Divide { -2$}$ By { -3 \frac{4}{5}$}$.

by ADMIN 39 views

Understanding the Problem

When we are asked to divide two numbers, we are essentially finding out how many times one number fits into the other. However, when dealing with fractions and mixed numbers, things can get a bit more complicated. In this case, we are tasked with dividing −2-2 by −345-3 \frac{4}{5}. To approach this problem, we need to first understand the concept of dividing by a mixed number.

What is a Mixed Number?

A mixed number is a combination of a whole number and a fraction. In this case, −345-3 \frac{4}{5} can be broken down into −3-3 and 45\frac{4}{5}. When we divide by a mixed number, we need to convert it into an improper fraction first.

Converting the Mixed Number to an Improper Fraction

To convert a mixed number to an improper fraction, we need to multiply the whole number by the denominator and then add the numerator. In this case, we have:

−345=(−3×5)+45-3 \frac{4}{5} = \frac{(-3 \times 5) + 4}{5}

=−15+45= \frac{-15 + 4}{5}

=−115= \frac{-11}{5}

So, −345-3 \frac{4}{5} is equivalent to −115\frac{-11}{5}.

Dividing by a Fraction

When we divide by a fraction, we can actually multiply by its reciprocal instead. The reciprocal of a fraction is obtained by swapping the numerator and the denominator. In this case, the reciprocal of −115\frac{-11}{5} is 5−11\frac{5}{-11}.

How to Divide by a Fraction

To divide by a fraction, we can follow these steps:

  1. Multiply the dividend by the reciprocal of the divisor.
  2. Simplify the resulting fraction, if possible.

In this case, we have:

−2÷−115=−2×5−11-2 \div \frac{-11}{5} = -2 \times \frac{5}{-11}

Multiplying the Numbers

When we multiply two fractions, we need to multiply the numerators and the denominators separately. In this case, we have:

−2×5−11=(−2×5)(−11)-2 \times \frac{5}{-11} = \frac{(-2 \times 5)}{(-11)}

=−10−11= \frac{-10}{-11}

Simplifying the Result

When we simplify a fraction, we need to find the greatest common divisor (GCD) of the numerator and the denominator and divide both numbers by it. In this case, the GCD of −10-10 and −11-11 is 11, so the fraction is already in its simplest form.

The Final Answer

Therefore, the result of dividing −2-2 by −345-3 \frac{4}{5} is −10−11\frac{-10}{-11}, which can be simplified to 1011\frac{10}{11}.

Conclusion

Dividing by a mixed number can be a bit tricky, but by converting it to an improper fraction and then multiplying by its reciprocal, we can simplify the process. In this case, we were able to divide −2-2 by −345-3 \frac{4}{5} and obtain the result 1011\frac{10}{11}.

Frequently Asked Questions

  • What is a mixed number? A mixed number is a combination of a whole number and a fraction.
  • How do I convert a mixed number to an improper fraction? To convert a mixed number to an improper fraction, multiply the whole number by the denominator and then add the numerator.
  • How do I divide by a fraction? To divide by a fraction, multiply the dividend by the reciprocal of the divisor.
  • What is the reciprocal of a fraction? The reciprocal of a fraction is obtained by swapping the numerator and the denominator.

Further Reading

Q&A: Dividing by Mixed Numbers

Q: What is a mixed number?

A: A mixed number is a combination of a whole number and a fraction. For example, −345-3 \frac{4}{5} is a mixed number.

Q: How do I convert a mixed number to an improper fraction?

A: To convert a mixed number to an improper fraction, multiply the whole number by the denominator and then add the numerator. For example, −345=(−3×5)+45=−15+45=−115-3 \frac{4}{5} = \frac{(-3 \times 5) + 4}{5} = \frac{-15 + 4}{5} = \frac{-11}{5}.

Q: How do I divide by a mixed number?

A: To divide by a mixed number, first convert it to an improper fraction, and then multiply the dividend by the reciprocal of the divisor. For example, −2÷−345=−2×5−11-2 \div -3 \frac{4}{5} = -2 \times \frac{5}{-11}.

Q: What is the reciprocal of a fraction?

A: The reciprocal of a fraction is obtained by swapping the numerator and the denominator. For example, the reciprocal of ab\frac{a}{b} is ba\frac{b}{a}.

Q: How do I simplify a fraction?

A: To simplify a fraction, find the greatest common divisor (GCD) of the numerator and the denominator and divide both numbers by it. For example, −10−11\frac{-10}{-11} is already in its simplest form.

Q: Can I divide by a negative mixed number?

A: Yes, you can divide by a negative mixed number. To do this, first convert the mixed number to an improper fraction, and then multiply the dividend by the reciprocal of the divisor. For example, −2÷−345=−2×5−11-2 \div -3 \frac{4}{5} = -2 \times \frac{5}{-11}.

Q: Can I divide by a mixed number with a negative whole number?

A: Yes, you can divide by a mixed number with a negative whole number. To do this, first convert the mixed number to an improper fraction, and then multiply the dividend by the reciprocal of the divisor. For example, −2÷−345=−2×5−11-2 \div -3 \frac{4}{5} = -2 \times \frac{5}{-11}.

Q: Can I divide by a mixed number with a negative fraction?

A: Yes, you can divide by a mixed number with a negative fraction. To do this, first convert the mixed number to an improper fraction, and then multiply the dividend by the reciprocal of the divisor. For example, −2÷−345=−2×5−11-2 \div -3 \frac{4}{5} = -2 \times \frac{5}{-11}.

Q: Can I divide by a mixed number with a zero denominator?

A: No, you cannot divide by a mixed number with a zero denominator. This is because division by zero is undefined.

Q: Can I divide by a mixed number with a zero numerator?

A: No, you cannot divide by a mixed number with a zero numerator. This is because division by zero is undefined.

Q: Can I divide by a mixed number with a negative numerator?

A: Yes, you can divide by a mixed number with a negative numerator. To do this, first convert the mixed number to an improper fraction, and then multiply the dividend by the reciprocal of the divisor. For example, −2÷−345=−2×5−11-2 \div -3 \frac{4}{5} = -2 \times \frac{5}{-11}.

Q: Can I divide by a mixed number with a negative denominator?

A: Yes, you can divide by a mixed number with a negative denominator. To do this, first convert the mixed number to an improper fraction, and then multiply the dividend by the reciprocal of the divisor. For example, −2÷−345=−2×5−11-2 \div -3 \frac{4}{5} = -2 \times \frac{5}{-11}.

Conclusion

Dividing by mixed numbers can be a bit tricky, but by following the steps outlined in this article, you can simplify the process and obtain the correct result. Remember to convert the mixed number to an improper fraction, multiply the dividend by the reciprocal of the divisor, and simplify the resulting fraction, if possible.

Further Reading