Question

Say true or false
The distributive property can work if there is multiplication or division inside the parentheses
A). True
B). False

Answer 1

Hint: The distributive property of multiplication is a very useful property that lets us simplify expressions in which you are multiplying a number by a sum or difference. But in the statement, it was asking whether the distributive property can work if there is multiplication or division inside the parentheses. But it cannot work, the distributive works only for when there is an addition or subtraction inside the parentheses.

Complete step-by-step answer:
The distributive property tells us how to solve expressions in the form of $a\left( {b+c} \right)$. The distributive property is sometimes called the distributive law of multiplication and division.
Normally when we see an expression like
$4\left( {8 + 3} \right)$
We just evaluate what’s in the parentheses first and then solve it:
$4(8 + 3) \Rightarrow 4(11) \Rightarrow 44$
The above example is for order of operations rule
With the distributive property, we multiply the 4 first:
$4(8 + 3) \Rightarrow 4.8 + 4.3$
We distribute the 4 to the 8, then to the 3.
Then we need to multiply first, before doing the addition.
$4.8 + 4.3 \Rightarrow 32 + 12 = 44$
If there is multiplication or division inside the parentheses, distribution property cannot work
For example $a\left( {b \times c} \right) \ne \left( {ab \times ac} \right)$
Or $a\left( {b \div c} \right) \ne ab \div ac$
For real numbers, $4(8 \times 3) \ne 4.8 \times 4.3$
Here in the above expression, the value given in the left hand side is less than and not equal to the value on the right hand side.
Therefore, the distributive works only for when there is an addition or subtraction inside the parentheses but not when there is a multiplication or division inside the parentheses.

Note: We usually use the distributive property because the two terms inside the parentheses can’t be added because they’re not like terms. Make sure you apply the outside number to all of the terms inside the parentheses or brackets.