8 times the product of 5 and t
The Correct Answer and Explanation is:
The phrase “8 times the product of 5 and t” refers to a mathematical expression that involves multiplication. To break this down, we need to understand each part of the phrase and how to interpret it.
- Product of 5 and t: The word “product” refers to the result of multiplying two numbers. In this case, the two numbers being multiplied are 5 and the variable t. So, the product of 5 and t is expressed mathematically as: 5×t=5t5 \times t = 5t5×t=5t Here, t is a variable, which means it can represent any number. So the product of 5 and t is just 5t.
- 8 times: The phrase “8 times” means multiplying whatever comes after by 8. This part of the expression tells us that we need to multiply the product of 5 and t (which we found to be 5t) by 8. Mathematically, this looks like: 8×(5t)8 \times (5t)8×(5t) When we multiply 8 by 5t, we apply the distributive property of multiplication, which states that we can multiply 8 by both the 5 and the t individually. So the expression becomes: 8×5×t=40t8 \times 5 \times t = 40t8×5×t=40t This means that “8 times the product of 5 and t” simplifies to the expression 40t.
Explanation
To sum up, “8 times the product of 5 and t” means we first find the product of 5 and t, which is 5t. Then we multiply that result by 8, giving us the final expression 40t. This is an example of applying basic multiplication and the distributive property to simplify a word problem into a straightforward algebraic expression. In essence, the problem is asking you to perform two steps of multiplication in sequence: first multiply 5 by t, and then multiply the result by 8.
