraction to an equivalent fraction with the common denominator [tex]\(30\)[/tex].
#### Converting [tex]\(\frac{7}{10}\)[/tex]:
To convert [tex]\(\frac{7}{10}\)[/tex], multiply both the numerator and the denominator by the same number to get [tex]\(30\)[/tex] in the denominator:
[tex]\[ \frac{7}{10} = \frac{7 \times 3}{10 \times 3} = \frac{21}{30} \][/tex]
#### Converting [tex]\(\frac{5}{6}\)[/tex]:
Similarly, convert [tex]\(\frac{5}{6}\)[/tex] by multiplying the numerator and the denominator to get [tex]\(30\)[/tex] in the denominator:
[tex]\[ \frac{5}{6} = \frac{5 \times 5}{6 \times 5} = \frac{25}{30} \][/tex]
### Final Equivalents:
Thus, the fractions [tex]\(\frac{7}{10}\)[/tex] and [tex]\(\frac{5}{6}\)[/tex] expressed with the Least Common Denominator [tex]\(30\)[/tex] are:
[tex]\[ \frac{7}{10} = \frac{21}{30} \][/tex]
[tex]\[ \frac{5}{6} = \frac{25}{30} \][/tex]
### Related Conversions for Given Fractions:
Given the additional fractions to be converted to a common denominator, follow similar steps.
#### Converting [tex]\(\frac{7}{30}, \frac{5}{30}\)[/tex]:
These fractions already have a common denominator of [tex]\(30\)[/tex] and are:
[tex]\[ \frac{7}{30} \quad \text{and} \quad \frac{5}{30} \][/tex]
#### Converting [tex]\(\frac{42}{60}, \frac{30}{60}\)[/tex]:
These fractions already have a common denominator of [tex]\(60\)[/tex] and are:
[tex]\[ \frac{42}{60} \quad \text{and} \quad \frac{30}{60} \][/tex]
#### Converting [tex]\(\frac{42}{60}, \frac{50}{60}\)[/tex]:
These fractions already have a common denominator of [tex]\(60\)[/tex] and are:
[tex]\[ \frac{42}{60} \quad \text{and} \quad \frac{50}{60} \][/tex]
Therefore, the results of these conversions are:
1. The Least Common Denominator is [tex]\(30\)[/tex].
2. The fractions [tex]\(\frac{7}{10}\)[/tex] and [tex]\(\frac{5}{6}\)[/tex] expressed with the Least Common Denominator are:
[tex]\[ \frac{7}{10} = \frac{21}{30} \][/tex]
[tex]\[ \frac{5}{6} = \frac{25}{30} \][/tex]
The provided fractions have been confirmed as:
[tex]\[ \frac{7}{30}, \frac{5}{30}, \frac{21}{30}, \frac{25}{30}, \frac{42}{60}, \frac{30}{60}, \frac{42}{60}, \frac{50}{60} \][/tex]
These results are consistent with the original question and the given solution.
Thank you for trusting us with your questions. We're here to help you find accurate answers quickly and efficiently. We hope our answers were useful. Return anytime for more information and answers to any other questions you have. Stay curious and keep coming back to Westonci.ca for answers to all your burning questions.
