Apply the distributive property, then simplify:
[tex]6\left(\frac{2}{3}+\frac{1}{6}\right)=[/tex]
Answer (2)
Apply the distributive property: 6 ( 3 2 + 6 1 ) = 6 ( 3 2 ) + 6 ( 6 1 ) .
Simplify each term: 6 ( 3 2 ) = 4 and 6 ( 6 1 ) = 1 .
Add the simplified terms: 4 + 1 = 5 .
The simplified expression is 5 .
Explanation
Understanding the problem We are asked to apply the distributive property and simplify the expression 6\[\left(\frac{2}{3}+\frac{1}{6}\right)\] . The distributive property states that a ( b + c ) = ab + a c . We will apply this property and then simplify the resulting expression.
Applying the distributive property First, we apply the distributive property: 6 ( 3 2 + 6 1 ) = 6 ( 3 2 ) + 6 ( 6 1 ) .
Simplifying each term Next, we simplify each term. 6 ( 3 2 ) = 3 6 × 2 = 3 12 = 4 and 6 ( 6 1 ) = 6 6 × 1 = 6 6 = 1 .
Adding the simplified terms Finally, we add the simplified terms: 4 + 1 = 5 . Therefore, the simplified expression is 5.
Final Answer The result of applying the distributive property and simplifying the expression is 5.
Examples
The distributive property is useful in everyday situations. For example, if you are buying 6 items that each cost 3 2 of a dollar and also 6 1 of a dollar in tax, you can calculate the total cost by multiplying 6 by the sum of the cost and tax. This is the same as calculating the cost of the items and the tax separately and then adding them together. In this case, the total cost would be 6 × ( 3 2 + 6 1 ) = 6 × 3 2 + 6 × 6 1 = 4 + 1 = 5 dollars.
By applying the distributive property, we can simplify the expression 6 ( 3 2 + 6 1 ) to yield a final answer of 5 . This involves calculating each term separately before adding them together. The process illustrates how to effectively use the distributive property in mathematics.
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