Let's solve the equation step by step.
### Step 1: Convert mixed and improper fractions to improper fractions
First, we'll convert the mixed fractions to improper fractions to make calculations easier.
#### Left Side:
[tex]\[2 \frac{1}{2} + \frac{1}{2}\][/tex]
1. Convert [tex]\(2 \frac{1}{2}\)[/tex] to an improper fraction:
- [tex]\(2 \frac{1}{2} = 2 + \frac{1}{2} = \frac{4}{2} + \frac{1}{2} = \frac{5}{2}\)[/tex]
2. Then add [tex]\(\frac{1}{2}\)[/tex] to it:
- [tex]\(\frac{5}{2} + \frac{1}{2} = \frac{6}{2} = 3\)[/tex]
So, the left side becomes:
[tex]\[25 \times 3\][/tex]
#### Right Side:
[tex]\[5 \frac{1}{6} + \frac{2}{3}\][/tex]
1. Convert [tex]\(5 \frac{1}{6}\)[/tex] to an improper fraction:
- [tex]\(5 \frac{1}{6} = 5 + \frac{1}{6} = \frac{30}{6} + \frac{1}{6} = \frac{31}{6}\)[/tex]
2. Convert [tex]\(\frac{2}{3}\)[/tex] to a fraction with the same denominator (6):
- [tex]\(\frac{2}{3} = \frac{4}{6}\)[/tex]
3. Then add [tex]\(\frac{4}{6}\)[/tex] to [tex]\(\frac{31}{6}\)[/tex]:
- [tex]\(\frac{31}{6} + \frac{4}{6} = \frac{35}{6}\)[/tex]
So, the right side becomes:
[tex]\[10 - \frac{35}{6}\][/tex]
### Step 2: Calculate each side of the equation
#### Left Side:
[tex]\[25 \times 3 = 75\][/tex]
#### Right Side:
Convert 10 to a fraction with the same denominator (6):
[tex]\[10 = \frac{60}{6}\][/tex]
Then, subtract [tex]\(\frac{35}{6}\)[/tex]:
[tex]\[\frac{60}{6} - \frac{35}{6} = \frac{25}{6}\][/tex]
Converting [tex]\(\frac{25}{6}\)[/tex] back to a decimal:
[tex]\[\frac{25}{6} \approx 4.1667\][/tex] (approximation)
### Step 3: Compare the results
The left side is:
[tex]\[75\][/tex]
The right side is:
[tex]\[10 - \frac{35}{6} \approx 4.1667\][/tex]
So the detailed step-by-step solution for the given problem is:
- The left side evaluates to [tex]\(75\)[/tex]
- The right side evaluates to [tex]\(\approx 4.1667\)[/tex]
Therefore:
[tex]\[ 25 \times\left(2 \frac{1}{2}+\frac{1}{2}\right)= 10-\left(5 \frac{1}{6}+\frac{2}{3}\right) \][/tex]
becomes:
[tex]\[ 75 = 4.1667 \][/tex]
