Perform The Following Divisions:1. $11115 \div \frac{11}{5}$2. $117 \div \frac{3}{7}$3. 1.311 ÷ 5 6 1.311 \div \frac{5}{6} 1.311 ÷ 6 5 ​

In mathematics, division is a fundamental operation that involves finding the quotient of two numbers. When dealing with fractions and decimals, division can be a bit more complex. In this article, we will explore how to perform divisions involving fractions and decimals.

Division with Fractions

When dividing a number by a fraction, we can invert the fraction and multiply instead. This is based on the rule that division is the inverse operation of multiplication. Let's consider the first division problem:

1. $11115 \div \frac{11}{5}$

To solve this problem, we can invert the fraction $\frac{11}{5}$ and multiply:

$$\frac{11115}{\frac{11}{5}} = 11115 \times \frac{5}{11}$$

Now, we can multiply the numbers:

$$11115 \times \frac{5}{11} = 5055$$

Therefore, the result of the division is $5055$.

2. $117 \div \frac{3}{7}$

Using the same approach, we can invert the fraction $\frac{3}{7}$ and multiply:

$$\frac{117}{\frac{3}{7}} = 117 \times \frac{7}{3}$$

Now, we can multiply the numbers:

$$117 \times \frac{7}{3} = 294$$

Therefore, the result of the division is $294$.

3. $1.311 \div \frac{5}{6}$

To solve this problem, we can invert the fraction $\frac{5}{6}$ and multiply:

$$\frac{1.311}{\frac{5}{6}} = 1.311 \times \frac{6}{5}$$

Now, we can multiply the numbers:

$$1.311 \times \frac{6}{5} = 1.5682$$

Therefore, the result of the division is $1.5682$.

Division with Decimals

When dividing a decimal by a fraction, we can use the same approach as before. Let's consider the third division problem:

3. $1.311 \div \frac{5}{6}$

We can invert the fraction $\frac{5}{6}$ and multiply:

$$\frac{1.311}{\frac{5}{6}} = 1.311 \times \frac{6}{5}$$

Now, we can multiply the numbers:

$$1.311 \times \frac{6}{5} = 1.5682$$

Therefore, the result of the division is $1.5682$.

Conclusion

In conclusion, performing divisions with fractions and decimals involves inverting the fraction and multiplying instead. This approach allows us to simplify the division process and find the quotient. By following the steps outlined in this article, you can perform divisions with fractions and decimals with ease.

Tips and Tricks

• When dividing a number by a fraction, invert the fraction and multiply instead.
• Use the same approach when dividing a decimal by a fraction.
• Make sure to multiply the numbers correctly to avoid errors.
• Practice performing divisions with fractions and decimals to build your confidence and skills.

Common Mistakes

• Failing to invert the fraction when dividing by a fraction.
• Not multiplying the numbers correctly.
• Not following the order of operations (PEMDAS).
• Not checking the result for errors.

Real-World Applications

Performing divisions with fractions and decimals has many real-world applications. For example:

• In finance, dividing a stock price by a fraction can help investors calculate the dividend yield.
• In science, dividing a measurement by a fraction can help researchers calculate the concentration of a solution.
• In engineering, dividing a distance by a fraction can help designers calculate the length of a component.

In this article, we will address some of the most common questions and concerns related to performing divisions with fractions and decimals.

Q: What is the rule for dividing a number by a fraction?

A: When dividing a number by a fraction, you can invert the fraction and multiply instead. This is based on the rule that division is the inverse operation of multiplication.

Q: How do I invert a fraction?

A: To invert a fraction, you simply flip the numerator and denominator. For example, the fraction $\frac{3}{4}$ becomes $\frac{4}{3}$.

Q: What if I have a decimal number to divide by a fraction?

A: When dividing a decimal number by a fraction, you can use the same approach as before. Invert the fraction and multiply instead.

Q: Can I use a calculator to perform divisions with fractions and decimals?

A: Yes, you can use a calculator to perform divisions with fractions and decimals. However, make sure to enter the numbers correctly and follow the order of operations (PEMDAS).

Q: What are some common mistakes to avoid when performing divisions with fractions and decimals?

A: Some common mistakes to avoid include:

• Failing to invert the fraction when dividing by a fraction.
• Not multiplying the numbers correctly.
• Not following the order of operations (PEMDAS).
• Not checking the result for errors.

Q: How do I check my work when performing divisions with fractions and decimals?

A: To check your work, you can:

• Multiply the numbers correctly.
• Follow the order of operations (PEMDAS).
• Check the result for errors.
• Use a calculator to verify the result.

Q: What are some real-world applications of performing divisions with fractions and decimals?

A: Some real-world applications of performing divisions with fractions and decimals include:

• In finance, dividing a stock price by a fraction can help investors calculate the dividend yield.
• In science, dividing a measurement by a fraction can help researchers calculate the concentration of a solution.
• In engineering, dividing a distance by a fraction can help designers calculate the length of a component.

Q: Can I use a formula to perform divisions with fractions and decimals?

A: Yes, you can use a formula to perform divisions with fractions and decimals. The formula is:

$$\frac{a}{\frac{b}{c}} = a \times \frac{c}{b}$$

Where $a$ is the dividend, $b$ is the numerator of the fraction, and $c$ is the denominator of the fraction.

Q: How do I convert a decimal to a fraction?

A: To convert a decimal to a fraction, you can:

• Write the decimal as a fraction with a denominator of 1.
• Multiply the numerator and denominator by the same number to eliminate the decimal.
• Simplify the fraction.

Q: Can I use a calculator to convert a decimal to a fraction?

A: Yes, you can use a calculator to convert a decimal to a fraction. However, make sure to enter the numbers correctly and follow the order of operations (PEMDAS).

Q: What are some tips for performing divisions with fractions and decimals?

A: Some tips for performing divisions with fractions and decimals include:

• Make sure to invert the fraction when dividing by a fraction.
• Multiply the numbers correctly.
• Follow the order of operations (PEMDAS).
• Check the result for errors.
• Use a calculator to verify the result.

By following these tips and avoiding common mistakes, you can perform divisions with fractions and decimals with ease and accuracy.