Question

Answer the following questions using the distributive property. You can state the distributive property of multiplication over algebraically by using variables:

a.(b + c) = (a • b) + (ac)
The distributive property tells you that a(b+c) and (a • b) + (ac) are equivalent algebraic expressions.
1.Use the distributive property to write the following expression in an equivalent form: 3 • (5 + 25).
2.Create an example based on making a purchase at a candy store to model the expression

Answer 1

The expression 3 • (5 + 25) evaluated using the distributive property is equivalent to 90, as shown by the calculations (3 • 5) + (3 • 25), which sum to 90. An example involving a candy store mirrors this calculation, where buying 5 chocolate bars and 25 lollipops at $3 each also totals $90.

Step-by-step explanation:

Using the distributive property of multiplication over addition, the expression 3 • (5 + 25) can be rewritten in its equivalent form by multiplying the number outside the parentheses by each number inside the parentheses separately and then adding the results together.

So, 3 • (5 + 25) becomes (3 • 5) + (3 • 25). Performing the multiplication, we get 15 + 75, which results in the sum 90.

To create an example involving a candy store, consider buying 5 chocolate bars and 25 lollipops, where each item costs $3. Applying the distributive property, the total cost would be 3 • (5 + 25), which we've calculated as $90.