Lesson 3

Adding and Subtracting Decimals with Few Non-Zero Digits

Problem 1

Here is a base-ten diagram that represents 1.13. Use the diagram to find $$1.13 - 0.46$$.

Problem 2

Compute the following sums. If you get stuck, consider drawing base-ten diagrams.

1. $$0.027 + 0.004$$

2. $$0.203 + 0.01$$

3. $$1.2 + 0.145$$

Problem 3

A student said we cannot subtract 1.97 from 20 because 1.97 has two decimal digits and 20 has none. Do you agree with him? Explain or show your reasoning.

Problem 4

Decide which calculation shows the correct way to find $$0.3-0.006$$ and explain your reasoning.

Problem 5

Complete the calculations so that each shows the correct difference.

Problem 6

The school store sells pencils for $0.30 each, hats for$14.50 each, and binders for $3.20 each. Elena would like to buy 3 pencils, a hat, and 2 binders. She estimated that the cost will be less than$20.

1. Do you agree with her estimate? Explain your reasoning.
2. Estimate the number of pencils could she buy with \$5. Explain or show your reasoning.
(From Unit 5, Lesson 1.)

Problem 7

A rectangular prism measures $$7\frac{1}{2}$$ cm by 12 cm by $$15\frac{1}{2}$$ cm.

1. Calculate the number of cubes with edge length $$\frac{1}{2}$$ cm that fit in this prism.
2. What is the volume of the prism in $$\text{cm}^3$$? Show your reasoning. If you are stuck, think about how many cubes with $$\frac12$$-cm edge lengths fit into $$1\text{ cm}^3$$.
(From Unit 4, Lesson 15.)

Problem 8

At a constant speed, a car travels 75 miles in 60 minutes. How far does the car travel in 18 minutes? If you get stuck, consider using the table.

minutes distance in miles
60 75
6
18
(From Unit 2, Lesson 12.)