Simplifying the Difference: 2 1/2 - 1 7/8 as a Fraction
When working with mixed numbers, it's essential to understand how to perform arithmetic operations like subtraction. In this article, we'll explore how to simplify the difference between 2 1/2 and 1 7/8 as a fraction.
Converting Mixed Numbers to Improper Fractions
To subtract these mixed numbers, we need to convert them into improper fractions. Let's do that:
2 1/2
- The whole number part is 2.
- The fractional part is 1/2.
- To convert, multiply the whole number part by the denominator (2): 2 × 2 = 4
- Add the numerator (1) to the product: 4 + 1 = 5
- So, 2 1/2 becomes the improper fraction: 5/2
1 7/8
- The whole number part is 1.
- The fractional part is 7/8.
- To convert, multiply the whole number part by the denominator (8): 1 × 8 = 8
- Add the numerator (7) to the product: 8 + 7 = 15
- So, 1 7/8 becomes the improper fraction: 15/8
Subtracting the Improper Fractions
Now that we have the improper fractions, we can subtract them:
5/2 - 15/8
To subtract these fractions, we need a common denominator, which is the least common multiple (LCM) of 2 and 8. The LCM is 8. We can convert the first fraction to have a denominator of 8:
5/2 = 20/8
Now we can subtract:
20/8 - 15/8 = 5/8
So, the difference between 2 1/2 and 1 7/8 as a fraction is 5/8.
Conclusion
In conclusion, we've successfully simplified the difference between 2 1/2 and 1 7/8 as a fraction. By converting the mixed numbers to improper fractions and finding a common denominator, we were able to perform the subtraction and obtain the result: 5/8.
