Let's say we have the expression \(2 \times (40 + 10)\).
What We normally do:
(i) First add inside the bracket: \(40 + 10 = 50\)
(ii) Then, multiply: \(2 \times 50 = 100\)
Now, what if we don't use the bracket?
Do this instead:
\(2 \times 40 + 2 \times 10 = 80 + 20 = 100\)
The answer is same.
Let's try with subtraction:
Take the expression \(3 \times (50 - 20)\)
(i) First, do the subtraction inside the bracket: \(50 - 20 = 30\)
(ii) Then, multiply: \(3 \times 30 = 90\)
Now, split it: \(3 \times 50 - 3 \times 20 = 150 - 60 = 90\)
The answer is same.
Thus,
If there's a number outside the bracket, you can multiply it with each number inside, and then add or subtract. This is called distributive property.
Sometimes, multiplying big numbers directly can feel hard. But what if we change one of the numbers to make it easier? We break it into simpler parts and then solve!
Example:
Expression: \(96 \times 25\)
\(96\) is closer to \(100\). So, we can write:
\(96 \times 25 = (100 - 4) \times 25\)
\(= 100 \times 25 - 4 \times 25\)
\(= 2500 - 100\)
\(= 2400\)
We are Tinkering (Changing) the Number!
\((a + b) \times c = a \times c + b \times c\)
\((a - b) \times c = a \times c - b \times c\)