One movie ticket costs 7 dollars, and one small bag of...

Name: Problem 27, Chapter 3: Prealgebra
Uploaded: 2020-05-18T17:38:55-08:00
Duration: 48 s
Channel: Brittany Scott
Description: One movie ticket costs 7 dollars, and one small bag of popcorn costs 3 dollars. Write two equivalent expressions for the total cost of four movie tickets and four bags of popcorn. Then find the cost.

One movie ticket costs 7 dollars, and one small bag of popcorn costs 3 dollars. Write two equivalent expressions for the total cost of four movie tickets and four bags of popcorn. Then find the cost.

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Key Concepts

Multiplication as Repeated Addition

This concept explains that multiplying a number by a given count is equivalent to adding that number repeatedly. It is fundamental in situations where a constant cost is incurred multiple times, allowing one to succinctly represent repeated additions as multiplications.

Distributive Property

The distributive property allows one to multiply a sum by a number by multiplying each addend individually and then summing the results. It is used to simplify expressions and demonstrate equivalent forms of an algebraic expression, which is especially useful when dealing with grouped items and their costs.

Equivalent Algebraic Expressions

This concept involves recognizing that different algebraic expressions can represent the same quantity or value. By applying properties like the distributive property, one can rewrite an expression in multiple equivalent forms, which is a key skill in algebra for simplifying problems and verifying solutions.

Linear Combination

A linear combination involves summing multiples of constants, which is common when calculating total costs or sums in real-life scenarios. It provides a structured method for combining different quantities, each scaled by a constant factor, to arrive at a total sum.

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