Adding Without Regrouping

When the sum of digits in each place value is less than 10, we do not need to regroup.

Adding Horizontally

Example: $3246 + 2312 = ?$

Step 1: Write the numbers with place values aligned:

Step 2: Add from right to left:

• Ones: $6 + 2 = 8$
• Tens: $4 + 1 = 5$
• Hundreds: $2 + 3 = 5$
• Thousands: $3 + 2 = 5$

Answer: $3246 + 2312 = 5558$

Adding Vertically

Example:

  6118
+ 1211
_____

Step 1: Align the numbers vertically by place value:

• Ones: $8 + 1 = 9$
• Tens: $1 + 1 = 2$
• Hundreds: $1 + 2 = 3$
• Thousands: $6 + 1 = 7$

Answer: $7329$

Adding With Regrouping

When the sum of digits in any place value is 10 or more, we regroup (carry over) to the next place.

Adding Horizontally

Example: $6327 + 3496 = ?$

Step 1: Add from right to left:

• Ones: $7 + 6 = 13$. Write 3, regroup 1 ten to tens place.
• Tens: $1 + 2 + 9 = 12$. Write 2, regroup 1 hundred to hundreds place.
• Hundreds: $1 + 3 + 4 = 8$
• Thousands: $6 + 3 = 9$

Answer: $6327 + 3496 = 9823$

Adding Vertically

Example:

  2361
+ 3899
_____

Step 1: Add the ones: $1 + 9 = 10$. Write 0, regroup 1 to tens.

Step 2: Add the tens: $1 + 6 + 9 = 16$. Write 6, regroup 1 to hundreds.

Step 3: Add the hundreds: $1 + 3 + 8 = 12$. Write 2, regroup 1 to thousands.

Step 4: Add the thousands: $1 + 2 + 3 = 6$

Answer: $6260$

Subtracting Without Regrouping

When each digit in the top number is greater than or equal to the digit below it, we subtract directly.

Subtracting Horizontally

Example: $6874 - 2430 = ?$

Step 1: Subtract from right to left:

• Ones: $4 - 0 = 4$
• Tens: $7 - 3 = 4$
• Hundreds: $8 - 4 = 4$
• Thousands: $6 - 2 = 4$

Answer: $6874 - 2430 = 4444$

Subtracting Vertically

Example:

  86597
- 54326
_____

• Ones: $7 - 6 = 1$
• Tens: $9 - 2 = 7$
• Hundreds: $5 - 3 = 2$
• Thousands: $6 - 4 = 2$
• Ten thousands: $8 - 5 = 3$

Answer: $32271$

Subtracting With Regrouping

When a digit in the top number is smaller than the digit below it, we need to regroup (borrow) from the next place value.

Subtracting Horizontally

Example: $5371 - 3282 = ?$

Step 1: Subtract the ones: $1 - 2$. We cannot take 2 from 1, so borrow 1 ten (making it 10 ones): $10 + 1 = 11$. Now $11 - 2 = 9$. (7 tens becomes 6 tens)

Step 2: Subtract the tens: $6 - 8$. Borrow 1 hundred (making it 10 tens): $10 + 6 = 16$. Now $16 - 8 = 8$. (3 hundreds becomes 2 hundreds)

Step 3: Subtract the hundreds: $2 - 2 = 0$

Step 4: Subtract the thousands: $5 - 3 = 2$

Answer: $2089$

Subtracting Vertically

Example:

  6854
- 3887
_____

Step 1: Ones: $4 - 7$. Borrow 1 ten: $14 - 7 = 7$. (5 tens becomes 4 tens)

Step 2: Tens: $4 - 8$. Borrow 1 hundred: $14 - 8 = 6$. (8 hundreds becomes 7 hundreds)

Step 3: Hundreds: $7 - 8$. Borrow 1 thousand: $17 - 8 = 9$. (6 thousands becomes 5 thousands)

Step 4: Thousands: $5 - 3 = 2$

Answer: $2967$

Steps to Solve Word Problems

1. Read the problem carefully.
2. Identify what is being asked.
3. Decide whether to add or subtract.
4. Calculate the answer.
5. Write the final answer with units.

Addition Word Problem

A farmer has 1,982 timber trees and 7,291 fruit trees. How many trees does the farmer have in total?

Solution: $1,982 + 7,291 = 9,273$

The farmer has 9,273 trees in total.

Subtraction Word Problem

A school needs 3,749 desks. Parents contributed 2,997 desks. How many more desks are still needed?

Solution: $3,749 - 2,997 = 752$

The school still needs 752 more desks.

In everyday life in Tanzania, we use addition and subtraction when buying and selling at the market. For example, if Mama Amina sells tomatoes for TSh 15,500 and TSh 22,300 on two different days, she adds these amounts to know her total earnings: $15,500 + 22,300 = TSh 37,800$. If she then spends TSh 14,500 on school fees for her child, she subtracts to find how much money she has left: $37,800 - 14,500 = TSh 23,300$.