Four Operations and BODMAS

The four operations — addition, subtraction, multiplication, and division — are the building blocks of all mathematics. In the FSCE 11+ exam, you will need to carry out these operations quickly and accurately, often as part of larger multi-step problems. You also need to understand the order of operations (BODMAS) so you can evaluate expressions correctly. This lesson covers all four operations in depth, compares different methods, and teaches you exactly how BODMAS works.

Addition and Subtraction

Column Addition

When adding numbers, line up the digits by place value and add from right to left, carrying over when a column totals 10 or more.

Example: 4,567 + 2,845

    4 5 6 7
+   2 8 4 5
-----------
    7 4 1 2

Working from right to left:

• Ones: 7 + 5 = 12. Write 2, carry 1.
• Tens: 6 + 4 + 1 (carried) = 11. Write 1, carry 1.
• Hundreds: 5 + 8 + 1 (carried) = 14. Write 4, carry 1.
• Thousands: 4 + 2 + 1 (carried) = 7.

Answer: 7,412

Column Subtraction

Line up the digits and subtract from right to left. If the top digit is smaller, borrow (exchange) from the next column to the left.

Example: 5,302 - 1,847

Working from right to left:

• Ones: need to subtract 7 from 2. Borrow from the tens column. Tens is 0, so borrow from hundreds first. Hundreds (3) becomes 2; tens becomes 10. Now borrow from tens for ones: tens becomes 9; ones becomes 12. Then 12 - 7 = 5.
• Tens: 9 - 4 = 5.
• Hundreds: 2 - 8 — cannot do. Borrow from thousands. Thousands (5) becomes 4; hundreds becomes 12. Then 12 - 8 = 4.
• Thousands: 4 - 1 = 3.

Answer: 3,455. Check: 3,455 + 1,847 = 5,302. ✓

Multiplication

Grid Method vs Column Method

There are two main methods for multiplying larger numbers. Both give the same answer — choose the one you find most reliable.

Grid Method

Break each number into its parts (partitioning), multiply each pair, and add the results.

Example: 347 x 26

×	300	40	7
20	6,000	800	140
6	1,800	240	42

Now add all the parts: 6,000 + 800 + 140 + 1,800 + 240 + 42 = 9,022

Advantages of the grid method: Easy to see where each part comes from. Good for checking your work. Fewer carrying errors.

Disadvantages: Takes longer. Uses more space.

Column Method (Long Multiplication)

Example: 347 x 26

      3 4 7
    x   2 6
    -------
    2 0 8 2    (347 x 6)
  6 9 4 0      (347 x 20)
  ---------
  9 0 2 2

Advantages of the column method: Faster once you are confident. Takes less space. Standard method used in secondary school.

Disadvantages: Easy to make carrying errors. Harder to spot where you went wrong.

Comparison Table

Feature	Grid Method	Column Method
Speed	Slower	Faster
Accuracy for beginners	Higher	Lower
Space needed	More	Less
Easy to check?	Yes	Harder
Best for	Understanding and checking	Speed in exams

Recommendation: Learn both. Use the column method in the exam for speed, but switch to the grid method if you need to check a calculation.

Division

Short Division (Bus Stop Method)

Used when dividing by a single-digit number.

Example: 7,856 ÷ 4

    1 9 6 4
  --------
4 | 7 8 5 6

• 7 ÷ 4 = 1 remainder 3. Write 1, carry 3.
• 38 ÷ 4 = 9 remainder 2. Write 9, carry 2.
• 25 ÷ 4 = 6 remainder 1. Write 6, carry 1.
• 16 ÷ 4 = 4 remainder 0. Write 4.

Answer: 1,964

Long Division

Used when dividing by a two-digit (or larger) number.

Example: 4,368 ÷ 14

Step 1: 14 does not go into 4 (too small). Try 43: 14 x 3 = 42. Write 3 above the 3 in 43. Remainder = 43 - 42 = 1.

Step 2: Bring down the 6 to make 16. 14 x 1 = 14. Write 1. Remainder = 16 - 14 = 2.

Step 3: Bring down the 8 to make 28. 14 x 2 = 28. Write 2. Remainder = 0.

Answer: 312

Check: 312 x 14 = 4,368. Correct!

BODMAS: The Order of Operations

BODMAS tells you the order in which to carry out operations in a calculation:

Letter	Stands For	Meaning
B	Brackets	Do brackets first
O	Orders	Powers and roots (e.g. squared, cubed)
D	Division	Do division and multiplication...
M	Multiplication	...from left to right (equal priority)
A	Addition	Do addition and subtraction...
S	Subtraction	...from left to right (equal priority)

Important: Division and multiplication have equal priority — work left to right. The same applies to addition and subtraction.

Worked Examples