To divide the fraction [tex]\(\frac{-7}{25}\)[/tex] by the fraction [tex]\(\frac{14}{5}\)[/tex], follow these steps:
1. Understand Division of Fractions:
To divide one fraction by another, you multiply the first fraction by the reciprocal (or inverse) of the second fraction. The reciprocal of a fraction [tex]\( \frac{a}{b} \)[/tex] is [tex]\( \frac{b}{a} \)[/tex].
2. Find the Reciprocal:
The reciprocal of [tex]\(\frac{14}{5}\)[/tex] is [tex]\(\frac{5}{14}\)[/tex].
3. Set Up the Multiplication:
Now, multiply [tex]\(\frac{-7}{25}\)[/tex] by [tex]\(\frac{5}{14}\)[/tex]:
[tex]\[
\frac{-7}{25} \times \frac{5}{14}
\][/tex]
4. Multiply the Numerators:
Multiply the numerators of the fractions together:
[tex]\[
-7 \times 5 = -35
\][/tex]
5. Multiply the Denominators:
Multiply the denominators of the fractions together:
[tex]\[
25 \times 14 = 350
\][/tex]
6. Construct the Resulting Fraction:
Combine the results of the multiplication of the numerators and the denominators to form the new fraction:
[tex]\[
\frac{-35}{350}
\][/tex]
7. Simplify the Fraction:
Simplify the fraction by finding the greatest common divisor (GCD) of the numerator and the denominator and dividing both by this number. The GCD of 35 and 350 is 35.
[tex]\[
\frac{-35 \div 35}{350 \div 35} = \frac{-1}{10}
\][/tex]
So, the result of dividing [tex]\(\frac{-7}{25}\)[/tex] by [tex]\(\frac{14}{5}\)[/tex] is:
[tex]\[
\frac{-1}{10} \approx -0.1
\][/tex]
Numerically, we obtain approximately -0.10000000000000002 as the precise value when considering floating-point arithmetic.
