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Answer :
To solve the problem of finding the quotient [tex]\(\frac{13}{15} \div \frac{1}{6}\)[/tex], we can follow these steps:
1. Understand the Division of Fractions:
Dividing by a fraction is the same as multiplying by its reciprocal. This means that [tex]\(\frac{13}{15} \div \frac{1}{6}\)[/tex] can be rewritten as [tex]\(\frac{13}{15} \times \frac{6}{1}\)[/tex].
2. Multiply the Fractions:
When multiplying two fractions, you multiply the numerators together and the denominators together.
- Numerator: Multiply the numerators of the fractions: [tex]\(13 \times 6 = 78\)[/tex].
- Denominator: Multiply the denominators of the fractions: [tex]\(15 \times 1 = 15\)[/tex].
So, the product of the fractions is [tex]\(\frac{78}{15}\)[/tex].
3. Simplify the Fraction:
To simplify the fraction [tex]\(\frac{78}{15}\)[/tex], we need to find the greatest common divisor (GCD) of 78 and 15 and then divide both the numerator and the denominator by this number.
- The GCD of 78 and 15 is 3.
- Divide both the numerator and the denominator by 3:
- Numerator: [tex]\(78 \div 3 = 26\)[/tex]
- Denominator: [tex]\(15 \div 3 = 5\)[/tex]
Therefore, the simplified form of [tex]\(\frac{78}{15}\)[/tex] is [tex]\(\frac{26}{5}\)[/tex].
So, the quotient [tex]\(\frac{13}{15} \div \frac{1}{6}\)[/tex] simplifies to [tex]\(\frac{26}{5}\)[/tex].
1. Understand the Division of Fractions:
Dividing by a fraction is the same as multiplying by its reciprocal. This means that [tex]\(\frac{13}{15} \div \frac{1}{6}\)[/tex] can be rewritten as [tex]\(\frac{13}{15} \times \frac{6}{1}\)[/tex].
2. Multiply the Fractions:
When multiplying two fractions, you multiply the numerators together and the denominators together.
- Numerator: Multiply the numerators of the fractions: [tex]\(13 \times 6 = 78\)[/tex].
- Denominator: Multiply the denominators of the fractions: [tex]\(15 \times 1 = 15\)[/tex].
So, the product of the fractions is [tex]\(\frac{78}{15}\)[/tex].
3. Simplify the Fraction:
To simplify the fraction [tex]\(\frac{78}{15}\)[/tex], we need to find the greatest common divisor (GCD) of 78 and 15 and then divide both the numerator and the denominator by this number.
- The GCD of 78 and 15 is 3.
- Divide both the numerator and the denominator by 3:
- Numerator: [tex]\(78 \div 3 = 26\)[/tex]
- Denominator: [tex]\(15 \div 3 = 5\)[/tex]
Therefore, the simplified form of [tex]\(\frac{78}{15}\)[/tex] is [tex]\(\frac{26}{5}\)[/tex].
So, the quotient [tex]\(\frac{13}{15} \div \frac{1}{6}\)[/tex] simplifies to [tex]\(\frac{26}{5}\)[/tex].
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