Fraction Operations: Understanding 6 1/2 and 4 3/4
In mathematics, fractions are used to represent part of a whole. They consist of a numerator (the top number) and a denominator (the bottom number). In this article, we will focus on two specific mixed numbers: 6 1/2 and 4 3/4. We'll explore their meanings, conversions, and operations.
What do 6 1/2 and 4 3/4 represent?
6 1/2
6 1/2 is a mixed number, which is a combination of a whole number and a fraction. In this case, the whole number is 6, and the fraction is 1/2. To understand what it represents, let's break it down:
- The whole number 6 represents 6 complete units.
- The fraction 1/2 represents half of a unit.
Therefore, 6 1/2 represents 6 complete units plus half of another unit.
4 3/4
Similar to 6 1/2, 4 3/4 is also a mixed number. Here, the whole number is 4, and the fraction is 3/4. Let's analyze it:
- The whole number 4 represents 4 complete units.
- The fraction 3/4 represents three-quarters of a unit.
Thus, 4 3/4 represents 4 complete units plus three-quarters of another unit.
Converting to Improper Fractions
We can convert mixed numbers to improper fractions by multiplying the whole number part by the denominator and then adding the numerator.
6 1/2
To convert 6 1/2 to an improper fraction:
- Multiply 6 (whole number) by 2 (denominator): 6 × 2 = 12
- Add 1 (numerator): 12 + 1 = 13
- Write the result as an improper fraction: 13/2
4 3/4
To convert 4 3/4 to an improper fraction:
- Multiply 4 (whole number) by 4 (denominator): 4 × 4 = 16
- Add 3 (numerator): 16 + 3 = 19
- Write the result as an improper fraction: 19/4
Operations with 6 1/2 and 4 3/4
Now that we have a better understanding of these mixed numbers, let's explore some basic operations:
Addition
To add 6 1/2 and 4 3/4, we need to convert them to improper fractions:
- 6 1/2 = 13/2
- 4 3/4 = 19/4
Add the two fractions:
- 13/2 + 19/4 = (13 × 2) / (2 × 2) + (19 × 2) / (4 × 2) = 26/4 + 38/4 = 64/4
Simplify the result:
- 64/4 = 16
So, 6 1/2 + 4 3/4 = 16.
Subtraction
Subtracting 4 3/4 from 6 1/2:
- 6 1/2 = 13/2
- 4 3/4 = 19/4
Subtract the two fractions:
- 13/2 - 19/4 = (13 × 2) / (2 × 2) - (19 × 2) / (4 × 2) = 26/4 - 38/4 = -12/4
Simplify the result:
- -12/4 = -3
So, 6 1/2 - 4 3/4 = -3.
In conclusion, understanding mixed numbers like 6 1/2 and 4 3/4 is essential for performing various mathematical operations. By converting them to improper fractions, we can simplify calculations and achieve accurate results.
