Activity 6.2a: Addition and Subtraction of Decimals

Purpose: Explore models for addition and subtraction of decimals.

Materials: Base-ten blocks or app Links to an external site., paper, calculator, spreadsheet

Part 1: Addition

We can model addition of decimals with base-ten blocks to illustrate why we carry in our addition algorithm.

For example, 2.5 + 3.7 (app example Links to an external site.)

To add means to combine and count.

So, combined we have 5 wholes and 12 tenths, so 2.5 + 3.7 = 5.12?

Wait. That's not right. There are no hundredths here, only ones and tenths.

If you have 12 tenths, then you also have 1 whole and 2 tenths. $\frac{12}{10}=1\frac{2}{10}$

So, 2.5 + 3.7 is 5 + 1.2, which is 6.2

Your turn. Using base-ten blocks illustrate and explain the following.

1. 2.5 + 2.4
   
   
2. 1.8 + 1.7
   
   
3. 1.37 + 2.15
   
   
4. 2.36 + 3.89
   
   

Part 2: Subtraction

We can model subtraction of decimals with base-ten blocks to illustrate why we borrow in our subtraction algorithm.

For example, 2.3 - 1.5 (app example Links to an external site.)

To subtract means to compare, i.e., 2.3 is how much more than 1.5?

Ok, so, they each have a whole and then 3 tenths in common, so is the difference 1 and 2 tenths? 1.2?

Um, that doesn't seem right.

I think we need to do a trade, 2 and 3/10, for 1 and 13/10.

This seems better. Now I can compare wholes and tenths fully with both numbers. It seems that 2.3 is 0.8 more than 1.5.

That is, 2.3 - 1.5 = 0.8.

Your turn. Use base-ten block to illustrate and explain the following.

1. 2.5 – 1.4
   
   
2. 3.5 – 1.7
   
   
3. 3.52 – 2.15
   
   
4. 3.25 – 1.89