Evaluate The Following Expression:$\[ 9 \frac{1}{10} - 4 \frac{7}{10} = \\]

Introduction

In this article, we will evaluate the given mathematical expression, which involves subtracting two mixed numbers. Mixed numbers are a combination of a whole number and a fraction. The expression to be evaluated is $9 \frac{1}{10} - 4 \frac{7}{10}$. We will break down the steps to simplify this expression and provide a clear understanding of the process.

Understanding Mixed Numbers

Before we proceed with the evaluation, let's understand what mixed numbers are. A mixed number is a combination of a whole number and a fraction. It is written in the form of $a \frac{b}{c}$, where $a$ is the whole number, $b$ is the numerator, and $c$ is the denominator. For example, $3 \frac{2}{5}$ is a mixed number, where $3$ is the whole number, $2$ is the numerator, and $5$ is the denominator.

Evaluating the Expression

To evaluate the expression $9 \frac{1}{10} - 4 \frac{7}{10}$, we need to follow the order of operations (PEMDAS):

1. Subtract the fractions: First, we need to subtract the fractions $1/10$ and $7/10$. To do this, we need to find a common denominator, which is $10$ in this case. We can rewrite the fractions as $1/10$ and $7/10$.
2. Subtract the numerators: Now that we have a common denominator, we can subtract the numerators. $1 - 7 = -6$. So, the result of subtracting the fractions is $-6/10$.
3. Simplify the fraction: We can simplify the fraction $-6/10$ by dividing both the numerator and the denominator by their greatest common divisor, which is $2$. This gives us $-3/5$.
4. Subtract the whole numbers: Now that we have the result of subtracting the fractions, we can subtract the whole numbers. $9 - 4 = 5$.
5. Combine the results: Finally, we can combine the results of subtracting the fractions and the whole numbers. $5 - 3/5$.

Simplifying the Result

To simplify the result $5 - 3/5$, we need to find a common denominator, which is $5$ in this case. We can rewrite the whole number $5$ as $25/5$. Now, we can subtract the fractions: $25/5 - 3/5 = 22/5$.

Conclusion

In conclusion, the expression $9 \frac{1}{10} - 4 \frac{7}{10}$ can be evaluated by following the order of operations (PEMDAS). We need to subtract the fractions, simplify the result, and then subtract the whole numbers. The final result is $22/5$.

Example Use Cases

Here are some example use cases for evaluating expressions with mixed numbers:

• Subtracting mixed numbers: $3 \frac{2}{5} - 2 \frac{3}{5} = 1 \frac{4}{5}$
• Adding mixed numbers: $4 \frac{1}{3} + 2 \frac{2}{3} = 6 \frac{3}{3} = 7$
• Multiplying mixed numbers: $3 \frac{1}{2} \times 2 \frac{1}{2} = 7 \frac{3}{4}$

Tips and Tricks

Here are some tips and tricks for evaluating expressions with mixed numbers:

• Use a common denominator: When subtracting or adding fractions, use a common denominator to make the calculation easier.
• Simplify the fractions: Simplify the fractions before subtracting or adding them.
• Use the order of operations: Follow the order of operations (PEMDAS) to evaluate the expression correctly.

Conclusion

In conclusion, evaluating expressions with mixed numbers requires following the order of operations (PEMDAS) and using a common denominator. By simplifying the fractions and subtracting or adding the whole numbers, we can arrive at the final result. With practice and patience, you can become proficient in evaluating expressions with mixed numbers.

Introduction

In our previous article, we discussed how to evaluate expressions with mixed numbers. Mixed numbers are a combination of a whole number and a fraction. In this article, we will answer some frequently asked questions about evaluating expressions with mixed numbers.

Q&A

Q: What is a mixed number?

A: A mixed number is a combination of a whole number and a fraction. It is written in the form of $a \frac{b}{c}$, where $a$ is the whole number, $b$ is the numerator, and $c$ is the denominator.

Q: How do I subtract mixed numbers?

A: To subtract mixed numbers, you need to follow the order of operations (PEMDAS). First, subtract the fractions. Then, subtract the whole numbers. For example, $9 \frac{1}{10} - 4 \frac{7}{10} = 5 - 3/5 = 22/5$.

Q: How do I add mixed numbers?

A: To add mixed numbers, you need to follow the order of operations (PEMDAS). First, add the fractions. Then, add the whole numbers. For example, $4 \frac{1}{3} + 2 \frac{2}{3} = 6 \frac{3}{3} = 7$.

Q: How do I multiply mixed numbers?

A: To multiply mixed numbers, you need to multiply the whole numbers and the fractions separately. Then, multiply the results. For example, $3 \frac{1}{2} \times 2 \frac{1}{2} = 7 \frac{3}{4}$.

Q: What is the common denominator?

A: The common denominator is the smallest number that both fractions can be divided by. For example, if you have two fractions with denominators of 4 and 6, the common denominator is 12.

Q: How do I simplify a fraction?

A: To simplify a fraction, you need to divide both the numerator and the denominator by their greatest common divisor (GCD). For example, $6/8$ can be simplified to $3/4$ by dividing both the numerator and the denominator by 2.

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

A: The order of operations (PEMDAS) is a set of rules that tells you which operations to perform first when you 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.

Example Use Cases

Here are some example use cases for evaluating expressions with mixed numbers:

• Subtracting mixed numbers: $3 \frac{2}{5} - 2 \frac{3}{5} = 1 \frac{4}{5}$
• Adding mixed numbers: $4 \frac{1}{3} + 2 \frac{2}{3} = 6 \frac{3}{3} = 7$
• Multiplying mixed numbers: $3 \frac{1}{2} \times 2 \frac{1}{2} = 7 \frac{3}{4}$

Tips and Tricks

Here are some tips and tricks for evaluating expressions with mixed numbers:

• Use a common denominator: When subtracting or adding fractions, use a common denominator to make the calculation easier.
• Simplify the fractions: Simplify the fractions before subtracting or adding them.
• Use the order of operations: Follow the order of operations (PEMDAS) to evaluate the expression correctly.

Conclusion

In conclusion, evaluating expressions with mixed numbers requires following the order of operations (PEMDAS) and using a common denominator. By simplifying the fractions and subtracting or adding the whole numbers, we can arrive at the final result. With practice and patience, you can become proficient in evaluating expressions with mixed numbers.