Answer :
To solve the division of fractions problem [tex]\(-\frac{16}{5} \div \frac{12}{25}\)[/tex], follow these steps:
1. Understand the Division of Fractions: Dividing by a fraction is the same as multiplying by its reciprocal. Therefore, [tex]\(-\frac{16}{5} \div \frac{12}{25}\)[/tex] becomes [tex]\(-\frac{16}{5} \times \frac{25}{12}\)[/tex].
2. Multiply the Fractions: Multiply the numerators together and the denominators together:
[tex]\[
\text{Numerator: } (-16) \times 25 = -400
\][/tex]
[tex]\[
\text{Denominator: } 5 \times 12 = 60
\][/tex]
So the fraction becomes [tex]\(-\frac{400}{60}\)[/tex].
3. Simplify the Fraction: To simplify [tex]\(-\frac{400}{60}\)[/tex], find the greatest common divisor (GCD) of 400 and 60. The GCD is 20.
4. Divide the Numerator and Denominator by the GCD:
[tex]\[
\text{Simplified Numerator: } \frac{-400}{20} = -20
\][/tex]
[tex]\[
\text{Simplified Denominator: } \frac{60}{20} = 3
\][/tex]
So the simplified fraction is [tex]\(-\frac{20}{3}\)[/tex].
5. Convert to a Mixed Number: If needed, convert the improper fraction [tex]\(-\frac{20}{3}\)[/tex] into a mixed number.
[tex]\[
-20 \div 3 = -6 \text{ remainder } 2
\][/tex]
Therefore, [tex]\(-\frac{20}{3}\)[/tex] can be expressed as [tex]\(-6 \frac{2}{3}\)[/tex].
Thus, the answer to [tex]\(-\frac{16}{5} \div \frac{12}{25}\)[/tex] is [tex]\(-6 \frac{2}{3}\)[/tex] or [tex]\(-\frac{20}{3}\)[/tex] as a fraction.
1. Understand the Division of Fractions: Dividing by a fraction is the same as multiplying by its reciprocal. Therefore, [tex]\(-\frac{16}{5} \div \frac{12}{25}\)[/tex] becomes [tex]\(-\frac{16}{5} \times \frac{25}{12}\)[/tex].
2. Multiply the Fractions: Multiply the numerators together and the denominators together:
[tex]\[
\text{Numerator: } (-16) \times 25 = -400
\][/tex]
[tex]\[
\text{Denominator: } 5 \times 12 = 60
\][/tex]
So the fraction becomes [tex]\(-\frac{400}{60}\)[/tex].
3. Simplify the Fraction: To simplify [tex]\(-\frac{400}{60}\)[/tex], find the greatest common divisor (GCD) of 400 and 60. The GCD is 20.
4. Divide the Numerator and Denominator by the GCD:
[tex]\[
\text{Simplified Numerator: } \frac{-400}{20} = -20
\][/tex]
[tex]\[
\text{Simplified Denominator: } \frac{60}{20} = 3
\][/tex]
So the simplified fraction is [tex]\(-\frac{20}{3}\)[/tex].
5. Convert to a Mixed Number: If needed, convert the improper fraction [tex]\(-\frac{20}{3}\)[/tex] into a mixed number.
[tex]\[
-20 \div 3 = -6 \text{ remainder } 2
\][/tex]
Therefore, [tex]\(-\frac{20}{3}\)[/tex] can be expressed as [tex]\(-6 \frac{2}{3}\)[/tex].
Thus, the answer to [tex]\(-\frac{16}{5} \div \frac{12}{25}\)[/tex] is [tex]\(-6 \frac{2}{3}\)[/tex] or [tex]\(-\frac{20}{3}\)[/tex] as a fraction.