Use the distributive property to solve the following:
(a) [tex]$650 \times 267$[/tex]
(b) [tex]$7,634 \times 123-7,634 \times 3$[/tex]
(c) [tex]$456 \times 230$[/tex]
(d) [tex]$625 \times 3+2 \times 25 \times 18$[/tex]
(e) [tex]$34,645 \times 309-34,645 \times 9$[/tex]

Apply the distributive property to expand the expressions.
Calculate each term in the expanded expressions.
Sum the terms to find the final result for each problem.
The solutions are: (a) 173550 , (b) 916080 , (c) 104880 , (d) 2775 , (e) 10393500 .

Explanation

Understanding the Distributive Property We will use the distributive property to solve the given arithmetic problems. The distributive property states that a × ( b + c ) = a × b + a × c . We will apply this property to simplify each expression and find the final result.

Solving (a) (a) 650 × 267 = 650 × ( 200 + 60 + 7 ) = 650 × 200 + 650 × 60 + 650 × 7 . Now, we calculate each term: 650 × 200 = 130000 650 × 60 = 39000 650 × 7 = 4550 Adding these up: 130000 + 39000 + 4550 = 173550 .

Solving (b) (b) 7 , 634 × 123 − 7 , 634 × 3 = 7 , 634 × ( 123 − 3 ) = 7 , 634 × 120 . Now, we calculate the final product: 7 , 634 × 120 = 916080 .

Solving (c) (c) 456 × 230 = 456 × ( 200 + 30 ) = 456 × 200 + 456 × 30 . Now, we calculate each term: 456 × 200 = 91200 456 × 30 = 13680 Adding these up: 91200 + 13680 = 104880 .

Solving (d) (d) 625 × 3 + 2 × 25 × 18 = 625 × 3 + 50 × 18 = 625 × 3 + 50 × ( 20 − 2 ) = 625 × 3 + 50 × 20 − 50 × 2 = 625 × 3 + 1000 − 100 . Now, we calculate each term: 625 × 3 = 1875 50 × 20 = 1000 50 × 2 = 100 So, 1875 + 1000 − 100 = 2875 − 100 = 2775 .

Solving (e) (e) 34 , 645 × 309 − 34 , 645 × 9 = 34 , 645 × ( 309 − 9 ) = 34 , 645 × 300 . Now, we calculate the final product: 34 , 645 × 300 = 10393500 .

Final Answer Therefore, the solutions are: (a) 650 × 267 = 173550 (b) 7 , 634 × 123 − 7 , 634 × 3 = 916080 (c) 456 × 230 = 104880 (d) 625 × 3 + 2 × 25 × 18 = 2775 (e) 34 , 645 × 309 − 34 , 645 × 9 = 10393500


Examples
The distributive property is a fundamental concept in mathematics that simplifies calculations and is widely used in various real-life scenarios. For example, imagine you're buying multiple items at a store. If you buy 3 shirts for $25 each and 3 pairs of socks for $5 each, you can calculate the total cost using the distributive property: $3 \times (25 + 5) = 3 \times 25 + 3 \times 5 = 75 + 15 = $90. This property helps in quick mental calculations and is crucial in algebra for simplifying expressions and solving equations.

Answered by GinnyAnswer | 2025-07-08

Using the distributive property, we've calculated the results for several expressions, resulting in: (a) 173550, (b) 916080, (c) 104880, (d) 2775, and (e) 10393500.
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Answered by Anonymous | 2025-07-13