Knowing Our Numbers - Using Brackets

Brackets are used to group numbers and operations together, indicating that the operations inside the brackets must be performed first. For example, in the expression $(10 + 5) \times 2$, we first add $10$ and $5$ to get $15$, then multiply by $2$.

The use of brackets helps in simplifying calculations by breaking down large numbers. For instance, multiplying $102 \times 7$ can be visualized as splitting a large area into two smaller, manageable rectangles: one of $100 \times 7$ and another of $2 \times 7$.

The Distributive Property is the core concept behind using brackets. It allows us to distribute a multiplier to each term inside the bracket, such as $a \times (b + c) = (a \times b) + (a \times c)$.

Brackets help maintain the correct order of operations. When you see an expression like $10 \times (2 + 3)$, the brackets act as a 'priority wall,' ensuring the addition happens before the multiplication, which would otherwise be performed in a different order under standard BODMAS rules.

Expansion of brackets is a process where we remove brackets by multiplying the term outside with every term inside. If we have $(10 + 2) \times (10 + 3)$, we can think of it as distributing the first group over the second, resulting in a sum of four separate products.

Using brackets makes mental math easier. To calculate $9 \times 108$, we can visualize it as $9 \times (100 + 8)$. This transforms one difficult multiplication into two simple ones: $900$ and $72$, which are then summed to find the total.