Find The Product. Write The Product As A Mixed Number.$\frac{5}{8} \times 28 = \frac{? \times ?}{?} = \frac{?}{?} = ? \frac{?}{?} = ? \frac{?}{?}$
Understanding Mixed Numbers and Whole Numbers
In mathematics, a mixed number is a combination of a whole number and a fraction. It is written in the form of a whole number followed by a fraction, such as 5 3/4. On the other hand, a whole number is a positive integer that is not a fraction, such as 1, 2, 3, and so on.
The Problem: Multiplying a Mixed Number by a Whole Number
The problem we are given is to find the product of a mixed number and a whole number. The mixed number is 5/8 and the whole number is 28. We need to find the product of these two numbers.
Step 1: Convert the Mixed Number to an Improper Fraction
To multiply a mixed number by a whole number, we need to convert the mixed number to an improper fraction. An improper fraction is a fraction where the numerator is greater than or equal to the denominator. To convert a mixed number to an improper fraction, we multiply the whole number by the denominator and add the numerator. Then, we write the result as the new numerator over the denominator.
In this case, the mixed number is 5/8. To convert it to an improper fraction, we multiply the whole number (5) by the denominator (8) and add the numerator (5). This gives us:
5 × 8 = 40 40 + 5 = 45
So, the improper fraction is 45/8.
Step 2: Multiply the Improper Fraction by the Whole Number
Now that we have the improper fraction, we can multiply it by the whole number. To multiply a fraction by a whole number, we multiply the numerator by the whole number and keep the denominator the same.
In this case, we multiply the numerator (45) by the whole number (28):
45 × 28 = 1260
So, the product is 1260/8.
Step 3: Simplify the Fraction
To simplify a fraction, we divide the numerator by the denominator. In this case, we divide 1260 by 8:
1260 ÷ 8 = 157.5
So, the simplified fraction is 157.5/1.
Step 4: Write the Product as a Mixed Number
Finally, we can write the product as a mixed number. To do this, we divide the numerator by the denominator and write the result as a whole number followed by a fraction.
In this case, we divide 1575 by 1:
1575 ÷ 1 = 1575
So, the product as a mixed number is 1575 0/1.
Conclusion
In conclusion, we have found the product of a mixed number and a whole number. We converted the mixed number to an improper fraction, multiplied the improper fraction by the whole number, simplified the fraction, and finally wrote the product as a mixed number.
The product of 5/8 and 28 is 1575 0/1.
Real-World Applications
This problem has real-world applications in various fields such as finance, engineering, and science. For example, in finance, you may need to calculate the interest on a loan or investment. In engineering, you may need to calculate the stress on a material or the force on a structure. In science, you may need to calculate the velocity of an object or the acceleration of a particle.
Tips and Tricks
Here are some tips and tricks to help you solve this problem:
- Make sure to convert the mixed number to an improper fraction before multiplying.
- Multiply the numerator by the whole number and keep the denominator the same.
- Simplify the fraction by dividing the numerator by the denominator.
- Write the product as a mixed number by dividing the numerator by the denominator.
Common Mistakes
Here are some common mistakes to avoid when solving this problem:
- Failing to convert the mixed number to an improper fraction.
- Multiplying the denominator by the whole number instead of the numerator.
- Not simplifying the fraction.
- Writing the product as a whole number instead of a mixed number.
Practice Problems
Here are some practice problems to help you practice solving this type of problem:
- Find the product of 3/4 and 12.
- Find the product of 2/3 and 9.
- Find the product of 5/6 and 8.
Conclusion
In conclusion, finding the product of a mixed number and a whole number requires converting the mixed number to an improper fraction, multiplying the improper fraction by the whole number, simplifying the fraction, and finally writing the product as a mixed number. With practice and patience, you can become proficient in solving this type of problem.
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 whole number followed by a fraction, such as 5 3/4.
Q: How do I convert a mixed number to an improper fraction?
A: To convert a mixed number to an improper fraction, you multiply the whole number by the denominator and add the numerator. Then, you write the result as the new numerator over the denominator.
Q: What is an improper fraction?
A: An improper fraction is a fraction where the numerator is greater than or equal to the denominator. For example, 5/8 is an improper fraction because the numerator (5) is greater than the denominator (8).
Q: How do I multiply a mixed number by a whole number?
A: To multiply a mixed number by a whole number, you first convert the mixed number to an improper fraction. Then, you multiply the numerator of the improper fraction by the whole number and keep the denominator the same.
Q: Can I multiply a mixed number by a fraction?
A: Yes, you can multiply a mixed number by a fraction. To do this, you first convert the mixed number to an improper fraction. Then, you multiply the numerator of the improper fraction by the numerator of the fraction and multiply the denominator of the improper fraction by the denominator of the fraction.
Q: How do I simplify a fraction?
A: To simplify a fraction, you divide the numerator by the denominator. If the result is a whole number, you can write it as a whole number. If the result is a fraction, you can write it as a fraction.
Q: Can I write a product as a mixed number?
A: Yes, you can write a product as a mixed number. To do this, you divide the numerator by the denominator and write the result as a whole number followed by a fraction.
Q: What are some common mistakes to avoid when finding the product of a mixed number and a whole number?
A: Some common mistakes to avoid include:
- Failing to convert the mixed number to an improper fraction
- Multiplying the denominator by the whole number instead of the numerator
- Not simplifying the fraction
- Writing the product as a whole number instead of a mixed number
Q: How can I practice finding the product of a mixed number and a whole number?
A: You can practice finding the product of a mixed number and a whole number by working through examples and exercises. You can also try creating your own problems and solving them.
Q: What are some real-world applications of finding the product of a mixed number and a whole number?
A: Some real-world applications of finding the product of a mixed number and a whole number include:
- Calculating interest on a loan or investment
- Calculating stress on a material or force on a structure
- Calculating velocity of an object or acceleration of a particle
Q: Can I use a calculator to find the product of a mixed number and a whole number?
A: Yes, you can use a calculator to find the product of a mixed number and a whole number. However, it's also important to understand the steps involved in finding the product and to be able to do it by hand.
Q: How can I check my work when finding the product of a mixed number and a whole number?
A: You can check your work by plugging in the numbers and making sure that the product is correct. You can also try working through the problem again and making sure that you get the same result.
Q: What are some tips for finding the product of a mixed number and a whole number?
A: Some tips for finding the product of a mixed number and a whole number include:
- Make sure to convert the mixed number to an improper fraction
- Multiply the numerator by the whole number and keep the denominator the same
- Simplify the fraction by dividing the numerator by the denominator
- Write the product as a mixed number by dividing the numerator by the denominator