Lesson 6: Practice Problems

Problem 1

Find each product. Show your reasoning.

$(1.2) \cdot (0.11)$
$(0.34) \cdot (0.02)$
$120 \cdot (0.002)$

Problem 2

You can use a rectangle to represent $(0.3) \cdot (0.5)$ .

A rectangle area model. The rectangle is partitioned into 15 identical squares. There are 5 rows of 3 squares in each row.

What must the side length of each square represent for the rectangle to correctly represent $(0.3) \cdot (0.5)$ ?
What area is represented by each square?
What is $(0.3) \cdot (0.5)$ ? Show your reasoning.

Problem 3

One gallon of gasoline in Buffalo, New York costs $2.29. In Toronto, Canada, one liter of gasoline costs $0.91. There are 3.8 liters in one gallon.

How much does one gallon of gas cost in Toronto? Round your answer to the nearest cent.
Is the cost of gas greater in Buffalo or in Toronto? How much greater?

Problem 4 From Unit 5 Lesson 2

Calculate each sum or difference.

$10.3 + 3.7$
$20.99 - 4.97$
$15.99 + 23.51$
$1.893 - 0.353$

Problem 5 From Unit 4 Lesson 11

Find the value of $\frac{49}{50} \div \frac{7}{6}$ using any method.

Problem 6 From Unit 1 Lesson 1

Find the area of the shaded region. All angles are right angles. Show your reasoning.

A multi-sided figure. The sides on top measure 10 units, 35 units, and 15 units. Two of the three sides on the left measure 10 units. One of the two sides on the right measures 10 units. One of the two sides on the bottom measure 15 units. The total width of the figure is 60 units, and the total height is 30 units. All angles are right angles.

Problem 7

Priya finds $(1.05) \cdot (2.8)$ by calculating $105 \cdot 28$ , then moving the decimal point three places to the left. Why does Priya’s method make sense?
Use Priya’s method to calculate $(1.05) \cdot (2.8)$ . You can use the fact that $105 \cdot 28 = 2, 940$ .
Use Priya’s method to calculate $(0.0015) \cdot (0.024)$ .