Which number property shows that the two sides of the equation are equal?

841 + 841(37) + 841(623) = 841 + 841(37 + 623)

The one that says that

a (b + c) = ab + ac

http://math.about.com/od/algebra/a/distributive.htm

The number property that shows that the two sides of the equation are equal in this case is the distributive property.

To demonstrate this, let's simplify the equation on both sides using the distributive property:

Left side: 841 + 841(37) + 841(623)
= 841 + 841 * 37 + 841 * 623

Right side: 841 + 841(37 + 623)
= 841 + 841 * 660

Now, we can see that both sides have the same expressions:

841 + 841 * 37 + 841 * 623 = 841 + 841 * 660

Therefore, the distributive property confirms that the two sides of the equation are equal.

The property that shows that the two sides of the equation are equal in this case is called the Distributive Property.

To understand this, let's break down the equation step by step.

The left side of the equation is:

841 + 841(37) + 841(623)

In this expression, we have 841 multiplied by 37, and 841 multiplied by 623.

The Distributive Property states that when we multiply a number by a sum of two or more numbers, we can multiply the number by each of the individual numbers and then add the products.

So in this case, we can apply the Distributive Property to the left side of the equation as follows:

841 + (841 * 37) + (841 * 623)

Calculating the products:

841 * 37 = 31,117
841 * 623 = 524,843

Now we can substitute the calculated values back into the equation:

841 + 31,117 + 524,843

Summing up the values:

841 + 31,117 = 31,958
31,958 + 524,843 = 556,801

So the left side of the equation simplifies to 556,801:

556,801 = 841 + 841(37 + 623)

Now let's look at the right side of the equation:

841 + 841(37 + 623)

The addition inside the parentheses can be simplified:

37 + 623 = 660

Substituting the simplified value back into the equation:

841 + 841(660)

We can use the Distributive Property again:

841 * 660 = 555,660

Substituting the calculated value back into the equation:

841 + 555,660

The sum of 841 and 555,660 also equals 556,801:

841 + 555,660 = 556,801

Therefore, we see that both sides of the equation simplify to the same value, which is 556,801. This demonstrates that the two sides are equal, and the Distributive Property was used to show this equivalence.