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Answer :
To solve the division of fractions [tex]\(\frac{13}{15} \div \frac{7}{10}\)[/tex], you can follow these steps:
1. Understand Division of Fractions: Dividing by a fraction is the same as multiplying by its reciprocal. So, [tex]\(\frac{13}{15} \div \frac{7}{10}\)[/tex] is equivalent to [tex]\(\frac{13}{15} \times \frac{10}{7}\)[/tex].
2. Multiply the Fractions:
- To multiply fractions, multiply the numerators together and multiply the denominators together:
- The numerator: [tex]\(13 \times 10 = 130\)[/tex]
- The denominator: [tex]\(15 \times 7 = 105\)[/tex]
- So, the product is [tex]\(\frac{130}{105}\)[/tex].
3. Simplify the Fraction:
- To simplify [tex]\(\frac{130}{105}\)[/tex], find the greatest common divisor (GCD) of 130 and 105.
- The GCD of 130 and 105 is 5.
- Divide both the numerator and the denominator by their GCD:
- Numerator: [tex]\(130 \div 5 = 26\)[/tex]
- Denominator: [tex]\(105 \div 5 = 21\)[/tex]
4. Final Simplified Fraction:
- The simplified form of [tex]\(\frac{130}{105}\)[/tex] is [tex]\(\frac{26}{21}\)[/tex].
Therefore, the answer to [tex]\(\frac{13}{15} \div \frac{7}{10}\)[/tex] is [tex]\(\frac{26}{21}\)[/tex].
1. Understand Division of Fractions: Dividing by a fraction is the same as multiplying by its reciprocal. So, [tex]\(\frac{13}{15} \div \frac{7}{10}\)[/tex] is equivalent to [tex]\(\frac{13}{15} \times \frac{10}{7}\)[/tex].
2. Multiply the Fractions:
- To multiply fractions, multiply the numerators together and multiply the denominators together:
- The numerator: [tex]\(13 \times 10 = 130\)[/tex]
- The denominator: [tex]\(15 \times 7 = 105\)[/tex]
- So, the product is [tex]\(\frac{130}{105}\)[/tex].
3. Simplify the Fraction:
- To simplify [tex]\(\frac{130}{105}\)[/tex], find the greatest common divisor (GCD) of 130 and 105.
- The GCD of 130 and 105 is 5.
- Divide both the numerator and the denominator by their GCD:
- Numerator: [tex]\(130 \div 5 = 26\)[/tex]
- Denominator: [tex]\(105 \div 5 = 21\)[/tex]
4. Final Simplified Fraction:
- The simplified form of [tex]\(\frac{130}{105}\)[/tex] is [tex]\(\frac{26}{21}\)[/tex].
Therefore, the answer to [tex]\(\frac{13}{15} \div \frac{7}{10}\)[/tex] is [tex]\(\frac{26}{21}\)[/tex].
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