Use the Distributive Property to find the missing factors.
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6 × = 3 × 7 + ( × 7)
6*7 = 3*7 + 3*7
To find the missing factors using the Distributive Property, we need to distribute the 3 to both terms inside the parentheses.
6 × ____ = 3 × 7 + (____ × 7)
The distributed expression becomes:
6 × ____ = 21 + (____ × 7)
Now, we need to find the missing factors that will make the equation true.
To find the missing factor on the left side of the equation, we can divide both sides by 6. This gives us:
____ = (21 + (____ × 7)) ÷ 6
Now let's solve for the missing factor on the right side of the equation. We can subtract 21 from both sides:
____ - 21 = (____ × 7) ÷ 6
Now we can divide both sides by 7 to find the value of the missing factor:
(____ - 21) ÷ 7 = ____
So, the missing factor on the left side of the equation is (21 + (____ × 7)) ÷ 6, and the missing factor on the right side of the equation is (____ - 21) ÷ 7.
To solve this problem using the Distributive Property, we need to consider how multiplication distributes over addition.
The Distributive Property states that for any 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.
So, let's fill in the missing factors step by step:
6 × ( ) = 3 × 7 + ( × 7)
The first term on the right side of the equation is 3 × 7, which equals 21.
So, we have:
6 × ( ) = 21 + ( × 7)
Now let's say the missing factor we are trying to find is represented by the letter "x".
We can rewrite the equation as:
6 × x = 21 + (x × 7)
To simplify further, we can distribute the x in the second term on the right side:
6 × x = 21 + 7x
Now we can solve for x by isolating it on one side of the equation:
6x - 7x = 21
Combining like terms:
-1x = 21
Simplifying:
x = -21
So, the missing factor is -21.
Therefore, the complete equation is:
6 × (-21) = 3 × 7 + (-21 × 7)