Distributing A Negative Calculator

Distributing a negative number in algebra involves applying the negative sign to each term inside parentheses. This fundamental operation is essential for simplifying expressions and solving equations. Our calculator simplifies this process with clear step-by-step results.

What is distributing negatives?

Distributing a negative number is a process in algebra where the negative sign is multiplied by each term inside parentheses. This operation is based on the distributive property of multiplication over addition, which states that a(b + c) = ab + ac.

When dealing with negative numbers, the negative sign is distributed to each term inside the parentheses, changing the sign of each term. For example, -2(3 + 4) becomes -2×3 + (-2×4) = -6 - 8 = -14.

Distributive Property Formula

a(b + c) = ab + ac

When a is negative: -a(b + c) = -ab - ac

The process of distributing negatives is crucial in simplifying algebraic expressions, solving equations, and working with polynomials. It helps to eliminate parentheses and make expressions easier to work with.

How to distribute negatives

To distribute a negative number, follow these steps:

Identify the negative number outside the parentheses.
Multiply this negative number by each term inside the parentheses.
Apply the correct sign to each resulting term.
Combine the terms to simplify the expression.

Key Rule

Remember that a negative times a positive is negative, and a negative times a negative is positive.

Let's look at an example to illustrate this process.

Examples

Here are some examples of distributing negative numbers:

Example 1

Expression: -3(2 + 5)

Step 1: Distribute -3 to each term inside the parentheses.

Step 2: -3 × 2 = -6 and -3 × 5 = -15

Result: -6 - 15 = -21

Example 2

Expression: -2(x - 4)

Step 1: Distribute -2 to each term inside the parentheses.

Step 2: -2 × x = -2x and -2 × -4 = 8

Result: -2x + 8

Example 3

Expression: -5(3y - 2y + 7)

Step 1: Distribute -5 to each term inside the parentheses.

Step 2: -5 × 3y = -15y, -5 × -2y = 10y, and -5 × 7 = -35

Result: -15y + 10y - 35 = -5y - 35

Common mistakes

When distributing negative numbers, it's easy to make a few common mistakes:

Forgetting to distribute the negative sign to each term inside the parentheses.
Incorrectly changing the sign of terms, especially when dealing with negative coefficients.
Not simplifying the expression after distribution, leading to incorrect results.

Tip

Double-check each step to ensure the negative sign is correctly applied to every term inside the parentheses.

By being mindful of these common mistakes, you can avoid errors and ensure accurate results when distributing negative numbers.

FAQ

What is the rule for distributing a negative number?

The rule for distributing a negative number is to multiply the negative number by each term inside the parentheses, changing the sign of each term accordingly.

How do you distribute a negative number with variables?

When distributing a negative number with variables, multiply the negative number by each variable term inside the parentheses, applying the correct sign to each variable.

What happens when you distribute a negative number to a negative term?

When you distribute a negative number to a negative term, the result is positive because a negative times a negative is positive.

Can you distribute a negative number to a fraction?

Yes, you can distribute a negative number to a fraction. Multiply the negative number by the numerator and denominator of the fraction, applying the correct sign.

How do you distribute a negative number in an equation?

To distribute a negative number in an equation, multiply the negative number by each term on one side of the equation, simplifying the expression to solve the equation.