Multiply. Write Your Answer As A Fraction In Simplest Form.$\[ 10 \times \frac{3}{25} \\]
Understanding the Problem
When multiplying a whole number by a fraction, we need to multiply the numerator of the fraction by the whole number and keep the denominator the same. This is a fundamental concept in mathematics, and it's essential to understand how to multiply fractions by whole numbers.
Multiplying a Whole Number by a Fraction
To multiply a whole number by a fraction, we follow these steps:
- Multiply the numerator of the fraction by the whole number.
- Keep the denominator the same.
- Simplify the resulting fraction, if possible.
For example, let's multiply 10 by 3/25.
Example: 10 × 3/25
To multiply 10 by 3/25, we follow the steps above:
- Multiply the numerator of the fraction (3) by the whole number (10): 3 × 10 = 30.
- Keep the denominator the same (25).
- Write the resulting fraction: 30/25.
Simplifying the Fraction
The fraction 30/25 can be simplified by dividing both the numerator and the denominator by their greatest common divisor (GCD). In this case, the GCD of 30 and 25 is 5.
Calculating the GCD
To calculate the GCD of 30 and 25, we can use the Euclidean algorithm or list the factors of each number.
Factors of 30
1, 2, 3, 5, 6, 10, 15, 30
Factors of 25
1, 5, 25
The greatest common divisor of 30 and 25 is 5.
Simplifying the Fraction
Now that we know the GCD of 30 and 25 is 5, we can simplify the fraction by dividing both the numerator and the denominator by 5.
30 ÷ 5 = 6 25 ÷ 5 = 5
The simplified fraction is 6/5.
Conclusion
In conclusion, when multiplying a whole number by a fraction, we need to multiply the numerator of the fraction by the whole number and keep the denominator the same. We can then simplify the resulting fraction, if possible, by dividing both the numerator and the denominator by their greatest common divisor.
Practice Problems
- Multiply 4 by 2/3.
- Multiply 6 by 5/8.
- Multiply 9 by 3/4.
Solutions
- 4 × 2/3 = 8/3
- 6 × 5/8 = 15/4
- 9 × 3/4 = 27/4
Final Thoughts
Multiplying fractions by whole numbers is a fundamental concept in mathematics, and it's essential to understand how to do it correctly. By following the steps outlined above and simplifying the resulting fraction, if possible, we can ensure that our answers are accurate and in simplest form.
Additional Resources
For more practice problems and examples, check out the following resources:
- Khan Academy: Multiplying Fractions by Whole Numbers
- Mathway: Multiplying Fractions by Whole Numbers
- IXL: Multiplying Fractions by Whole Numbers
Final Answer
The final answer is: 6/5
Frequently Asked Questions
When multiplying fractions by whole numbers, it's common to have questions and doubts. Here are some frequently asked questions and their answers:
Q: What is the rule for multiplying a whole number by a fraction?
A: The rule for multiplying a whole number by a fraction is to multiply the numerator of the fraction by the whole number and keep the denominator the same.
Q: How do I simplify a fraction after multiplying it by a whole number?
A: To simplify a fraction after multiplying it by a whole number, you need to find the greatest common divisor (GCD) of the numerator and the denominator and divide both numbers by the GCD.
Q: What is the greatest common divisor (GCD)?
A: The greatest common divisor (GCD) is the largest number that divides both the numerator and the denominator of a fraction without leaving a remainder.
Q: How do I find the GCD of two numbers?
A: There are several ways to find the GCD of two numbers, including:
- Listing the factors of each number
- Using the Euclidean algorithm
- Using a calculator or online tool
Q: Can I multiply a fraction by a decimal?
A: Yes, you can multiply a fraction by a decimal. To do this, you need to convert the decimal to a fraction and then multiply the fractions.
Q: What is the rule for multiplying a negative number by a fraction?
A: The rule for multiplying a negative number by a fraction is to multiply the numerator and the denominator by the negative number.
Q: How do I multiply a fraction by a mixed number?
A: To multiply a fraction by a mixed number, you need to convert the mixed number to an improper fraction and then multiply the fractions.
Q: Can I multiply a fraction by a percentage?
A: Yes, you can multiply a fraction by a percentage. To do this, you need to convert the percentage to a decimal and then multiply the fractions.
Common Mistakes
When multiplying fractions by whole numbers, it's easy to make mistakes. Here are some common mistakes to avoid:
- Forgetting to multiply the numerator by the whole number
- Forgetting to keep the denominator the same
- Not simplifying the fraction after multiplying it by a whole number
- Not finding the greatest common divisor (GCD) of the numerator and the denominator
Tips and Tricks
Here are some tips and tricks to help you multiply fractions by whole numbers:
- Use a multiplication chart to help you multiply the numerator by the whole number
- Use a calculator or online tool to help you find the greatest common divisor (GCD) of the numerator and the denominator
- Practice, practice, practice! The more you practice multiplying fractions by whole numbers, the more comfortable you will become with the process.
Conclusion
Multiplying fractions by whole numbers is a fundamental concept in mathematics, and it's essential to understand how to do it correctly. By following the rules and tips outlined above, you can ensure that your answers are accurate and in simplest form.
Additional Resources
For more practice problems and examples, check out the following resources:
- Khan Academy: Multiplying Fractions by Whole Numbers
- Mathway: Multiplying Fractions by Whole Numbers
- IXL: Multiplying Fractions by Whole Numbers
Final Thoughts
Multiplying fractions by whole numbers is a skill that takes practice to develop. With patience, persistence, and practice, you can become proficient in multiplying fractions by whole numbers and apply this skill to a wide range of mathematical problems.
Final Answer
The final answer is: 6/5