Answer :
To solve the division of two fractions [tex]\(\frac{14}{15} \div \frac{35}{55}\)[/tex], follow these simple steps:
1. Understand the Operation:
- Dividing fractions is equivalent to multiplying by the reciprocal. This means [tex]\(\frac{14}{15} \div \frac{35}{55}\)[/tex] is the same as [tex]\(\frac{14}{15} \times \frac{55}{35}\)[/tex].
2. Simplify the Second Fraction:
- First, simplify [tex]\(\frac{35}{55}\)[/tex] if possible. The greatest common divisor (GCD) of 35 and 55 is 5.
- Divide both the numerator and the denominator by 5:
[tex]\[
\frac{35}{55} = \frac{35 \div 5}{55 \div 5} = \frac{7}{11}
\][/tex]
3. Find the Reciprocal:
- The reciprocal of [tex]\(\frac{7}{11}\)[/tex] is [tex]\(\frac{11}{7}\)[/tex].
4. Multiply by the Reciprocal:
- Multiply [tex]\(\frac{14}{15}\)[/tex] by [tex]\(\frac{11}{7}\)[/tex]:
[tex]\[
\frac{14}{15} \times \frac{11}{7} = \frac{14 \times 11}{15 \times 7} = \frac{154}{105}
\][/tex]
5. Simplify if Necessary:
- Simplify [tex]\(\frac{154}{105}\)[/tex] further if possible by finding the GCD of 154 and 105. The numerator and denominator share a factor of 7:
[tex]\[
\frac{154}{105} = \frac{154 \div 7}{105 \div 7} = \frac{22}{15}
\][/tex]
Thus, the result of [tex]\(\frac{14}{15} \div \frac{35}{55}\)[/tex] is [tex]\(\frac{22}{15}\)[/tex], which is approximately [tex]\(1.4667\)[/tex] when expressed as a decimal.
1. Understand the Operation:
- Dividing fractions is equivalent to multiplying by the reciprocal. This means [tex]\(\frac{14}{15} \div \frac{35}{55}\)[/tex] is the same as [tex]\(\frac{14}{15} \times \frac{55}{35}\)[/tex].
2. Simplify the Second Fraction:
- First, simplify [tex]\(\frac{35}{55}\)[/tex] if possible. The greatest common divisor (GCD) of 35 and 55 is 5.
- Divide both the numerator and the denominator by 5:
[tex]\[
\frac{35}{55} = \frac{35 \div 5}{55 \div 5} = \frac{7}{11}
\][/tex]
3. Find the Reciprocal:
- The reciprocal of [tex]\(\frac{7}{11}\)[/tex] is [tex]\(\frac{11}{7}\)[/tex].
4. Multiply by the Reciprocal:
- Multiply [tex]\(\frac{14}{15}\)[/tex] by [tex]\(\frac{11}{7}\)[/tex]:
[tex]\[
\frac{14}{15} \times \frac{11}{7} = \frac{14 \times 11}{15 \times 7} = \frac{154}{105}
\][/tex]
5. Simplify if Necessary:
- Simplify [tex]\(\frac{154}{105}\)[/tex] further if possible by finding the GCD of 154 and 105. The numerator and denominator share a factor of 7:
[tex]\[
\frac{154}{105} = \frac{154 \div 7}{105 \div 7} = \frac{22}{15}
\][/tex]
Thus, the result of [tex]\(\frac{14}{15} \div \frac{35}{55}\)[/tex] is [tex]\(\frac{22}{15}\)[/tex], which is approximately [tex]\(1.4667\)[/tex] when expressed as a decimal.
