The distributive property of multiplication is a fundamental algebraic principle that states you can distribute a multiplication operation over addition or subtraction. In simpler terms, it allows you to multiply a number by a sum or difference by multiplying each addend or subtrahend individually and then summing or subtracting the results.
The formal expression of the distributive property can be written as:
a × (b + c) = (a × b) + (a × c)
Or for subtraction:
a × (b – c) = (a × b) – (a × c)
Here’s an example to illustrate:
- If we take 3 multiplied by the sum of 4 and 5, it can be expressed as: 3 × (4 + 5).
- Using the distributive property, we can distribute 3 to both 4 and 5: (3 × 4) + (3 × 5).
- This simplifies to 12 + 15, which equals 27.
Therefore:
3 × (4 + 5) = 27
Let’s consider a subtraction example:
- If we have 5 multiplied by the difference of 10 and 3, it’s represented as: 5 × (10 – 3).
- Applying the distributive property leads us to distribute 5 to both 10 and -3: (5 × 10) – (5 × 3).
- This results in 50 – 15, which equals 35.
Hence:
5 × (10 – 3) = 35
In summary, the distributive property is a powerful tool that simplifies calculations and helps in solving algebraic expressions more easily. By mastering this property, you can enhance your mathematical skills and improve your problem-solving abilities.