Multiply three or more numbers: word problems

Learning Objectives Identify scenarios in word problems that require multiplying three or more integers. Translate word problems into numerical expressions involving the multiplication of multiple integers. Apply the rules for determining the sign of a product when multiplying three or more positive and negative integers. Solve multi-step word problems that involve multiplying three or more integers. Interpret the product of multiple integers within the context of a given word problem. Check the reasonableness of their solutions to word problems involving integer multiplication. Ever wondered how many total items you'd have if you packed several boxes, each with multiple layers of items? 📦 Or how a company's total profit changes over time? Let's find out! In...

TermDefinitionExample IntegerA whole number (not a fraction or decimal) that can be positive, negative, or zero. Examples include -3, 0, 5.In a problem about temperature change, -5 degrees Celsius is an integer representing a drop in temperature. ProductThe result obtained when two or more numbers are multiplied together.The product of 2, 3, and 4 is 24 ($2 imes 3 imes 4 = 24$). FactorA number that is multiplied by another number to get a product.In the expression $5 imes (-2) imes 3$, the numbers 5, -2, and 3 are factors. Word ProblemA mathematical problem presented in a narrative or descriptive form, requiring translation into numerical operations to find a solution.If a factory produces 3 batches of toys, with 10 toys per batch, and each toy uses 2 units of plastic, how many units...

Rule for Determining the Sign of a Product with Multiple Integers When multiplying three or more integers: 1. Count the number of negative factors. 2. If the count of negative factors is even, the product is positive. 3. If the count of negative factors is odd, the product is negative. 4. Then, multiply the absolute values of all factors. This rule helps you quickly determine if your final answer will be positive or negative before performing the full multiplication. For example, $(-2) imes 3 imes (-4)$ has two negative factors (an even number), so the product will be positive. Associative Property of Multiplication $(a \times b) \times c = a \times (b \times c)$ This property allows you to group factors in any way when multiplying three or more numbers without changin...