Question

Evaluate the expression. Use estimation to check your answer. $$ 8.9-(-2.1)-7.3 $$

Short answer

The solution to the given expression is \(3.7\). Using estimation also confirms that this answer is approximately correct.

Step-by-step solution

Apply negative number rules

The operators immediately before and after the parentheses are a subtraction and a negation respectively. According to the rule of signs, subtracting a negative number is the same as adding a positive number. Therefore, the expression can be rewritten as: \(8.9 + 2.1 - 7.3\)

Perform addition

First, add \(8.9\) and \(2.1\) to get \(11.0\). The expression can now be rewritten as: \(11.0 - 7.3\)

Finish with subtraction

Finally, subtract \(7.3\) from \(11\). That leads to the final answer: \(3.7\)

Use estimation to check your work

For estimation purposes, rewrite the original expression, rounding each number to the nearest whole number: \(9 - (-2) - 7\). This simplifies to \(9 + 2 - 7 = 4\). This isn’t exactly \(3.7\), but it’s close, supporting the correctness of the exact calculation.