Answer :
To divide two fractions, we can multiply the first fraction by the reciprocal of the second fraction. Reciprocal means flipping the numerator and denominator of the fraction. Let's go through the steps to solve [tex]\(-\frac{7}{12} \div \frac{14}{15}\)[/tex].
1. Identify the fractions:
The first fraction is [tex]\(-\frac{7}{12}\)[/tex] and the second fraction is [tex]\(\frac{14}{15}\)[/tex].
2. Find the reciprocal:
The reciprocal of [tex]\(\frac{14}{15}\)[/tex] is [tex]\(\frac{15}{14}\)[/tex].
3. Multiply the first fraction by the reciprocal of the second:
Multiply [tex]\(-\frac{7}{12}\)[/tex] by [tex]\(\frac{15}{14}\)[/tex]:
[tex]\[
-\frac{7}{12} \times \frac{15}{14}
\][/tex]
4. Multiply the numerators:
[tex]\(-7 \times 15 = -105\)[/tex]
5. Multiply the denominators:
[tex]\(12 \times 14 = 168\)[/tex]
6. Write the result:
The result of the multiplication is [tex]\(-\frac{105}{168}\)[/tex].
7. Simplify the fraction:
To simplify [tex]\(-\frac{105}{168}\)[/tex], find the greatest common divisor (GCD) of 105 and 168, which is 21.
Divide the numerator and the denominator by their GCD:
[tex]\[
\frac{-105 \div 21}{168 \div 21} = \frac{-5}{8}
\][/tex]
So, [tex]\(-\frac{7}{12} \div \frac{14}{15}\)[/tex] simplifies to [tex]\(-\frac{5}{8}\)[/tex]. Therefore, the answer to the division is [tex]\(-\frac{5}{8}\)[/tex].
1. Identify the fractions:
The first fraction is [tex]\(-\frac{7}{12}\)[/tex] and the second fraction is [tex]\(\frac{14}{15}\)[/tex].
2. Find the reciprocal:
The reciprocal of [tex]\(\frac{14}{15}\)[/tex] is [tex]\(\frac{15}{14}\)[/tex].
3. Multiply the first fraction by the reciprocal of the second:
Multiply [tex]\(-\frac{7}{12}\)[/tex] by [tex]\(\frac{15}{14}\)[/tex]:
[tex]\[
-\frac{7}{12} \times \frac{15}{14}
\][/tex]
4. Multiply the numerators:
[tex]\(-7 \times 15 = -105\)[/tex]
5. Multiply the denominators:
[tex]\(12 \times 14 = 168\)[/tex]
6. Write the result:
The result of the multiplication is [tex]\(-\frac{105}{168}\)[/tex].
7. Simplify the fraction:
To simplify [tex]\(-\frac{105}{168}\)[/tex], find the greatest common divisor (GCD) of 105 and 168, which is 21.
Divide the numerator and the denominator by their GCD:
[tex]\[
\frac{-105 \div 21}{168 \div 21} = \frac{-5}{8}
\][/tex]
So, [tex]\(-\frac{7}{12} \div \frac{14}{15}\)[/tex] simplifies to [tex]\(-\frac{5}{8}\)[/tex]. Therefore, the answer to the division is [tex]\(-\frac{5}{8}\)[/tex].
