(1/7)+(-3/-2)+(9/-8)
Introduction
When it comes to simplifying complex fractions, it's essential to understand the rules and procedures involved. In this article, we'll delve into the world of mathematics and explore how to evaluate expressions like (1/7)+(-3/-2)+(9/-8). By breaking down each step and providing a clear explanation, we'll make this process accessible to everyone.
Understanding Complex Fractions
A complex fraction is a fraction that contains one or more fractions in its numerator or denominator. In the given expression, (1/7)+(-3/-2)+(9/-8), we have multiple fractions that need to be simplified and added together. To tackle this problem, we'll need to apply the rules of arithmetic operations, including addition, subtraction, multiplication, and division.
Order of Operations
Before we dive into simplifying the expression, it's crucial to understand the order of operations. The order of operations is a set of rules that dictates the order in which mathematical operations should be performed. The acronym PEMDAS is commonly used to remember the order of operations:
- Parentheses: Evaluate expressions inside parentheses first.
- Exponents: Evaluate any exponential expressions next.
- Multiplication and Division: Evaluate multiplication and division operations from left to right.
- Addition and Subtraction: Finally, evaluate any addition and subtraction operations from left to right.
Simplifying the Expression
Now that we've covered the basics, let's simplify the expression (1/7)+(-3/-2)+(9/-8). To do this, we'll follow the order of operations and simplify each fraction individually.
Step 1: Simplify the First Fraction
The first fraction is 1/7. Since this fraction is already simplified, we can move on to the next step.
Step 2: Simplify the Second Fraction
The second fraction is -3/-2. To simplify this fraction, we'll divide the numerator and denominator by their greatest common divisor (GCD). In this case, the GCD of -3 and -2 is 1, so we can't simplify the fraction further.
Step 3: Simplify the Third Fraction
The third fraction is 9/-8. To simplify this fraction, we'll divide the numerator and denominator by their GCD. In this case, the GCD of 9 and -8 is 1, so we can't simplify the fraction further.
Step 4: Add the Fractions
Now that we've simplified each fraction, we can add them together. However, since the fractions have different denominators, we'll need to find a common denominator. The least common multiple (LCM) of 7, 2, and 8 is 56, so we'll convert each fraction to have a denominator of 56.
Step 5: Convert the Fractions
To convert the fractions, we'll multiply the numerator and denominator of each fraction by the necessary factor to get a denominator of 56.
- 1/7 = (1 × 8) / (7 × 8) = 8/56
- -3/-2 = (-3 × 28) / (-2 × 28) = 84/56
- 9/-8 = (9 × 7) / (-8 × 7) = -63/56
Step 6: Add the Fractions
Now that we've converted each fraction to have a denominator of 56, we can add them together.
(8/56) + (84/56) + (-63/56) = (8 + 84 - 63) / 56 = 29/56
Conclusion
In this article, we've explored how to simplify complex fractions by following the order of operations and applying the rules of arithmetic operations. By breaking down each step and providing a clear explanation, we've made this process accessible to everyone. Whether you're a student or a professional, understanding complex fractions is an essential skill that can help you tackle a wide range of mathematical problems.
Final Answer
The final answer to the expression (1/7)+(-3/-2)+(9/-8) is 29/56.
Additional Resources
If you're looking for additional resources to help you understand complex fractions, here are a few suggestions:
- Khan Academy: Complex Fractions
- Mathway: Complex Fractions
- Wolfram Alpha: Complex Fractions
By following these resources and practicing with different examples, you'll become more confident in your ability to simplify complex fractions and tackle a wide range of mathematical problems.
Introduction
In our previous article, we explored how to simplify complex fractions by following the order of operations and applying the rules of arithmetic operations. However, we know that practice makes perfect, and there's no better way to learn than by asking questions and getting answers. In this article, we'll address some of the most frequently asked questions about simplifying complex fractions.
Q1: What is a complex fraction?
A complex fraction is a fraction that contains one or more fractions in its numerator or denominator. In other words, it's a fraction that has a fraction within it.
Example: (1/7)+(-3/-2)+(9/-8)
Q2: How do I simplify a complex fraction?
To simplify a complex fraction, you'll need to follow the order of operations and apply the rules of arithmetic operations. Here's a step-by-step guide:
- Simplify any fractions within the numerator or denominator.
- Find a common denominator for all the fractions.
- Convert each fraction to have the common denominator.
- Add or subtract the fractions as needed.
Q3: What is the order of operations?
The order of operations is a set of rules that dictates the order in which mathematical operations should be performed. The acronym PEMDAS is commonly used to remember the order of operations:
- Parentheses: Evaluate expressions inside parentheses first.
- Exponents: Evaluate any exponential expressions next.
- Multiplication and Division: Evaluate multiplication and division operations from left to right.
- Addition and Subtraction: Finally, evaluate any addition and subtraction operations from left to right.
Q4: How do I find a common denominator?
To find a common denominator, you'll need to find the least common multiple (LCM) of all the denominators. You can use a calculator or a formula to find the LCM.
Example: Find the LCM of 7, 2, and 8.
- LCM(7, 2) = 14
- LCM(14, 8) = 56
Q5: Can I simplify a complex fraction with a variable?
Yes, you can simplify a complex fraction with a variable. However, you'll need to follow the same steps as before, and you may need to use algebraic properties to simplify the expression.
Example: Simplify the complex fraction (x/2) + (3/x) + (5/2x)
Q6: How do I add or subtract complex fractions?
To add or subtract complex fractions, you'll need to follow the same steps as before, and you may need to use algebraic properties to simplify the expression.
Example: Simplify the complex fraction (1/7) + (-3/-2) + (9/-8)
Q7: Can I use a calculator to simplify complex fractions?
Yes, you can use a calculator to simplify complex fractions. However, it's essential to understand the underlying math and be able to explain the steps involved.
Example: Use a calculator to simplify the complex fraction (1/7) + (-3/-2) + (9/-8)
Conclusion
In this article, we've addressed some of the most frequently asked questions about simplifying complex fractions. By following the order of operations and applying the rules of arithmetic operations, you'll be able to simplify complex fractions with ease. Whether you're a student or a professional, understanding complex fractions is an essential skill that can help you tackle a wide range of mathematical problems.
Additional Resources
If you're looking for additional resources to help you understand complex fractions, here are a few suggestions:
- Khan Academy: Complex Fractions
- Mathway: Complex Fractions
- Wolfram Alpha: Complex Fractions
By following these resources and practicing with different examples, you'll become more confident in your ability to simplify complex fractions and tackle a wide range of mathematical problems.