Evaluate ( − 3 7 ) ÷ 7 8 \left(-\frac{3}{7}\right) \div \frac{7}{8} ( − 7 3 ​ ) ÷ 8 7 ​ , Giving Your Answer In Simplest Form.

by ADMIN 127 views

=====================================================

Introduction

When dealing with fractions, division can be a bit tricky. However, with the right approach, we can simplify the process and arrive at the correct answer. In this article, we will evaluate the expression (−37)÷78\left(-\frac{3}{7}\right) \div \frac{7}{8} and provide the result in its simplest form.

Understanding the Problem

To begin with, let's break down the given expression and understand what it means. The expression (−37)÷78\left(-\frac{3}{7}\right) \div \frac{7}{8} involves two fractions: (−37)\left(-\frac{3}{7}\right) and 78\frac{7}{8}. The task is to divide the first fraction by the second fraction.

The Division of Fractions

When dividing fractions, we need to follow a specific procedure. The key concept here is that division is equivalent to multiplication by the reciprocal of the divisor. In other words, to divide a fraction by another fraction, we can multiply the first fraction by the reciprocal of the second fraction.

Reciprocal of a Fraction

The reciprocal of a fraction is obtained by swapping its numerator and denominator. For example, the reciprocal of ab\frac{a}{b} is ba\frac{b}{a}. In our case, the reciprocal of 78\frac{7}{8} is 87\frac{8}{7}.

Evaluating the Expression

Now that we have a clear understanding of the concept, let's apply it to the given expression. We can rewrite the expression as follows:

(−37)÷78=(−37)×87\left(-\frac{3}{7}\right) \div \frac{7}{8} = \left(-\frac{3}{7}\right) \times \frac{8}{7}

Multiplying the Fractions

To multiply fractions, we simply multiply the numerators and denominators separately. In this case, we have:

(−37)×87=−3×87×7\left(-\frac{3}{7}\right) \times \frac{8}{7} = \frac{-3 \times 8}{7 \times 7}

Simplifying the Result

Now that we have the product of the fractions, let's simplify the result. We can start by multiplying the numerators and denominators:

−3×87×7=−2449\frac{-3 \times 8}{7 \times 7} = \frac{-24}{49}

Conclusion

In conclusion, the expression (−37)÷78\left(-\frac{3}{7}\right) \div \frac{7}{8} can be evaluated by multiplying the first fraction by the reciprocal of the second fraction. The result is −2449\frac{-24}{49}, which is the simplest form of the expression.

Final Answer

The final answer is −2449\boxed{\frac{-24}{49}}.

Frequently Asked Questions

Q: What is the reciprocal of a fraction?

A: The reciprocal of a fraction is obtained by swapping its numerator and denominator.

Q: How do we divide fractions?

A: To divide fractions, we multiply the first fraction by the reciprocal of the second fraction.

Q: Can we simplify the result of the expression?

A: Yes, we can simplify the result by multiplying the numerators and denominators.

Q: What is the final answer to the expression?

A: The final answer is −2449\boxed{\frac{-24}{49}}.

Additional Resources

For more information on fractions and division, you can refer to the following resources:

References

=====================================================

Q&A: Evaluating (−37)÷78\left(-\frac{3}{7}\right) \div \frac{7}{8}

Q: What is the reciprocal of a fraction?

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

Q: How do we divide fractions?

A: To divide fractions, we multiply the first fraction by the reciprocal of the second fraction. This means that we can rewrite the division as a multiplication by the reciprocal.

Q: Can we simplify the result of the expression?

A: Yes, we can simplify the result by multiplying the numerators and denominators. This will help us to obtain the simplest form of the expression.

Q: What is the final answer to the expression?

A: The final answer to the expression (−37)÷78\left(-\frac{3}{7}\right) \div \frac{7}{8} is −2449\boxed{\frac{-24}{49}}.

Q: Why do we need to multiply the fractions by the reciprocal?

A: We need to multiply the fractions by the reciprocal because division is equivalent to multiplication by the reciprocal of the divisor. This is a fundamental concept in mathematics that helps us to simplify complex expressions.

Q: Can we use a calculator to evaluate the expression?

A: Yes, we can use a calculator to evaluate the expression. However, it's always a good idea to understand the underlying math and simplify the expression before using a calculator.

Q: How do we know if the result is in its simplest form?

A: We can check if the result is in its simplest form by looking for any common factors between the numerator and denominator. If there are any common factors, we can simplify the result by dividing both the numerator and denominator by the common factor.

Q: Can we apply this concept to other types of fractions?

A: Yes, we can apply this concept to other types of fractions, including positive and negative fractions, as well as fractions with different denominators.

Additional Resources

For more information on fractions and division, you can refer to the following resources:

References

Conclusion

In conclusion, evaluating the expression (−37)÷78\left(-\frac{3}{7}\right) \div \frac{7}{8} requires a clear understanding of the concept of division and the reciprocal of a fraction. By following the steps outlined in this article, we can simplify the expression and arrive at the final answer.