Solve. Show All Your Work.${ 18 - 12 \frac{3}{4} = }$
Understanding the Problem
To solve the given equation, we need to first understand the concept of subtracting mixed numbers. A mixed number is a combination of a whole number and a fraction. In this case, we have 12 3/4, which can be written as 12 + 3/4.
Breaking Down the Problem
To solve the equation, we need to follow the order of operations (PEMDAS):
- Subtract the whole number part of the mixed number (12) from 18.
- Subtract the fraction part of the mixed number (3/4) from the result.
Step 1: Subtract the Whole Number Part
To subtract 12 from 18, we need to perform a simple subtraction operation.
18 - 12 = 6
Step 2: Subtract the Fraction Part
Now, we need to subtract 3/4 from 6. To do this, we need to convert 6 to a fraction with a denominator of 4.
6 = 24/4
Now, we can subtract 3/4 from 24/4.
24/4 - 3/4 = 21/4
Simplifying the Result
To simplify the result, we can convert the fraction to a mixed number.
21/4 = 5 1/4
Conclusion
Therefore, the solution to the given equation is 5 1/4.
Real-World Applications
This type of problem is commonly encountered in real-world scenarios, such as:
- Calculating the cost of a purchase with a discount
- Determining the amount of time left after a certain period has elapsed
- Finding the area of a shape with a complex boundary
Tips and Tricks
- When subtracting mixed numbers, it's essential to follow the order of operations (PEMDAS).
- To subtract a fraction from a whole number, convert the whole number to a fraction with the same denominator.
- Simplify the result by converting the fraction to a mixed number.
Common Mistakes
- Failing to follow the order of operations (PEMDAS)
- Not converting the whole number to a fraction with the same denominator
- Not simplifying the result
Practice Problems
Try solving the following problems:
- 15 - 8 1/2 =
- 20 - 3 3/4 =
- 12 - 9 1/2 =
Solutions
- 15 - 8 1/2 = 6 1/2
- 20 - 3 3/4 = 16 1/4
- 12 - 9 1/2 = 2 1/2
Conclusion
Solving equations with mixed numbers requires a clear understanding of the concept of subtracting mixed numbers. By following the order of operations (PEMDAS) and converting whole numbers to fractions with the same denominator, we can simplify the result and arrive at the correct solution.
Q: What is a mixed number?
A: A mixed number is a combination of a whole number and a fraction. For example, 12 3/4 is a mixed number.
Q: How do I subtract a mixed number from a whole number?
A: To subtract a mixed number from a whole number, follow these steps:
- Subtract the whole number part of the mixed number from the whole number.
- Subtract the fraction part of the mixed number from the result.
Q: What is the order of operations (PEMDAS)?
A: The order of operations (PEMDAS) is a set of rules that tells us which operations to perform first when we have multiple operations in an expression. The acronym PEMDAS stands for:
- Parentheses: Evaluate expressions inside parentheses first.
- Exponents: Evaluate any exponential expressions next.
- Multiplication and Division: Evaluate any multiplication and division operations from left to right.
- Addition and Subtraction: Finally, evaluate any addition and subtraction operations from left to right.
Q: How do I convert a whole number to a fraction with the same denominator?
A: To convert a whole number to a fraction with the same denominator, multiply the whole number by the denominator and write the result as a fraction. For example, to convert 6 to a fraction with a denominator of 4, multiply 6 by 4 and write the result as a fraction:
6 = 24/4
Q: What is the difference between a fraction and a mixed number?
A: A fraction is a part of a whole, while a mixed number is a combination of a whole number and a fraction. For example, 3/4 is a fraction, while 2 3/4 is a mixed number.
Q: Can I simplify a mixed number?
A: Yes, you can simplify a mixed number by converting it to an improper fraction and then simplifying the fraction. For example, to simplify 2 3/4, convert it to an improper fraction:
2 3/4 = 11/4
Then, simplify the fraction by dividing the numerator and denominator by their greatest common divisor:
11/4 = 2 3/4
Q: What are some common mistakes to avoid when solving equations with mixed numbers?
A: Some common mistakes to avoid when solving equations with mixed numbers include:
- Failing to follow the order of operations (PEMDAS)
- Not converting the whole number to a fraction with the same denominator
- Not simplifying the result
Q: How do I practice solving equations with mixed numbers?
A: To practice solving equations with mixed numbers, try the following:
- Start with simple equations and gradually move on to more complex ones.
- Use online resources or worksheets to practice solving equations with mixed numbers.
- Try solving equations with mixed numbers in different contexts, such as real-world applications or word problems.
Q: What are some real-world applications of solving equations with mixed numbers?
A: Solving equations with mixed numbers has many real-world applications, including:
- Calculating the cost of a purchase with a discount
- Determining the amount of time left after a certain period has elapsed
- Finding the area of a shape with a complex boundary
Q: Can I use a calculator to solve equations with mixed numbers?
A: Yes, you can use a calculator to solve equations with mixed numbers. However, it's essential to understand the concept of subtracting mixed numbers and to be able to solve equations with mixed numbers without a calculator.
Q: How do I know if I've solved an equation with mixed numbers correctly?
A: To know if you've solved an equation with mixed numbers correctly, follow these steps:
- Check your work by plugging the solution back into the original equation.
- Simplify the result to ensure it's in the correct form.
- Check your solution against the original equation to ensure it's correct.
Q: What are some common types of equations with mixed numbers?
A: Some common types of equations with mixed numbers include:
- Simple equations with mixed numbers, such as 18 - 12 3/4
- Equations with multiple mixed numbers, such as 15 - 8 1/2 + 3 3/4
- Equations with mixed numbers and fractions, such as 20 - 3 3/4 + 1/2
Q: Can I use a formula to solve equations with mixed numbers?
A: Yes, you can use a formula to solve equations with mixed numbers. However, it's essential to understand the concept of subtracting mixed numbers and to be able to solve equations with mixed numbers without a formula.
Q: How do I teach someone else to solve equations with mixed numbers?
A: To teach someone else to solve equations with mixed numbers, follow these steps:
- Start with the basics and explain the concept of subtracting mixed numbers.
- Use visual aids and examples to illustrate the concept.
- Practice solving equations with mixed numbers together.
- Encourage the student to practice solving equations with mixed numbers on their own.