Lesson 3: Adding and Subtracting Decimals with Few Non-Zero Digits
Let’s add and subtract decimals.
Illustrative Math Unit 6.5, Lesson 3 (printable worksheets)
Lesson 3 Summary
The following diagram shows how to use base-ten diagrams to represent and reason about subtracting of decimals.
Lesson 3.1 Do the Zeros Matter?
- Evaluate mentally:
- Decide if each equation is true or false. Be prepared to explain your reasoning.
a. 34.56000 = 34.56
b. 25 = 25.0
c. 2.405 = 2.45
Scroll down the page for the solutions to the “Are you ready for more?” section.
Lesson 3.2 Calculating Sums
- Andre and Jada drew base-ten diagrams to represent 0.007 + 0.004. Andre drew 11 small rectangles. Jada drew only two figures: a square and a small rectangle.
a. If both students represented the sum correctly, what value does each small rectangle represent? What value does each square represent?
b. Draw or describe a diagram that could represent the sum 0.008 + 0.07.
- Here are two calculations of 0.2 + 0.05. Which is correct? Explain why one is correct and the other is incorrect.
- Compute each sum. If you get stuck, draw base-ten diagrams to help you.
The applet has tools that create each of the base-ten blocks.
Select a Block tool, and then click on the screen to place it.
Lesson 3.3 Subtracting Decimals of Different Lengths
To represent , Diego and Noah drew different diagrams. Each rectangle shown here represents 0.1. Each square represents 0.01.
- Diego started by drawing 4 rectangles for 0.4. He then replaced 1 rectangle with 10 squares and crossed out 3 squares for the subtraction of 0.03, leaving 3 rectangles and 7 squares in his drawing.
- Noah started by drawing 4 rectangles for 0.4. He then crossed out 3 of them to represent the subtraction, leaving 1 rectangle in his drawing.
- Do you agree that either diagram correctly represents 0.4 - 0.03? Discuss your reasoning with a partner.
- To represent 0.4 - 0.03, Elena drew another diagram. She also started by drawing 4 rectangles. She then replaced all 4 rectangles with 40 squares and crossed out 3 squares for the subtraction of 0.03, leaving 37 squares in her drawing. Is her diagram correct? Discuss your reasoning with a partner.
- Find each difference. If you get stuck, you can use the applet to represent each expression and find its value.
a. 0.3 - 0.05
b. 2.1 - 0.4
c. 1.03- 0.06
d. 0.02 - 0.007
Be prepared to explain your reasoning.
- The applet has tools that create each of the base-ten blocks. This time you need to decide the value of each block before you begin.
- Select a Block tool, and then click on the screen to place it.
Are you ready for more?
A distant, magical land uses jewels for their bartering system. The jewels are valued and ranked in order of their rarity. Each jewel is worth 3 times the jewel immediately below it in the ranking. The ranking is red, orange, yellow, green, blue, indigo, and violet. So a red jewel is worth 3 orange jewels, a green jewel is worth 3 blue jewels, and so on.
At the Auld Shoppe, a shopper buys items that are worth 2 yellow jewels, 2 green jewels, 2 blue jewels, and 1 indigo jewel. If they came into the store with 1 red jewel, 1 yellow jewel, 2 green jewels, 1 blue jewel, and 2 violet jewels, what jewels do they leave with? Assume the shopkeeper gives them their change using as few jewels as possible.
Lesson 3 Practice Problems
- Here is a base-ten diagram that represents 1.13. Use the diagram to find 1.13 - 0.46.
Explain how you found the difference, or label your diagram to show your steps.
- Compute the following sums. If you get stuck, you can draw base-ten diagrams.
a. 0.027 + 0.004
b. 0.203 + 0.1
c. 1.2 + 0.145
- 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 his statement? Explain or show your reasoning.
- Decide which calculation shows the correct way to find 0.3 - 0.006 and explain your reasoning.
- Complete the calculations so that each shows the correct difference.
- 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.
a. Do you agree with her estimate? Explain your reasoning.
b. Estimate the number of pencils could she buy with $5. Explain or show your reasoning.
- A rectangular prism measures 7½ cm by 12 cm by 15½ cm.
a. Calculate the number of cubes with edge length ½ cm that fit in this prism.
b. What is the volume of the prism in cm3? Show your reasoning. If you are stuck, think about how many cubes with ½-cm edge lengths fit into 1 cm3.
- 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.
||distance in miles
The Open Up Resources math curriculum is free to download from the Open Up Resources website and is also available from Illustrative Mathematics.
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