A mathematical quantity is anything that can be measured or counted. The value of the quantity is its measure or the number of items that are counted. Quantities whose values do not change are called constants. In other situations, the value of a quantity can change. Quantities whose values change or vary are called variable quantities.
Definition | Examples | |
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A variable is a symbol, usually a letter, that represents one or more numbers. | n | x |
A numerical expression is a mathematical phrase that contains numbers and operation symbols. | 3 + 5 |
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An algebraic expression is a mathematical phrase that contains one or more variables. |
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Tables are a convenient way to organize data and discover patterns. They work much like an “input/output” machine: a machine that takes one value as an input, processes it, and gives a value as an output. A process column in the table provides a way to understand what happens to the input values.
Use a pattern to answer each question.
Use a table. Look for a pattern that relates the figure number to the number of toothpicks.
Pattern: Multiply the figure number by 4 to get the number of toothpicks. So, there are 20(4) = 80 toothpicks in the 20th figure.
Use the pattern from part (A). There are 4n toothpicks in the nth figure.
What would the process look like for the nth row?
Multiply the figure number, n, by 4.