Lesson 10: Practice Problems

Problem 1

Evaluate each expression:

$- 12 \cdot \frac{1}{3}$
$- 12 \cdot (- \frac{1}{3})$
$12 \cdot (- \frac{5}{4})$
$- 12 \cdot (- \frac{5}{4})$

Problem 2

Evaluate each expression:

$(- 1) \cdot 2 \cdot 3$
$(- 1) \cdot (- 2) \cdot 3$
$(- 1) \cdot (- 2) \cdot (- 3)$

Problem 3 From Unit 5 Lesson 1

Order each set of numbers from least to greatest.

1. $4$
2. $8$
3. $- 2$
4. $- 6$
5. $0$
1. $- 5$
2. $- 5.2$
3. $- 5.5$
4. $- 5 \frac{1}{2}$
5. $\frac{- 5}{2}$

Problem 4 From Unit 5 Lesson 3

$30 + (- 30) = 0$ .

Write another sum of two numbers that equals 0.
Write a sum of three numbers that equals 0.
Write a sum of four numbers that equals 0, none of which are opposites.

Problem 5 From Unit 5 Lesson 6

A submarine is searching for underwater features. It is accompanied by a small aircraft and an underwater robotic vehicle.

At one time the aircraft is 200 m above the surface, the submarine is 55 m below the surface, and the underwater robotic vehicle is 227 m below the surface.

What is the difference in height between the submarine and the aircraft?
What is the distance between the underwater robotic vehicle and the submarine?

Problem 6 From Unit 5 Lesson 8

Clare is cycling at a speed of 12 miles per hour. If she starts at a position chosen as zero, what will her position be after 45 minutes?
Han is cycling at a speed of -8 miles per hour; if he starts at the same zero point, what will his position be after 45 minutes?
What will the distance between them be after 45 minutes?

Problem 7 From Unit 5 Lesson 9

Fill in the missing numbers in these equations

$(- 7) \cdot$ $= - 14$
$\cdot 3 = - 15$
$\cdot 4 = 32$
$- 49 \cdot 3 =$