Number System & Simplification • Topic 5 of 6

BODMAS & Simplification

Simplification tests order of operations: BODMAS — Brackets, Of/Orders (powers), Division, Multiplication, Addition, Subtraction. Work brackets inside-out, convert 'of' to multiplication, then divide and multiply left to right, finally add and subtract. With fractions, convert mixed numbers to improper fractions first, and cancel common factors before multiplying to keep numbers small.

✅ Solved examples

1. Simplify 12 + 6 / 2 x 3.
Division and multiplication left to right: 6/2 = 3, 3 x 3 = 9, then 12 + 9 = 21.
2. Simplify 1/2 of 60 + 25% of 80.
1/2 of 60 = 30; 25% of 80 = 20; total 50.
3. Simplify (15 - 3 x 4) + 8 / 4.
Brackets: 3 x 4 = 12, 15 - 12 = 3. Then 8/4 = 2. Total 3 + 2 = 5.
4. Simplify 2 + 1/2 + 3/4 as a single number.
LCD 4: 8/4 + 2/4 + 3/4 = 13/4 = 3.25.

✏️ Practice — try these, take hints as needed

1. Simplify 20 - 4 x 3 + 6 / 2.
Multiply/divide first.
12 and 3.
20 - 12 + 3.
11
2. Simplify 1/3 of 90 - 10% of 50.
1/3 of 90 = 30.
10% of 50 = 5.
Subtract.
25
3. Simplify (8 + 2) x 3 - 4.
Brackets first = 10.
10 x 3.
Minus 4.
26
4. Simplify 5/6 - 1/3 + 1/2.
LCD 6.
5/6 - 2/6 + 3/6.
Add numerators.
1
5. Simplify 36 / 6 / 3 x 2.
Left to right.
36/6 = 6, 6/3 = 2.
2 x 2.
4

📝 Topic test — 8 questions

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