Use the Distributive Property to find the missing factors. Enter your answers in the boxes. 6 ×____ = 3 × 7 + ( ____ × 7) FILL OUT THE BLANKS
6 × 2 = 3 × 7 + (2 × 7)
Jack has an array with 3 rows of 10 to solve a multiplication fact. Which shows how Jack can solve the same fact with two arrays?
choose
Responses 3 rows of 5 and 3 rows of 5
3 rows of 5 and 3 rows of 5
3 rows of 5 and 3 rows of 7
3 rows of 5 and 3 rows of 7
3 rows of 3 and 3 rows of 5
3 rows of 3 and 3 rows of 5
3 rows of 7 and 5 rows of 7
3 rows of 3 and 3 rows of 5
To use the Distributive Property, we can rewrite the equation as:
6 × x = 3 × 7 + (y × 7)
We want to find the missing factors, so let's solve for x and y.
First, we simplify:
6 × x = 21 + 7y
Next, we can use the Distributive Property to distribute the 6 to both terms on the right side of the equation:
6x = 21 + 6 × 7 + 7y
Simplifying further:
6x = 21 + 42 + 7y
Combining like terms:
6x = 63 + 7y
Now, let's isolate the variable x by subtracting 7y from both sides of the equation:
6x - 7y = 63
So, the missing factor in the first blank is x and the missing factor in the second blank is y.
To find the missing factors using the Distributive Property, we need to distribute the 3 to the terms inside the parentheses on the right side of the equation.
We have 6 × ____ = 3 × 7 + (____ × 7)
First, let's distribute the 3 to 7, which gives us:
6 × ____ = 21 + (____ × 7)
Next, let's distribute the 3 to the second term inside the parentheses, which gives us:
6 × ____ = 21 + (____ × 7)
We can simplify the equation to:
6 × ____ = 21 + 7 × ____
Now, to find the missing factors, let's equate the two sides of the equation.
6 × ____ = 21 + 7 × ____
Since the distributive property states that "a × (b + c) = a × b + a × c," we can rewrite the equation as:
6 × ____ = 21 + 7 × ____
6 × ____ = 21 + 7 × ____
Now, we can see that the missing factors are ____ and ____, which can be any value that satisfies the equation.