To solve the problem of adding the fractions [tex]\(1 \frac{6}{10} + \frac{3}{5}\)[/tex], follow these steps:
### Step 1: Convert the mixed number to an improper fraction or a decimal
1. Identify the mixed number: [tex]\(1 \frac{6}{10}\)[/tex].
2. Convert the mixed number to a decimal: [tex]\(1 \frac{6}{10}\)[/tex] means [tex]\(1 + \frac{6}{10}\)[/tex].
- [tex]\(\frac{6}{10}\)[/tex] as a decimal is [tex]\(0.6\)[/tex].
- Therefore, [tex]\(1 + 0.6 = 1.6\)[/tex].
Hence, [tex]\(1 \frac{6}{10} = 1.6\)[/tex].
### Step 2: Convert the second fraction to a decimal
1. Identify the fraction: [tex]\(\frac{3}{5}\)[/tex].
2. Convert the fraction to a decimal:
- [tex]\(\frac{3}{5} = 0.6\)[/tex].
### Step 3: Add the decimals
1. Add the decimals:
- [tex]\(1.6 + 0.6 = 2.2\)[/tex].
### Step 4: Separate the integral part and the fractional part of the result
1. Identify the integral part: The integral part of [tex]\(2.2\)[/tex] is [tex]\(2\)[/tex].
2. Identify the fractional part: The fractional part of [tex]\(2.2\)[/tex] is [tex]\(0.2\)[/tex].
Therefore, the final result of adding [tex]\(1 \frac{6}{10} + \frac{3}{5}\)[/tex] is:
- The first fraction as a decimal: [tex]\(1.6\)[/tex].
- The second fraction as a decimal: [tex]\(0.6\)[/tex].
- The sum of the fractions: [tex]\(2.2\)[/tex].
- The integral part of the sum: [tex]\(2\)[/tex].
- The fractional part of the sum: [tex]\(0.2\)[/tex].
Note: The fractional part [tex]\(0.2\)[/tex] might have a slight imperfection due to floating-point arithmetic, resulting in a tiny deviation ([tex]\(0.20000000000000018\)[/tex]), but the main value remains [tex]\(0.2\)[/tex].
