What Number Is Midway Between $\frac{2}{5}$ And 1?A. $\frac{5}{6}$ B. $\frac{7}{10}$ C. $\frac{4}{5}$
What Number is Midway Between and 1?
Understanding the Concept of Midpoint
In mathematics, the midpoint of two numbers is the number that lies exactly in the middle of the two numbers. To find the midpoint, we need to average the two numbers. The formula for finding the midpoint is:
Midpoint = (Number 1 + Number 2) / 2
In this case, we are given two numbers: and 1. We need to find the number that lies midway between these two numbers.
Step 1: Convert the Numbers to a Common Denominator
To add the two numbers, we need to convert them to a common denominator. The least common multiple (LCM) of 5 and 10 is 10. So, we can convert to .
Step 2: Add the Numbers
Now that we have the two numbers with a common denominator, we can add them:
Step 3: Simplify the Fraction
We can simplify the fraction by dividing both the numerator and the denominator by their greatest common divisor (GCD), which is 2.
Step 4: Find the Midpoint
Now that we have the sum of the two numbers, we can find the midpoint by dividing the sum by 2:
Midpoint = (Sum of Numbers) / 2 = () / 2 =
Conclusion
Therefore, the number that lies midway between and 1 is .
Answer
The correct answer is B. .
Why is this Important?
Understanding the concept of midpoint is important in mathematics because it is used in various applications such as:
- Finding the average of two numbers
- Determining the midpoint of a line segment
- Calculating the midpoint of a range of values
Real-World Applications
The concept of midpoint is used in various real-world applications such as:
- Statistics: Finding the average of a set of numbers
- Geography: Determining the midpoint of a route
- Engineering: Calculating the midpoint of a range of values
Common Mistakes
Some common mistakes that people make when finding the midpoint include:
- Not converting the numbers to a common denominator
- Not simplifying the fraction
- Not dividing the sum by 2
Tips and Tricks
Here are some tips and tricks for finding the midpoint:
- Make sure to convert the numbers to a common denominator
- Simplify the fraction before finding the midpoint
- Use a calculator to check your answer
Conclusion
In conclusion, finding the midpoint between two numbers is an important concept in mathematics. By following the steps outlined in this article, you can find the midpoint between any two numbers. Remember to convert the numbers to a common denominator, simplify the fraction, and divide the sum by 2. With practice, you will become proficient in finding the midpoint and be able to apply this concept to various real-world applications.
Frequently Asked Questions (FAQs) About Midpoint
Q: What is the midpoint of two numbers?
A: The midpoint of two numbers is the number that lies exactly in the middle of the two numbers. It is found by averaging the two numbers.
Q: How do I find the midpoint of two numbers?
A: To find the midpoint of two numbers, you need to follow these steps:
- Convert the numbers to a common denominator.
- Add the numbers.
- Simplify the fraction.
- Divide the sum by 2.
Q: What is the formula for finding the midpoint?
A: The formula for finding the midpoint is:
Midpoint = (Number 1 + Number 2) / 2
Q: Can I use a calculator to find the midpoint?
A: Yes, you can use a calculator to find the midpoint. However, it's always a good idea to follow the steps outlined above to ensure accuracy.
Q: What if the numbers have different denominators?
A: If the numbers have different denominators, you need to convert them to a common denominator before finding the midpoint.
Q: Can I find the midpoint of a range of values?
A: Yes, you can find the midpoint of a range of values by finding the average of the highest and lowest values in the range.
Q: What is the midpoint of a line segment?
A: The midpoint of a line segment is the point that lies exactly in the middle of the line segment. It is found by averaging the x-coordinates and y-coordinates of the two endpoints of the line segment.
Q: Can I use the midpoint formula to find the midpoint of a line segment?
A: Yes, you can use the midpoint formula to find the midpoint of a line segment. The formula is:
Midpoint = ((x1 + x2) / 2, (y1 + y2) / 2)
Q: What is the significance of the midpoint in statistics?
A: The midpoint is an important concept in statistics because it is used to find the average of a set of numbers. It is also used to determine the range of values in a dataset.
Q: Can I use the midpoint to find the average of a set of numbers?
A: Yes, you can use the midpoint to find the average of a set of numbers. The midpoint is the average of the highest and lowest values in the set.
Q: What is the midpoint of a range of values in a dataset?
A: The midpoint of a range of values in a dataset is the value that lies exactly in the middle of the range. It is found by averaging the highest and lowest values in the range.
Q: Can I use the midpoint to determine the range of values in a dataset?
A: Yes, you can use the midpoint to determine the range of values in a dataset. The range is the difference between the highest and lowest values in the dataset.
Q: What is the midpoint of a set of numbers in a geometric sequence?
A: The midpoint of a set of numbers in a geometric sequence is the number that lies exactly in the middle of the sequence. It is found by averaging the first and last terms of the sequence.
Q: Can I use the midpoint to find the average of a set of numbers in a geometric sequence?
A: Yes, you can use the midpoint to find the average of a set of numbers in a geometric sequence. The midpoint is the average of the first and last terms of the sequence.
Conclusion
In conclusion, the midpoint is an important concept in mathematics that is used to find the average of two numbers, determine the midpoint of a line segment, and find the range of values in a dataset. By following the steps outlined above, you can find the midpoint of any two numbers or a range of values.