Distributive Property Calculator
How to use the ‘Distributive Property Calculator’?
Follow these steps to use the distributive property calculator:
Step 1: Toggle and select the option of your choice as ‘Two Numbers’ or ‘Three Numbers’ to calculate the result.
Step 2: Enter the numbers into the respective input boxes.
Step 3: Click on the ‘Solve’ button to obtain the answer.
Step 4: Click on the ‘Show Steps’ button to understand the stepwise procedure to find the final result.
Step 5: Click on the refresh button to enter new inputs and start again.
Step 6: Click on the ‘Example’ button to play with random input values and obtain results.
Step 7: Click on the ‘Explore’ button to select a number of your choice and visualize the result.
Step 8: When on the ‘Explore’ page, click the ‘Calculate’ button to go back to the calculator.
What is the Distributive Property?
The distributive property states that multiplying two or more addends by a number produces the same result as distributing the multiplier, multiplying each addend separately and adding the product. The same holds true when we are subtracting numbers instead of adding them.
How can we solve problems based on the distributive property?
The steps to solve problems based on the distributive property are:
Step 1: Multiply (distribute) the number or algebraic term that is outside the parentheses by both the terms or numbers inside the parentheses. Keep in mind that the sign inside the parentheses will change according to the multiplication operation.
Step 2: Group the like terms and simplify.
Solved Examples:
Example 1: Solve the given algebraic expression 6(x + 2) using the distributive property.
Solution:
\(6\left( x\text{ }+\text{ }2 \right)\)
\(\Rightarrow \left( 6 \times x \right)+ \left( 6 \times 2 \right)\)
\(\Rightarrow 6x + 12\)
Hence, \(6\left( x + 2 \right) = 6x + 12\)
Example 2: Find the value of the algebraic expression \(-4 \left( 3x^{2} +y+2\right)\) using the distributive property.
Solution:
\(-4 \left( 3x^{2} +y+2\right)\)
\(\Rightarrow \left( -4 \times 3x^{2} \right) + \left( -4 \right)\times y +\left( -4 \right)\times 2\)
\(\Rightarrow – 12x^{2} \text{ }- \text{ }4y -8\)
Hence, \(-4 \left( 3x^{2} + y+2\right)=\text{ }-\text{ }12x^{2}-4y-8\)
Example 3: Simplify the algebraic expression \(\frac{1}{5}\text{ }\left( 10 + 5p+1 \right) \)using the distributive property.
Solution:
\(\frac{1}{5}\text{ }\left( 10 + 5p+1 \right)\)
\(\Rightarrow \frac{1}{5}\times 10 + \frac{1}{5} \times 5p + \frac{1}{5}\times 1 \)
\(\Rightarrow 2 + p + \frac{1}{5}\)
\(\Rightarrow p + \frac{11}{5}\)
So, \(\frac{1}{5}\left( 10+5p+1 \right)= p + \frac{11}{5}\)
Example 4: Evaluate \(0.25x\left( 20x \text{ }-\text{ } 50 \right)\) using the distributive property.
Solution:
\(0.25x\left( 20x \text{ }-\text{ } 50 \right)\)
\(\Rightarrow 0.25x \times 20x + 0.25x \times \left( -50 \right)\)
\(\Rightarrow 5x^{2}-12.5x\)
So, \(0.25x\left( 20x \text{ }- \text{ }50 \right)= 5x^{2}\text{ } – \text{ }12.5x\)
Example 5: Find the value of the algebraic expression \(0.6m\left( 0.5-10z-\frac{1}{2} \right)\) using the distributive property.
Solution:
\(0.6m\left( 0.5-10z-\frac{1}{2} \right)\)
\(\Rightarrow 0.6m \times 0.5 + 0.6m \times \left( -10z \right)+ 0.6m \times \left( -\frac{1}{2} \right)\)
\(\Rightarrow 0.30m \text{ }- 6mz \text{ }- 0.3m\)
\(\Rightarrow -6mz + 0.30m – \text{ }0.30m\)
\(\Rightarrow -6mz\)
Hence, \(0.6m \left( 0.5 \text{ }- \text{ }10z \text{ }- \frac{1}{2} \right)= -6mz\)
The distributive property of multiplication is applied when multiplying an integer by the sum of two or more addends, or the difference between the minuend and the subtrahend. The addition and subtraction of two or more numbers are both associated with the distributive property of multiplication. In order to quickly solve equations, a number is distributed across the integers in the parentheses.
Large numbers are added, subtracted, multiplied, and divided using the distributive property. Being independent of the sequence that large equations are solved, grouping integers allows us to break expressions into smaller chunks. Hence, calculations become quicker and simpler.
The distributive property of multiplication over addition is often known as the distributive property of addition. The formula for this is ‘a(b + c) = ab + ac’.