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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.
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:
Answer: 7,412
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:
Answer: 3,455. Check: 3,455 + 1,847 = 5,302. ✓
There are two main methods for multiplying larger numbers. Both give the same answer — choose the one you find most reliable.
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.
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.
| 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.
Used when dividing by a single-digit number.
Example: 7,856 ÷ 4
1 9 6 4
--------
4 | 7 8 5 6
Answer: 1,964
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 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.
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