Use the distributive law to calculate $19 \times 6+19 \times$
Answer (2)
The problem is incomplete as it has a missing number in the expression.
Assume the missing number is x and rewrite the expression as 19 × 6 + 19 × x .
Apply the distributive law to get 19 × ( 6 + x ) .
The simplified expression is 114 + 19 x , but we cannot find a numerical answer without knowing the value of x .
Explanation
Understanding the Problem We are asked to use the distributive law to calculate an expression of the form 19 × 6 + 19 × … where the second factor in the second term is missing. This makes the problem incomplete as is. The distributive law states that a × ( b + c ) = a × b + a × c . We need to know the missing number to proceed.
Applying the Distributive Law Let's assume the missing number is x . Then the expression becomes 19 × 6 + 19 × x . We can rewrite this using the distributive law as 19 × ( 6 + x ) . Without knowing the value of x , we cannot find a numerical answer. We can only simplify the expression.
Illustrative Examples Let's consider a few possible values for x to illustrate how the distributive law works. If x = 4 , the expression is 19 × 6 + 19 × 4 = 19 × ( 6 + 4 ) = 19 × 10 = 190 . If x = 14 , the expression is 19 × 6 + 19 × 14 = 19 × ( 6 + 14 ) = 19 × 20 = 380 .
Final Expression Since we don't know the value of x , we can only simplify the expression using the distributive law: 19 × 6 + 19 × x = 19 × ( 6 + x ) = 114 + 19 x . The problem is incomplete and requires more information to provide a numerical answer. However, we have successfully applied the distributive law to simplify the expression.
Examples
The distributive law is useful in everyday calculations. For example, if you want to buy 6 apples at $1.99 each and 4 bananas at $1.99 each, you can calculate the total cost as $1.99 \times (6+4) = 1.99 \times 10 = $19.90. This simplifies the calculation by combining the quantities before multiplying by the price.
The distributive law allows us to simplify the expression 19 × 6 + 19 × x as 19 × ( 6 + x ) . We can calculate 19 × 6 to get 114, leading to the expression 114 + 19 x . Without the value of x , we cannot find a specific answer.
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