Question

question 6, 3.3.ps-27 matt evaluates the expression \\((45.6 + 21.4) - 4^2 + 3.9 - 9.1\\). he records the answer as 38. laura evaluates the expression \\(45.6 + 21.4 - 4^2 + 3.9 - 9.1\\). she records the answer as 45.8. the expressions have the same numbers and operations. explain how matt and laura can both be correct. choose the correct answer below. a. matt and laura cannot both be correct because their answers would be the same if they used the order of operations correctly. b. matt used the order of operations because his expression had grouping symbols. laura did not need to use the order of operations because her expression had no grouping symbols. their answers are different but both are correct. c. laura got a different answer because she used the reverse order of operation as matt did. d. they both followed the order of operations but the grouping symbols require matt to calculate the numbers in a different order than laura.

Explanation:

Step1: Calculate Matt's expression

First, solve inside grouping symbols, then exponents, then add/subtract left to right.

$$\begin{align*} &[(45.6 + 21.4) - (4^2 + 3.9)] - 9.1\\ =&[67 - (16 + 3.9)] - 9.1\\ =&[67 - 19.9] - 9.1\\ =&47.1 - 9.1\\ =&38 \end{align*}$$

Step2: Calculate Laura's expression

Follow order of operations: exponents first, then add/subtract left to right.

$$\begin{align*} &45.6 + 21.4 - 4^2 + 3.9 - 9.1\\ =&45.6 + 21.4 - 16 + 3.9 - 9.1\\ =&67 - 16 + 3.9 - 9.1\\ =&51 + 3.9 - 9.1\\ =&54.9 - 9.1\\ =&45.8 \end{align*}$$

Step3: Analyze the difference

Matt's expression has grouping symbols that change the calculation order, while Laura's does not. Both followed order of operations correctly for their respective expressions.

Answer:

D. They both followed the order of operations but the grouping symbols require Matt to calculate the numbers in a different order than Laura.