What is the sum of:   3/4(8p+12)+ 3/8(16p-8)

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To solve for `3/4(8p+12)+ 3/8(16p-8)`

Multiply all the factors in `3/4(8p+12)+ 3/8(16p-8)` .`(3(8p+12))/4 + (3(16p-8))/8` Factor out the GCF of `4` from `8p+12` . `(3(4(2p+3)))/4 + (3(16p-8))/8` Multiply 3 by `4` to get `12` . `((12)(2p+3))/4 + (3(16p-8))/8` Reduce the expression by canceling out all common factors from the numerator ...

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To solve for `3/4(8p+12)+ 3/8(16p-8)`


Multiply all the factors in `3/4(8p+12)+ 3/8(16p-8)` .

`(3(8p+12))/4 + (3(16p-8))/8`


Factor out the GCF of `4` from `8p+12` .

`(3(4(2p+3)))/4 + (3(16p-8))/8`


Multiply 3 by `4` to get `12` .

`((12)(2p+3))/4 + (3(16p-8))/8`


Reduce the expression by canceling out all common factors from the numerator and denominator.

`3(2p+3)+(3(16p-8))/8`


Multiply `3` by each term inside the parentheses.

`6p + 9 + (3(16p-8))/8`


Factor out the GCF of `8` from `16p-8` .

`6p + 9 + (3(8(2p-1)))/8`


Multiply `3` by `8` to get `24` .

`6p + 9 + ((24)(2p-1))/8`


Reduce the expression by canceling out all common factors from the numerator and denominator.

`6p+9+3(2p-1) `

Multiply `3` by each term inside the parentheses.

`6p+9+6p-3`


Combine all similar terms in the polynomial `6p+9+6p-3` .

Therefore, the answer is `12p+6`

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Find the sum of `3/4(8p + 12) + 3/8(16p-8).`

First, distribute the fractions.

`3/4(8p) + 3/4(12) + 3/8(16p) - 3/8(8)`

`6p + 9 + 6p - 3`

Combine like terms.

`12p + 6`

The sum is `12p + 6` .

Approved by eNotes Editorial Team