1. Find the sum of 12 over 13 , plus . open , negative , 1 thirteenth , close . .
2. Find the value of the expression (− 8.6) + 7.2.
3. Find the sum of − 7.5 + (− 7.6).
4. Find the sum of 2 thirds , plus . open , negative , 1 third , close . .
5. In her garden Pam plants a tomato seed 2 , and 3 fourths in. below the ground. After one month the tomato plant has grown a total of 12 , and 1 half in. How many inches is the plant above the ground?
6. Greg is at his house. He gets in his car, drives north 9.6 miles, and stops at a store. Then he turns around and drives south 8.4 miles to his friend's house. How far is the friend's house from Greg's house?
7. Simplify the expression. open . negative , 11 over 21 . close . plus , 9 twenty firsts , .
a. Writing Simplify the expression open , negative , 8 fifteenths , close . plus . open , 1 fifteenth , close . .
b. Show how to simplify in steps, using a property of operations for each step. Explain the property you use in each step.
a. Reasoning Simplify the expression (− 13.2) + 8.1.
b. How are (− 13.2) + 8.1 and 13.2 + (− 8.1) related? Explain without computing.
c. Using a property of operations, what can you say about their sums?
a. Error Analysis Simplify the expression − 2.6 + (− 5.4).
b. On the test, when Tom simplified the expression he got − 2.8. What mistake did Tom likely make when he simplified the expression?
A. He found the absolute value of just the second number.
B. He found the absolute value of just the first number.
C. He found the absolute value of both numbers, but then used the wrong sign.
D. He did not find the absolute value of either number.
11. Think About the Process
a. Which absolute value expression would you use to find the absolute value of 3.1 + (− 6.3)?
A. |3.1| + | − 6.3|
B. | − 6.3||-||3.1|
C. | − 6.3| + |3.1|
D. |3.1| + | − 6.3|
b. Find 3.1 + (− 6.3).
a. Mental Math Simplify the expression negative 5 , and 3 fourths , plus . open , negative , 1 fourth , close . .
b. Describe the steps you use to simplify this expression using mental math. Tell why this expression allows you to use mental math.
13. Stock Market At the beginning of the day the stock market goes up points and stays at this level for most of the day. At the end of the day the stock market goes down points from the high at the beginning of the day. What is the total change in the stock market from the beginning of the day to the end of the day?
a. Simplify the expression 100.9 + (− 70.5).
b. Show how, using the properties of operations, you can begin with the expression 100.9 + (− 70.5) and write an equivalent sum that has the form 125.9 + (a).
15. Estimation A group of students go out on a boat to go scuba diving. The instructor takes the group 54.96 feet below the surface to start. Then they go up 22.38 feet and stop to see some fish. Which of the following is the best estimate for the total change in distance from the group of students’ original position at the surface?
A. − 20 feet
B. − 50 feet
C. − 30 feet
D. − 70 feet