Subtraction Methods: Partial differences, Regrouping & Estimation

Introduction 

Regrouping:

Regrouping can be defined as the process of making a group of tens when carrying out operations like addition and subtraction with two-digit numbers or larger. To regroup means to rearrange groups in place value to carry out an operation.

How to Subtract by Three Methods:

In this session, you will learn to subtract by three methods:

1. Estimation
2. Partial Differences
3. Regrouping

Example: Find the difference between 258 and 179.

Solution:

Method 1: Estimation

258 – 179

300 – 200 = 100

Method 2: Partial Difference

Use place value to subtract.

Count back by hundreds, tens, and ones.

179 = 100 + 70 + 9

70 can split into 50 + 20

Method 3: Regrouping

Step 1: Draw the place-value blocks to show 258.

Step 2: Regroup the ones.

  In 258 and 179, the numbers 8 and 9 are in one’s place.

 1 ten is transferred to the Ones place to subtract the numbers in one’s place.

Subtract 9 ones.

Step 3: Regroup the tens.

Regroup 1 ten as 10 ones:

Step 4: Regroup the hundreds.

Subtract 7 tens.

Regroup 1 hundred as 10 tens:

Subtract 1 hundred

Problems with Subtraction Using Three Methods:

Example 1:

Mike and Linda play a game. Linda has 527 points. Mike has 349 points. How many more issues does Linda have than Mike? Find 527- 349.

Solution:

Method 1

Estimation:

 527 – 349 =?

 530 – 350 = 180

Method 2

Draw place-value blocks to show 527.

Step 1:

 Subtract 9 ones.

Regroup 1 ten as 10 ones

Step 2:

Subtract 4 tens.

Regroup 1 hundred as 10 tens.

Step 3:

Subtract 3 hundred.

Method 3:

Partial Difference

Linda has 178 more points.

178 is close to the estimate.

The answer is reasonable.

Example 2:

How many more swimmers signed up for the 1^st session at Oaks Pool than for the 2nd session? Find it by estimating or using partial difference.

Solution:

Number of swimmers at Oaks Pool in session 1 = 763

Number of swimmers at Oaks Pool in session 2 = 586

Estimation:

763 – 586 =?

800 – 600 = 200

Partial difference:

586 = 500 + 80 + 6

177 swimmers are signed more for session 1.

177 are close estimated to 200.

The answer is reasonable.

Exercise

(1 – 3) Estimate the differences.

1. 482 – 146                    
2. 753 – 310                    
3. 547 – 356 

(4 – 5) Use the partial difference to subtract.              

4. 865 – 513                     

5. 378 – 175

6. In a zoo, there are 145 reptiles and 431 amphibians. How many more amphibians than reptiles are there?

7. On a fishing trip, Tyler catches 276 fish, in which 97 fish were sold at the shore. How many fish were in total with Tyler after selling?

8. A sea turtle lays 516 eggs in the sand and buries them. 402 eggs hatch after 60 days. How many eggs were left in the sand?

9. There were 526 crows in a field. A loud noise scares 238 of them away. How many crows are left?

10. 956 children participated in the fest, out of which 219 were boys. How many girls participated in the fest?

Concept Summary:

   What We Have Learned

• Learn about the estimation of place values to do subtraction
• Learn about the partial differences by using place values
• Learn about different strategies to regroup when subtracting 3-digit numbers