Question

Use the Distributive Property to find each missing factor.6 x 8 = ( 4 x ____) + ( 2 x 8 )10 x 3 = (___ x 3 ) + ( 2 x 3 )(___ X 7 ) = ( 3 x 7 ) + ( 2 x ___)( 8 X ___) = (___ x 8 ) + ( 4 X 8 )3rd grade subject Distributive property

Answer 1

The question is given below as

`6*8=(4*\ldots)+(2*8)`

The distributive property of multiplication states that when a number is multiplied by the sum of two numbers, the first number can be distributed to both of those numbers and multiplied by each of them separately, then adding the two products together for the same result as multiplying the first number by the sum.

`a(b+c)=a* b+a* c`

Let the missing factor in the question be x

`\begin{gathered} 6*8=(4*\ldots)+(2*8) \\ 6*8=(4* x)+(2*8) \end{gathered}`

By multiplying,

We will have

`\begin{gathered} 6*8=(4* x)+(2*8) \\ 48=4x+16 \end{gathered}`

Collect like terms,by subtracting 16 from both sides

`\begin{gathered} 48=4x+16 \\ 48-16=4x+16-16 \\ 32=4x \end{gathered}`

Divide both sides by 4

`\begin{gathered} 4x=32 \\ (4x)/(4)=(32)/(4) \\ x=8 \end{gathered}`

Hence,

`\begin{gathered} 6*8=(4*8)+(2*8) \\ 6*8=8(4+2) \\ 6*8=6*8 \end{gathered}`

Therefore,

The missing factor = 8