Distribute A Negative Calculator
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Reviewed by Calculator Editorial Team
Distributing a negative value involves applying the distributive property of multiplication over addition (or subtraction) to negative numbers. This calculator helps you understand and perform this operation correctly.
How to Use This Calculator
To use the distribute a negative calculator:
- Enter the negative number you want to distribute in the first field.
- Enter the numbers you want to distribute across in the second field, separated by commas.
- Click "Calculate" to see the result.
- Review the step-by-step breakdown of the calculation.
The calculator will show you the result of distributing the negative number across the other numbers, along with a visual representation of the distribution.
The Formula
When you distribute a negative number across other numbers, you're applying the distributive property of multiplication:
a × (b + c + d) = a × b + a × c + a × d
For negative numbers, the same rule applies:
-a × (b + c + d) = -a × b - a × c - a × d
This means you multiply the negative number by each term inside the parentheses separately, then combine the results.
Worked Examples
Example 1: Simple Distribution
Let's distribute -3 across 2, 4, and 6:
-3 × (2 + 4 + 6) = -3 × 2 + -3 × 4 + -3 × 6
= -6 + -12 + -18
= -36
The result is -36, which is the sum of each term multiplied by -3.
Example 2: Mixed Numbers
Distribute -5 across 1, -2, and 3:
-5 × (1 + -2 + 3) = -5 × 1 + -5 × -2 + -5 × 3
= -5 + 10 + -15
= 0
The result is 0, showing how negative numbers can cancel each other out when distributed.
Frequently Asked Questions
What is the distributive property of multiplication?
The distributive property states that multiplying a number by a group of numbers added together is the same as doing each multiplication separately and then adding the results.
How do you distribute a negative number?
You distribute a negative number by multiplying it by each term inside the parentheses separately, then combining the results. Remember that a negative times a negative is positive.
What happens when you distribute a negative number across positive and negative numbers?
The negative number will change the sign of each term it's multiplied by. Positive terms become negative, and negative terms become positive when distributed.
Can you distribute a negative number across fractions?
Yes, you can distribute a negative number across fractions. The same rules apply: multiply the negative number by each numerator separately, keeping the denominators the same.