To add and subtract fractions with different denominators

Oct 13, 2025 by miodeya.com 116 views

$To add and subtract fractions with different denominators$

Introduction

In this article, we will delve into the world of mathematics and solve for the variable n in the given equation: $\frac{31}{6} \times 48 = n$ . This equation involves multiplication and division of fractions, which can be a bit challenging for some students. However, with a step-by-step approach and a clear understanding of the concepts, we can easily solve for n.

Understanding the Equation

The given equation is $\frac{31}{6} \times 48 = n$ . To solve for n, we need to follow the order of operations (PEMDAS):

Multiply the fractions
Multiply the result by 48
Simplify the expression

Step 1: Multiply the Fractions

To multiply fractions, we need to multiply the numerators (31 and 48) and multiply the denominators (6 and 1). However, since 48 is not a fraction, we can rewrite it as a fraction with a denominator of 1: $\frac{48}{1}$ . Now, we can multiply the fractions:

$\frac{31}{6} \times \frac{48}{1} = \frac{31 \times 48}{6 \times 1}$

Step 3: Simplify the Expression

Now, we can simplify the expression by multiplying the numerators and denominators:

$\frac{31 \times 48}{6 \times 1} = \frac{1488}{6}$

Step 4: Divide the Numerator by the Denominator

To simplify the fraction, we can divide the numerator by the denominator:

$\frac{1488}{6} = 248$

Conclusion

Therefore, the value of n is 248. We can verify this by plugging the value back into the original equation:

$\frac{31}{6} \times 48 = 248$

This confirms that our solution is correct.

Tips and Tricks

When solving equations involving fractions, it's essential to follow the order of operations (PEMDAS) and simplify the expression step by step. Additionally, make sure to multiply the numerators and denominators correctly, and don't forget to simplify the fraction by dividing the numerator by the denominator.

Real-World Applications

Solving equations involving fractions has numerous real-world applications in various fields, such as:

Finance: Calculating interest rates and investment returns
Science: Measuring quantities and rates of change
Engineering: Designing and optimizing systems

Practice Problems

Try solving the following problems:

$\frac{25}{8} \times 32 = n$
$\frac{37}{9} \times 27 = n$

Conclusion

In this article, we solved for the variable n in the equation $\frac{31}{6} \times 48 = n$ . We followed the order of operations (PEMDAS) and simplified the expression step by step. With practice and patience, you can become proficient in solving equations involving fractions and apply these skills to real-world problems.

Frequently Asked Questions

Q: What is the order of operations (PEMDAS)? A: PEMDAS stands for Parentheses, Exponents, Multiplication and Division, and Addition and Subtraction. It's a set of rules that dictates the order in which we perform mathematical operations.

Q: How do I simplify a fraction? A: To simplify a fraction, divide the numerator by the denominator.

Q: What are some real-world applications of solving equations involving fractions? A: Solving equations involving fractions has numerous real-world applications in finance, science, and engineering.

References

[1] Khan Academy. (n.d.). Fractions. Retrieved from https://www.khanacademy.org/math/fractions
[2] Mathway. (n.d.). Fractions. Retrieved from https://www.mathway.com/subjects/fractions

Note: The references provided are for educational purposes only and are not intended to be a comprehensive list of resources.

Introduction

Solving equations involving fractions can be a challenging task, especially for students who are new to the concept. However, with practice and patience, you can become proficient in solving these types of equations. In this article, we will answer some of the most frequently asked questions about solving equations involving fractions.

Q: What is the order of operations (PEMDAS)?

A: PEMDAS stands for Parentheses, Exponents, Multiplication and Division, and Addition and Subtraction. It's a set of rules that dictates the order in which we perform mathematical operations. When solving equations involving fractions, it's essential to follow the order of operations to ensure that you are performing the operations in the correct order.

Q: How do I simplify a fraction?

A: To simplify a fraction, divide the numerator by the denominator. For example, if you have the fraction $\frac{12}{4}$ , you can simplify it by dividing the numerator (12) by the denominator (4), which gives you 3. Therefore, the simplified fraction is $\frac{3}{1}$ .

Q: What is the difference between multiplying and dividing fractions?

A: Multiplying fractions involves multiplying the numerators and denominators separately, while dividing fractions involves inverting the second fraction and multiplying. For example, if you have the equation $\frac{1}{2} \div \frac{3}{4}$ , you can solve it by inverting the second fraction and multiplying: $\frac{1}{2} \times \frac{4}{3}$ .

Q: How do I add and subtract fractions with different denominators?

A: To add and subtract fractions with different denominators, you need to find the least common multiple (LCM) of the denominators and then convert each fraction to have the LCM as the denominator. For example, if you have the equation $\frac{1}{2} + \frac{1}{3}$ , you can solve it by finding the LCM of 2 and 3, which is 6, and then converting each fraction to have 6 as the denominator: $\frac{3}{6} + \frac{2}{6}$ .

Q: What are some real-world applications of solving equations involving fractions?

A: Solving equations involving fractions has numerous real-world applications in finance, science, and engineering. For example, in finance, you may need to calculate interest rates and investment returns, which involve solving equations involving fractions. In science, you may need to measure quantities and rates of change, which also involve solving equations involving fractions.

Q: How can I practice solving equations involving fractions?

A: To practice solving equations involving fractions, you can try solving problems on your own or use online resources such as Khan Academy or Mathway. You can also try solving word problems that involve fractions, such as calculating the cost of a product or the time it takes to complete a task.

Q: What are some common mistakes to avoid when solving equations involving fractions?

A: Some common mistakes to avoid when solving equations involving fractions include:

Not following the order of operations (PEMDAS)
Not simplifying fractions correctly
Not inverting the second fraction when dividing fractions
Not finding the least common multiple (LCM) when adding and subtracting fractions with different denominators

Conclusion

Solving equations involving fractions can be a challenging task, but with practice and patience, you can become proficient in solving these types of equations. By following the order of operations (PEMDAS) and simplifying fractions correctly, you can ensure that you are performing the operations in the correct order. Additionally, by practicing solving word problems and avoiding common mistakes, you can become more confident in your ability to solve equations involving fractions.

Tips and Tricks

Always follow the order of operations (PEMDAS)
Simplify fractions correctly
Invert the second fraction when dividing fractions
Find the least common multiple (LCM) when adding and subtracting fractions with different denominators
Practice solving word problems and avoid common mistakes

Real-World Applications

Finance: Calculating interest rates and investment returns
Science: Measuring quantities and rates of change
Engineering: Designing and optimizing systems

Practice Problems

Try solving the following problems:

$\frac{1}{2} \times \frac{3}{4} = n$
$\frac{1}{3} \div \frac{2}{5} = n$
$\frac{1}{2} + \frac{1}{3} = n$

Conclusion

In this article, we answered some of the most frequently asked questions about solving equations involving fractions. By following the order of operations (PEMDAS) and simplifying fractions correctly, you can ensure that you are performing the operations in the correct order. Additionally, by practicing solving word problems and avoiding common mistakes, you can become more confident in your ability to solve equations involving fractions.

Frequently Asked Questions

Q: What is the order of operations (PEMDAS)? A: PEMDAS stands for Parentheses, Exponents, Multiplication and Division, and Addition and Subtraction.

Q: How do I simplify a fraction? A: To simplify a fraction, divide the numerator by the denominator.

Q: What is the difference between multiplying and dividing fractions? A: Multiplying fractions involves multiplying the numerators and denominators separately, while dividing fractions involves inverting the second fraction and multiplying.

Q: How do I add and subtract fractions with different denominators? A: To add and subtract fractions with different denominators, you need to find the least common multiple (LCM) of the denominators and then convert each fraction to have the LCM as the denominator.

Q: What are some real-world applications of solving equations involving fractions? A: Solving equations involving fractions has numerous real-world applications in finance, science, and engineering.

References

[1] Khan Academy. (n.d.). Fractions. Retrieved from https://www.khanacademy.org/math/fractions
[2] Mathway. (n.d.). Fractions. Retrieved from https://www.mathway.com/subjects/fractions