Evaluate The Expression:${ \frac{2}{9} \div \frac{5}{7} = }$

by ADMIN 62 views

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

Introduction

In mathematics, division of fractions is a fundamental operation that involves dividing one fraction by another. It is an essential concept in algebra and arithmetic, and it is used extensively in various mathematical applications. In this article, we will evaluate the expression 29÷57\frac{2}{9} \div \frac{5}{7} and explore the concept of division of fractions in detail.

What is Division of Fractions?

Division of fractions is a mathematical operation that involves dividing one fraction by another. It is denoted by the symbol ÷\div and is used to find the quotient of two fractions. When we divide one fraction by another, we are essentially finding the ratio of the two fractions. For example, if we divide 23\frac{2}{3} by 45\frac{4}{5}, we are finding the ratio of 23\frac{2}{3} to 45\frac{4}{5}.

How to Evaluate Division of Fractions

To evaluate the division of fractions, we need to follow a specific procedure. The procedure involves inverting the second fraction and multiplying it by the first fraction. This is known as the "invert and multiply" rule. The rule states that to divide one fraction by another, we need to invert the second fraction and multiply it by the first fraction.

Evaluating the Expression 29÷57\frac{2}{9} \div \frac{5}{7}

To evaluate the expression 29÷57\frac{2}{9} \div \frac{5}{7}, we need to follow the "invert and multiply" rule. We will invert the second fraction 57\frac{5}{7} and multiply it by the first fraction 29\frac{2}{9}.

Step 1: Invert the Second Fraction

To invert the second fraction 57\frac{5}{7}, we need to swap its numerator and denominator. The inverted fraction is 75\frac{7}{5}.

Step 2: Multiply the First Fraction by the Inverted Second Fraction

Now that we have inverted the second fraction, we can multiply it by the first fraction 29\frac{2}{9}. To multiply two fractions, we need to multiply their numerators and denominators separately.

29×75=2×79×5=1445\frac{2}{9} \times \frac{7}{5} = \frac{2 \times 7}{9 \times 5} = \frac{14}{45}

Step 3: Simplify the Result

The result of the multiplication is 1445\frac{14}{45}. However, we can simplify this fraction by dividing both its numerator and denominator by their greatest common divisor (GCD).

The GCD of 14 and 45 is 1. Therefore, the simplified fraction is 1445\frac{14}{45}.

Conclusion

In conclusion, the expression 29÷57\frac{2}{9} \div \frac{5}{7} can be evaluated by following the "invert and multiply" rule. We inverted the second fraction 57\frac{5}{7} and multiplied it by the first fraction 29\frac{2}{9}. The result of the multiplication is 1445\frac{14}{45}, which is the final answer to the expression.

Frequently Asked Questions

Q: What is the "invert and multiply" rule?

A: The "invert and multiply" rule is a procedure for evaluating the division of fractions. It involves inverting the second fraction and multiplying it by the first fraction.

Q: How do I invert a fraction?

A: To invert a fraction, you need to swap its numerator and denominator.

Q: How do I multiply two fractions?

A: To multiply two fractions, you need to multiply their numerators and denominators separately.

Final Answer

The final answer to the expression 29÷57\frac{2}{9} \div \frac{5}{7} is 1445\frac{14}{45}.

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

Introduction

In our previous article, we evaluated the expression 29÷57\frac{2}{9} \div \frac{5}{7} and explored the concept of division of fractions in detail. In this article, we will answer some frequently asked questions about division of fractions.

Q&A

Q: What is the "invert and multiply" rule?

A: The "invert and multiply" rule is a procedure for evaluating the division of fractions. It involves inverting the second fraction and multiplying it by the first fraction.

Q: How do I invert a fraction?

A: To invert a fraction, you need to swap its numerator and denominator. For example, if you have the fraction 34\frac{3}{4}, the inverted fraction would be 43\frac{4}{3}.

Q: How do I multiply two fractions?

A: To multiply two fractions, you need to multiply their numerators and denominators separately. For example, if you have the fractions 23\frac{2}{3} and 45\frac{4}{5}, the product would be 2×43×5=815\frac{2 \times 4}{3 \times 5} = \frac{8}{15}.

Q: What is the difference between division and multiplication of fractions?

A: Division of fractions involves inverting the second fraction and multiplying it by the first fraction. Multiplication of fractions involves multiplying the numerators and denominators of the two fractions separately.

Q: Can I simplify a fraction before dividing it?

A: Yes, you can simplify a fraction before dividing it. In fact, it is often easier to simplify a fraction before dividing it, as it can make the division process simpler.

Q: How do I simplify a fraction?

A: To simplify a fraction, you need to find the greatest common divisor (GCD) of the numerator and denominator and divide both numbers by the GCD. For example, if you have the fraction 1218\frac{12}{18}, the GCD of 12 and 18 is 6. Dividing both numbers by 6 gives you the simplified fraction 23\frac{2}{3}.

Q: Can I divide a fraction by a whole number?

A: Yes, you can divide a fraction by a whole number. To do this, you need to multiply the fraction by the reciprocal of the whole number. For example, if you have the fraction 12\frac{1}{2} and you want to divide it by 3, you would multiply it by the reciprocal of 3, which is 13\frac{1}{3}. The result would be 12×13=16\frac{1}{2} \times \frac{1}{3} = \frac{1}{6}.

Q: Can I divide a whole number by a fraction?

A: Yes, you can divide a whole number by a fraction. To do this, you need to multiply the whole number by the reciprocal of the fraction. For example, if you have the whole number 6 and you want to divide it by the fraction 12\frac{1}{2}, you would multiply it by the reciprocal of 12\frac{1}{2}, which is 2. The result would be 6×2=126 \times 2 = 12.

Conclusion

In conclusion, division of fractions is a fundamental concept in mathematics that involves inverting the second fraction and multiplying it by the first fraction. We have answered some frequently asked questions about division of fractions and provided examples to illustrate the concepts.

Final Tips

  • Always follow the "invert and multiply" rule when dividing fractions.
  • Simplify fractions before dividing them to make the division process simpler.
  • Use the reciprocal of a whole number to divide a fraction by a whole number.
  • Use the reciprocal of a fraction to divide a whole number by a fraction.

Additional Resources

  • Khan Academy: Division of Fractions
  • Mathway: Division of Fractions
  • Wolfram Alpha: Division of Fractions

Final Answer

The final answer to the expression 29÷57\frac{2}{9} \div \frac{5}{7} is 1445\frac{14}{45}.