Verified Answer :

  • Compute each multiplication in the expression individually: \(1 \times 1 = 1\), \(8 \times \frac{1}{10} = \frac{8}{10}\), and \(2 \times \frac{1}{10} = \frac{2}{10}\).
  • Combine the fractional terms: \(\frac{8}{10} + \frac{2}{10} = \frac{10}{10} = 1\).
  • Add the products together to find the final result: \(1 + 1 = 2\).
  • The final result is \(\boxed{2}\).

Explanation

  1. Problem Analysis

We are asked to compute the value of the arithmetic expression:
\[ 1 \times 1 + 8 \times \frac{1}{10} + 2 \times \frac{1}{10} \]
Following the standard order of operations (PEMDAS/BODMAS), we must perform the multiplication operations before the addition. There are three products to compute.

  1. Step-by-Step Calculation

First, perform the multiplications:

  • The first term is \(1 \times 1 = 1\).
  • The second term is \(8 \times \frac{1}{10} = \frac{8}{10}\).
  • The third term is \(2 \times \frac{1}{10} = \frac{2}{10}\).

Now, add these results together:
\[ 1 + \frac{8}{10} + \frac{2}{10} = 1 + \left(\frac{8+2}{10}\right) = 1 + \frac{10}{10} = 1 + 1 = 2 \]
The value of the expression is 2.

Examples

This simple calculation represents a common real-life task: calculating a total cost. Imagine you buy 1 item for \$1, and 8 additional small components that cost 10 cents each, and 2 more components that cost 10 cents each. The total cost is \(\$1 \times 1 + 8 \times \$0.10 + 2 \times \$0.10 = \boxed{\$2.00}\). Understanding the order of operations helps in calculating total expenses correctly when items have different unit prices.

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