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Answer :
To simplify the given expression [tex]\(\frac{14}{15} \div \frac{21}{55}\)[/tex], follow these steps:
1. Understand the Division of Fractions: When you divide by a fraction, it is equivalent to multiplying by its reciprocal. In this case, [tex]\(\frac{14}{15} \div \frac{21}{55}\)[/tex] is the same as [tex]\(\frac{14}{15} \times \frac{55}{21}\)[/tex].
2. Multiply the Fractions: Multiply the numerators and the denominators separately:
[tex]\[
\text{Numerator: } 14 \times 55 = 770
\][/tex]
[tex]\[
\text{Denominator: } 15 \times 21 = 315
\][/tex]
This gives us the fraction [tex]\(\frac{770}{315}\)[/tex].
3. Simplify the Fraction: To simplify [tex]\(\frac{770}{315}\)[/tex], you need to find the greatest common divisor (GCD) of 770 and 315, which is a number that can divide both evenly.
4. Calculate the GCD: The GCD of 770 and 315 is 35.
5. Divide Both the Numerator and the Denominator by the GCD:
[tex]\[
\frac{770 \div 35}{315 \div 35} = \frac{22}{9}
\][/tex]
The simplified form of the expression is [tex]\(\frac{22}{9}\)[/tex].
1. Understand the Division of Fractions: When you divide by a fraction, it is equivalent to multiplying by its reciprocal. In this case, [tex]\(\frac{14}{15} \div \frac{21}{55}\)[/tex] is the same as [tex]\(\frac{14}{15} \times \frac{55}{21}\)[/tex].
2. Multiply the Fractions: Multiply the numerators and the denominators separately:
[tex]\[
\text{Numerator: } 14 \times 55 = 770
\][/tex]
[tex]\[
\text{Denominator: } 15 \times 21 = 315
\][/tex]
This gives us the fraction [tex]\(\frac{770}{315}\)[/tex].
3. Simplify the Fraction: To simplify [tex]\(\frac{770}{315}\)[/tex], you need to find the greatest common divisor (GCD) of 770 and 315, which is a number that can divide both evenly.
4. Calculate the GCD: The GCD of 770 and 315 is 35.
5. Divide Both the Numerator and the Denominator by the GCD:
[tex]\[
\frac{770 \div 35}{315 \div 35} = \frac{22}{9}
\][/tex]
The simplified form of the expression is [tex]\(\frac{22}{9}\)[/tex].
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