Answer :
To solve the division of fractions problem and express the result in its lowest terms, we need to follow these steps:
1. Understand the Division of Fractions:
Dividing fractions means you multiply by the reciprocal of the second fraction. So, for [tex]\(\frac{5}{6} \div \frac{14}{15}\)[/tex], you multiply [tex]\(\frac{5}{6}\)[/tex] by the reciprocal of [tex]\(\frac{14}{15}\)[/tex], which is [tex]\(\frac{15}{14}\)[/tex].
2. Multiply the Fractions:
[tex]\[
\frac{5}{6} \times \frac{15}{14} = \frac{5 \times 15}{6 \times 14}
\][/tex]
3. Calculate the Numerator and Denominator:
- Multiply the numerators: [tex]\(5 \times 15 = 75\)[/tex].
- Multiply the denominators: [tex]\(6 \times 14 = 84\)[/tex].
4. Form the New Fraction:
[tex]\[
\frac{75}{84}
\][/tex]
5. Simplify the Fraction:
To simplify [tex]\(\frac{75}{84}\)[/tex], find the greatest common divisor (GCD) of 75 and 84. The GCD here is 3.
Divide both the numerator and the denominator by their GCD:
- Simplified numerator: [tex]\(75 \div 3 = 25\)[/tex]
- Simplified denominator: [tex]\(84 \div 3 = 28\)[/tex]
6. Result in Lowest Terms:
The fraction [tex]\(\frac{75}{84}\)[/tex] simplifies to [tex]\(\frac{25}{28}\)[/tex].
Therefore, [tex]\(\frac{5}{6} \div \frac{14}{15}\)[/tex] expressed in its lowest terms is [tex]\(\frac{25}{28}\)[/tex].
1. Understand the Division of Fractions:
Dividing fractions means you multiply by the reciprocal of the second fraction. So, for [tex]\(\frac{5}{6} \div \frac{14}{15}\)[/tex], you multiply [tex]\(\frac{5}{6}\)[/tex] by the reciprocal of [tex]\(\frac{14}{15}\)[/tex], which is [tex]\(\frac{15}{14}\)[/tex].
2. Multiply the Fractions:
[tex]\[
\frac{5}{6} \times \frac{15}{14} = \frac{5 \times 15}{6 \times 14}
\][/tex]
3. Calculate the Numerator and Denominator:
- Multiply the numerators: [tex]\(5 \times 15 = 75\)[/tex].
- Multiply the denominators: [tex]\(6 \times 14 = 84\)[/tex].
4. Form the New Fraction:
[tex]\[
\frac{75}{84}
\][/tex]
5. Simplify the Fraction:
To simplify [tex]\(\frac{75}{84}\)[/tex], find the greatest common divisor (GCD) of 75 and 84. The GCD here is 3.
Divide both the numerator and the denominator by their GCD:
- Simplified numerator: [tex]\(75 \div 3 = 25\)[/tex]
- Simplified denominator: [tex]\(84 \div 3 = 28\)[/tex]
6. Result in Lowest Terms:
The fraction [tex]\(\frac{75}{84}\)[/tex] simplifies to [tex]\(\frac{25}{28}\)[/tex].
Therefore, [tex]\(\frac{5}{6} \div \frac{14}{15}\)[/tex] expressed in its lowest terms is [tex]\(\frac{25}{28}\)[/tex].
