Which expression will follow the distributive property?

600 \div (20 + 5)

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(800 + 25) \div 25

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Solution

The correct option is B $(800 + 25) \div 25$
Let's discuss both the options one by one:

a.) $600 \div (20 + 5) = 600 \div 25 = 24$ as depicted in figure below,

Applying distributive property,
$600 \div (20 + 5) = 600 \div 20 + 600 \div 5$ ,

$600 \div 20 = 30$ as depicted figure below,

and $600 \div 5 = 120$ , as depicted in below figure

$∴$ $600 \div 20 + 600 \div 5$
$= 30 + 120 = 150$ but $600 \div 25 = 24$
$⟹ 600 \div (20 + 5) \neq 600 \div 20 + 600 \div 5$
Therefore, this expression: $600 \div (20 + 5)$ , will not follow distributive property.

b.) $(800 + 25) \div 25$
$= 825 \div 25 = 33$ as depicted in figure below,

Now, applying distributive property,
$(800 + 25) \div 25 = 800 \div 25 + 25 \div 25$
$800 \div 25 = 32$ , as depicted in figure below,

and $25 \div 25 = 1,$ as depicted in figure below,

$∴ 800 \div 25 + 25 \div 25 = 32 + 1 = 33$ ,
and $825 \div 25 = 33$ also.
$⟹ (800 + 25) \div 25 = 800 \div 25 + 25 \div 25$ ,

Therefore, expression $(800 + 25) \div 25$ , follows distributive property. (b) is the correct option.

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