Name: _________________________

Putting It All Together

Instructions: Apply the rules for order of operations to complete the following problems.

a) Evaluate expressions within parentheses

b) Simplify powers (apply exponents).

c) Perform multiplication and division as they occur from left to right.

d) Perform additions and subtractions as they occur from left to right.

Example: 10 – 3* 2 ≠ 7 * 2 = 14

10 – 3 * 2 = 10 – 6 = 4

1. The process used to code a message is “Add 1 to a letter’s position, then multiply 2.” (Hint: This process shifts before stretching.)

a) Draw an arrow diagram for the coding process.

b) Write a symbolic equation to represent the coding process.

c) Code the word variable.

d) Add the decoding process to the arrow diagram you drew in part (a).

e) Write a symbolic equation to represent the decoding process.

f) Decode 32 38 10 12 38.

2. a) Do c = 5p + 1 and c = 5(p+1) represent the same coding process or different coding processes? Describe how to confirm or verify your answer.

b) Represent each coding process with an arrow diagram.

c) Describe the decoding process for c = 5p + 1.

d) For the coding process c = 5p + 1, decode the coded value 46. That is, solve the

equation 46 = 5p + 1.

e) Another way to solve the equation 46 = 5p + 1 is with a graphing calculator.

Let Y1 = 5X + 1 and Y2 = 46. Graph both lines on the same screen. The place

where the two lines intersect is the point where Y1 = Y2. How do you find the

point where the two lines intersect?

f) Describe the decoding process for c = 5(p+1)