Evaluate The Expression:${ 9 \times 2 \frac{1}{3} = }$
Introduction
In this article, we will evaluate the expression 9 × 2 1/3. This involves multiplying a whole number by a mixed number. To solve this problem, we need to understand the concept of multiplying mixed numbers and how to convert them into improper fractions.
Understanding Mixed Numbers
A mixed number is a combination of a whole number and a fraction. It is written in the form a b/c, where a is the whole number and b/c is the fraction. For example, 2 1/3 is a mixed number where 2 is the whole number and 1/3 is the fraction.
Converting Mixed Numbers to Improper Fractions
To convert a mixed number to an improper fraction, we need to multiply the whole number by the denominator and then add the numerator. The result is then written as the new numerator over the denominator.
For example, to convert 2 1/3 to an improper fraction, we multiply 2 by 3 and add 1. This gives us 7/3.
Multiplying Mixed Numbers
To multiply mixed numbers, we need to convert them into improper fractions first. Then, we can multiply the numerators and denominators separately.
For example, to multiply 2 1/3 by 9, we first convert 2 1/3 to an improper fraction, which is 7/3. Then, we multiply 9 by 7/3.
Evaluating the Expression
Now, let's evaluate the expression 9 × 2 1/3.
First, we convert 2 1/3 to an improper fraction, which is 7/3.
Next, we multiply 9 by 7/3. To do this, we multiply the numerators (9 and 7) and the denominators (1 and 3) separately.
9 × 7 = 63 1 × 3 = 3
So, 9 × 7/3 = 63/3.
Simplifying the Result
To simplify the result, we can divide the numerator by the denominator.
63 ÷ 3 = 21
Therefore, the result of the expression 9 × 2 1/3 is 21.
Conclusion
In this article, we evaluated the expression 9 × 2 1/3. We converted the mixed number 2 1/3 to an improper fraction, multiplied the numerators and denominators separately, and simplified the result. The final answer is 21.
Frequently Asked Questions
- Q: What is a mixed number? A: A mixed number is a combination of a whole number and a fraction.
- Q: How do I convert a mixed number to an improper fraction? A: To convert a mixed number to an improper fraction, multiply the whole number by the denominator and add the numerator.
- Q: How do I multiply mixed numbers? A: To multiply mixed numbers, convert them into improper fractions first, then multiply the numerators and denominators separately.
Final Answer
The final answer is 21.
Introduction
In our previous article, we evaluated the expression 9 × 2 1/3. We converted the mixed number 2 1/3 to an improper fraction, multiplied the numerators and denominators separately, and simplified the result. In this article, we will answer some frequently asked questions related to 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 a b/c, where a is the whole number and b/c is the fraction.
Q: How do I convert a mixed number to an improper fraction?
A: To convert a mixed number to an improper fraction, multiply the whole number by the denominator and add the numerator. For example, to convert 2 1/3 to an improper fraction, we multiply 2 by 3 and add 1. This gives us 7/3.
Q: How do I multiply mixed numbers?
A: To multiply mixed numbers, convert them into improper fractions first, then multiply the numerators and denominators separately. For example, to multiply 2 1/3 by 9, we first convert 2 1/3 to an improper fraction, which is 7/3. Then, we multiply 9 by 7/3.
Q: What is the order of operations when evaluating expressions with mixed numbers?
A: The order of operations is the same as when evaluating expressions with whole numbers. First, convert any mixed numbers to improper fractions. Then, perform any multiplication or division operations from left to right. Finally, perform any addition or subtraction operations from left to right.
Q: Can I simplify the result of an expression with a mixed number?
A: Yes, you can simplify the result of an expression with a mixed number. To do this, divide the numerator by the denominator. For example, if the result of an expression is 21/3, you can simplify it by dividing 21 by 3, which gives you 7.
Q: What are some common mistakes to avoid when evaluating expressions with mixed numbers?
A: Some common mistakes to avoid when evaluating expressions with mixed numbers include:
- Forgetting to convert mixed numbers to improper fractions before performing operations
- Multiplying or dividing the whole number and fraction separately instead of converting the mixed number to an improper fraction
- Not simplifying the result of an expression with a mixed number
Q: How do I evaluate an expression with multiple mixed numbers?
A: To evaluate an expression with multiple mixed numbers, follow the same steps as when evaluating an expression with a single mixed number. First, convert each mixed number to an improper fraction. Then, perform any multiplication or division operations from left to right. Finally, perform any addition or subtraction operations from left to right.
Conclusion
In this article, we answered some frequently asked questions related to evaluating expressions with mixed numbers. We covered topics such as converting mixed numbers to improper fractions, multiplying mixed numbers, and simplifying the result of an expression with a mixed number. By following the steps outlined in this article, you should be able to evaluate expressions with mixed numbers with confidence.
Final Answer
The final answer is 21.