for any whole numbers a,b, and c, a times (b+c) = a times b + a times c
This statement is true. It follows from the distributive property of multiplication over addition. According to this property, for any whole numbers a, b, and c, the product of a and the sum of b and c is equal to the sum of the products of a and b and a and c. In other words:
a * (b + c) = a * b + a * c
This rule can be applied to any whole numbers a, b, and c.
To prove that for any whole numbers a, b, and c, a times (b+c) = a times b + a times c, we can use the distributive property of multiplication. The distributive property states that for any real numbers a, b, and c:
a times (b+c) = a times b + a times c
Now, let's proceed step by step to prove this:
Step 1: Start with the left-hand side of the equation: a times (b+c).
Step 2: Apply the distributive property by multiplying a with each term inside the parentheses: a times b + a times c.
Step 3: We have now arrived at the right-hand side of the equation, which proves that a times (b+c) = a times b + a times c.
Therefore, for any whole numbers a, b, and c, the equation holds true.
Please let me know if anything is unclear or if you have any further questions!
To prove the given statement, let's start with the left side of the equation:
a × (b + c)
Using the distributive property of multiplication over addition, we can expand this expression:
a × b + a × c
Now, we have the right side of the equation:
a × b + a × c
As we can see, the expanded form of the left side expression is identical to the right side expression. Therefore, we have proved that for any whole numbers a, b, and c, a × (b + c) equals a × b + a × c.
This property in mathematics is called the distributive property, and it holds true for any whole numbers. It states that multiplying a number by the sum of two other numbers is the same as multiplying that number by each of the two numbers individually and then adding the results together.