Use the distributive law to calculate $19 \times 6+19 \times 4$

Apply the distributive law in reverse: 19 × 6 + 19 × 4 = 19 × ( 6 + 4 ) .
Calculate the sum inside the parentheses: 6 + 4 = 10 .
Multiply the result by 19: 19 × 10 = 190 .
The final answer is: 190 ​ .

Explanation

Understanding the problem We are asked to calculate 19 × 6 + 19 × 4 using the distributive law. The distributive law states that a × ( b + c ) = a × b + a × c . We can also apply it in reverse: a × b + a × c = a × ( b + c ) .

Applying the distributive law In our case, we have 19 × 6 + 19 × 4 . We can identify a = 19 , b = 6 , and c = 4 . Applying the distributive law in reverse, we rewrite the expression as 19 × ( 6 + 4 ) .

Calculating the sum Now, we calculate the sum inside the parentheses: 6 + 4 = 10 .

Final Calculation Finally, we multiply the result by 19: 19 × 10 = 190 . Therefore, 19 × 6 + 19 × 4 = 190 .


Examples
The distributive law is useful in everyday situations. For example, suppose you want to buy 6 apples at $1.99 each and 4 bananas at $1.99 each. Instead of calculating the cost of the apples and bananas separately and then adding them, you can use the distributive law to find the total cost more easily: $1.99 \times 6 + 1.99 \times 4 = 1.99 \times (6+4) = 1.99 \times 10 = $19.90. This simplifies the calculation, especially when dealing with larger numbers or more items.

Answered by GinnyAnswer | 2025-07-08

Using the distributive law, we can simplify 19 × 6 + 19 × 4 to 19 × ( 6 + 4 ) . After calculating the sum inside the parentheses, we find it equals 10, so 19 × 10 = 190 . Ultimately, the answer is 190.
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Answered by Anonymous | 2025-07-13