The phrase \u201c8 times the product of 5 and t\u201d 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.<\/p>\n\n\n\n
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- Product of 5 and t<\/strong>: The word \u201cproduct\u201d refers to the result of multiplying two numbers. In this case, the two numbers being multiplied are 5 and the variable t<\/strong>. So, the product of 5 and t is expressed mathematically as: 5\u00d7t=5t5 \\times t = 5t5\u00d7t=5t Here, t<\/strong> is a variable, which means it can represent any number. So the product of 5 and t is just 5t<\/strong>.<\/li>\n\n\n\n
- 8 times<\/strong>: The phrase \u201c8 times\u201d 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<\/strong>) by 8. Mathematically, this looks like: 8\u00d7(5t)8 \\times (5t)8\u00d7(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\u00d75\u00d7t=40t8 \\times 5 \\times t = 40t8\u00d75\u00d7t=40t This means that \u201c8 times the product of 5 and t\u201d simplifies to the expression 40t<\/strong>.<\/li>\n<\/ol>\n\n\n\n
Explanation<\/h3>\n\n\n\n
To sum up, \u201c8 times the product of 5 and t\u201d means we first find the product of 5 and t, which is 5t<\/strong>. Then we multiply that result by 8, giving us the final expression 40t<\/strong>. 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.<\/p>\n\n\n\n
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- 8 times<\/strong>: The phrase \u201c8 times\u201d 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<\/strong>) by 8. Mathematically, this looks like: 8\u00d7(5t)8 \\times (5t)8\u00d7(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\u00d75\u00d7t=40t8 \\times 5 \\times t = 40t8\u00d75\u00d7t=40t This means that \u201c8 times the product of 5 and t\u201d simplifies to the expression 40t<\/strong>.<\/li>\n<\/ol>\n\n\n\n