Evaluating the Expression: 1 3/2 + 2 6/5 + 5 18/100 as a Fraction
When dealing with mixed numbers and fractions, it's essential to understand how to evaluate and simplify expressions. In this article, we'll explore how to evaluate the expression 1 3/2 + 2 6/5 + 5 18/100 as a fraction.
Step 1: Convert Mixed Numbers to Improper Fractions
To start, we need to convert the mixed numbers into improper fractions:
- 1 3/2 = (2 × 1) + 3/2 = 5/2
- 2 6/5 = (5 × 2) + 6/5 = 16/5
- 5 18/100 = (100 × 5) + 18/100 = 518/100 = 259/50 (simplified)
Step 2: Add the Fractions
Now that we have the improper fractions, we can add them:
- 5/2 + 16/5 = ?
To add these fractions, we need a common denominator. The least common multiple (LCM) of 2 and 5 is 10. So, we'll convert both fractions to have a denominator of 10:
- 5/2 = 25/10
- 16/5 = 32/10
Now we can add:
- 25/10 + 32/10 = 57/10
Step 3: Add the Remaining Fraction
Finally, we'll add the remaining fraction:
- 57/10 + 259/50 = ?
Again, we need a common denominator. The LCM of 10 and 50 is 50. So, we'll convert the first fraction to have a denominator of 50:
- 57/10 = 285/50
Now we can add:
- 285/50 + 259/50 = 544/50
The Final Answer
After simplifying, we get:
544/50 = 1088/100 = 10 88/100
Therefore, the evaluation of the expression 1 3/2 + 2 6/5 + 5 18/100 as a fraction is 10 88/100.
