Lesson 3
Adding and Subtracting Decimals with Few Non-Zero Digits
Let’s add and subtract decimals.
Problem 1
Here is a base-ten diagram that represents 1.13. Use the diagram to find \(1.13 - 0.46\).
Explain or show your reasoning.
![A base-ten diagram representing 1 point 1 3. 1 large square, 1 rectangle, and 3 small squares.](https://cms-im.s3.amazonaws.com/CoXZU7Sc4XdZEz44M4xHWYB5?response-content-disposition=inline%3B%20filename%3D%226-6.5.PP.Image.21.png%22%3B%20filename%2A%3DUTF-8%27%276-6.5.PP.Image.21.png&response-content-type=image%2Fpng&X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAXQCCIHWF3XOEFOW4%2F20240630%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240630T162113Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=71cec6d05833f01c8f90a8accba346807958dee2a3728fda93d738f24b3d273b)
Problem 2
Compute the following sums. If you get stuck, consider drawing base-ten diagrams.
-
\(0.027 + 0.004\)
-
\(0.203 + 0.01\)
-
\(1.2 + 0.145\)
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.
![4 subtraction problems.](https://cms-im.s3.amazonaws.com/XGz1yxbovtZ5fgDWm8cCvc1n?response-content-disposition=inline%3B%20filename%3D%226-6.5.B.PP.New.Image.04.png%22%3B%20filename%2A%3DUTF-8%27%276-6.5.B.PP.New.Image.04.png&response-content-type=image%2Fpng&X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAXQCCIHWF3XOEFOW4%2F20240630%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240630T162113Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=8581e0385b77da8bad74a91382b3c8df3513dd2bbfe1272b655ceaef7f6cb060)
Problem 5
Complete the calculations so that each shows the correct difference.
![3 decimal subtraction problems.](https://cms-im.s3.amazonaws.com/mxoUpGNK3wUCLUSdrBPEYM6H?response-content-disposition=inline%3B%20filename%3D%226-6.5.B.PP.New.Image.03.png%22%3B%20filename%2A%3DUTF-8%27%276-6.5.B.PP.New.Image.03.png&response-content-type=image%2Fpng&X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAXQCCIHWF3XOEFOW4%2F20240630%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240630T162113Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=388b3e21bbb363d482dcaaa3c2ef2e3f20c70817d3290f4083bcaef32f1bd1e3)
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.
- Do you agree with her estimate? Explain your reasoning.
- Estimate the number of pencils could she buy with $5. Explain or show your reasoning.
Problem 7
A rectangular prism measures \(7\frac{1}{2}\) cm by 12 cm by \(15\frac{1}{2}\) cm.
- Calculate the number of cubes with edge length \(\frac{1}{2}\) cm that fit in this prism.
- 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 \(1\text{ cm}^3\).
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 |