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Distributing A Negative Number Calculator

Reviewed by Calculator Editorial Team

Distributing a negative number involves applying the distributive property of multiplication over addition or subtraction to negative numbers. This fundamental algebraic operation is essential for simplifying expressions and solving equations. Our calculator provides a quick way to perform these calculations while our guide explains the underlying principles, common pitfalls, and practical applications.

What is distributing negative numbers?

The distributive property states that a(b + c) = ab + ac. When distributing a negative number, the negative sign is applied to each term inside the parentheses. This operation is crucial in algebra, calculus, and many real-world applications.

Distributive Property Formula:

a(b + c) = ab + ac

a(b - c) = ab - ac

For negative numbers, the same rules apply. For example, -3(4 + 2) becomes -3×4 + (-3×2) = -12 - 6 = -18. The negative sign is distributed to each term inside the parentheses.

How to distribute negative numbers

  1. Identify the negative number outside the parentheses.
  2. Multiply this number by each term inside the parentheses.
  3. Apply the negative sign to each product.
  4. Combine the results to get the final expression.

Tip: Remember that multiplying a negative number by another negative number yields a positive result. For example, -2 × -3 = 6.

Examples

Example 1: Simple Distribution

Calculate -4(3 + 2):

  1. -4 × 3 = -12
  2. -4 × 2 = -8
  3. Combine: -12 + (-8) = -20

Example 2: Distribution with Subtraction

Calculate -5(4 - 1):

  1. -5 × 4 = -20
  2. -5 × -1 = 5
  3. Combine: -20 + 5 = -15

Example 3: Complex Expression

Calculate -2(3x + 4y - 5):

  1. -2 × 3x = -6x
  2. -2 × 4y = -8y
  3. -2 × -5 = 10
  4. Combine: -6x - 8y + 10

Common mistakes

  • Forgetting to distribute the negative sign to each term inside the parentheses.
  • Incorrectly applying the negative sign to only one term.
  • Miscounting the number of terms inside the parentheses.
  • Confusing the order of operations (PEMDAS/BODMAS rules).

Remember: Always distribute the negative number to every term inside the parentheses, regardless of whether the terms are positive or negative.

FAQ

Why is distributing negative numbers important?
Distributing negative numbers is fundamental in algebra for simplifying expressions, solving equations, and working with polynomials. It's a key skill for more advanced mathematical concepts.
Can I distribute a negative number to a single term?
Yes, but this is essentially just multiplying the negative number by that term. Distribution becomes more useful when there are multiple terms inside the parentheses.
What happens when I distribute a negative number to a negative term?
The negative signs cancel out, resulting in a positive product. For example, -3 × -2 = 6.