Answer :
Sure! Let's work through the steps to rename the fractions [tex]\(\frac{3}{5}\)[/tex] and [tex]\(\frac{6}{7}\)[/tex] using the least common denominator.
1. Identify the Denominators:
- For [tex]\(\frac{3}{5}\)[/tex], the denominator is 5.
- For [tex]\(\frac{6}{7}\)[/tex], the denominator is 7.
2. Find the Least Common Denominator (LCD):
- The LCD of two numbers (5 and 7) is the smallest number that is a multiple of both.
- Since 5 and 7 are prime numbers, their LCD is their product: [tex]\(5 \times 7 = 35\)[/tex].
3. Convert Each Fraction:
- For [tex]\(\frac{3}{5}\)[/tex]:
- Multiply both the numerator and the denominator by the number that makes the denominator 35. Since [tex]\(35 \div 5 = 7\)[/tex], multiply by 7.
- So, [tex]\(\frac{3}{5} = \frac{3 \times 7}{5 \times 7} = \frac{21}{35}\)[/tex].
- For [tex]\(\frac{6}{7}\)[/tex]:
- Multiply both the numerator and the denominator by the number that makes the denominator 35. Since [tex]\(35 \div 7 = 5\)[/tex], multiply by 5.
- So, [tex]\(\frac{6}{7} = \frac{6 \times 5}{7 \times 5} = \frac{30}{35}\)[/tex].
4. Resulting Fractions:
- The renamed fractions with the common denominator of 35 are [tex]\(\frac{21}{35}\)[/tex] and [tex]\(\frac{30}{35}\)[/tex].
This matches the result [tex]\(((21, 35), (30, 35))\)[/tex], which lists the equivalent fractions with 35 as the common denominator.
1. Identify the Denominators:
- For [tex]\(\frac{3}{5}\)[/tex], the denominator is 5.
- For [tex]\(\frac{6}{7}\)[/tex], the denominator is 7.
2. Find the Least Common Denominator (LCD):
- The LCD of two numbers (5 and 7) is the smallest number that is a multiple of both.
- Since 5 and 7 are prime numbers, their LCD is their product: [tex]\(5 \times 7 = 35\)[/tex].
3. Convert Each Fraction:
- For [tex]\(\frac{3}{5}\)[/tex]:
- Multiply both the numerator and the denominator by the number that makes the denominator 35. Since [tex]\(35 \div 5 = 7\)[/tex], multiply by 7.
- So, [tex]\(\frac{3}{5} = \frac{3 \times 7}{5 \times 7} = \frac{21}{35}\)[/tex].
- For [tex]\(\frac{6}{7}\)[/tex]:
- Multiply both the numerator and the denominator by the number that makes the denominator 35. Since [tex]\(35 \div 7 = 5\)[/tex], multiply by 5.
- So, [tex]\(\frac{6}{7} = \frac{6 \times 5}{7 \times 5} = \frac{30}{35}\)[/tex].
4. Resulting Fractions:
- The renamed fractions with the common denominator of 35 are [tex]\(\frac{21}{35}\)[/tex] and [tex]\(\frac{30}{35}\)[/tex].
This matches the result [tex]\(((21, 35), (30, 35))\)[/tex], which lists the equivalent fractions with 35 as the common denominator.
