Definition of
more ...
To calculate the value of.
Example: Evaluate the cost of each pie when 3 pies cost $6.
Answer: $2 each.
Example: Evaluate x2 + 5
when x = 3
Answer: 32 + 5 = 9 + 5 = 14
Introduction to Algebra
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The ideas of equality, expressions, and evaluation are vital concepts when working with equations.An equation is a mathematical statement that tells you that two things have the same value — in other words, it’s a statement with an equal sign. The equation is one of the most important concepts in
mathematics because it allows you to boil down a bunch of complicated information into a single number. Mathematic equations come in lots of varieties, with the two most common being arithmetic and algebraic equations. The three properties of equality are called reflexivity, symmetry, and transitivity: Reflexivity says that everything is equal to itself. For example, 1 = 1 23 = 23 1,000,007 = 1,000,007 Symmetry says that you can switch around the order in which things are equal. For example, 4 · 5 = 20, so 20 = 4 · 5 Transitivity says that if something is equal to two other things, then those two other things are equal to each other. For example, 3 + 1 = 4 and 4 = 2 · 2, so 3 + 1 = 2 · 2 Because equality has all three of these properties, mathematicians call equality an equivalence relation. Here are a few examples of simple
arithmetic equations: 2 + 2 = 4 3 · 4 = 12 20 ÷ 2 = 10 And here are a few examples of more-complicated arithmetic equations: 1,000 – 1 – 1 – 1 = 997 (1 · 1) + (2 · 2) = 5Three properties of equality
What is an expression?
An expression is any string of mathematical symbols that can be placed on one side of an equation. Here are a few examples of simple expressions:
2 + 2
–17 + (–1)
14 ÷ 7
And here are a few examples of more-complicated expressions:
(88 – 23) ÷ 13
100 + 2 – 3 · 17
How to evaluate expressions
At the root of the word evaluation is the word value. In other words, when you evaluate something, you find its value. Evaluating an expression is also referred to as simplifying, solving, or finding the value of an expression. The words may change, but the idea is the same — boiling a string of numbers and math symbols down to a single number.
When you evaluate an arithmetic expression, you simplify it to a single numerical value — that is, you find the number that it’s equal to. For example, evaluate the following arithmetic expression:
7 · 5
How? Simplify it to a single number:
35
How do you connect equality, expressions, and evaluation?
The Three E’s — equality, expressions, and evaluation — are all connected. Evaluation allows you to take an expression containing more than one number and reduce it down to a single number. Then, you can make an equation, using an equal sign to connect the expression and the number. For example, here’s an expression containing four numbers:
1 + 2 + 3 + 4
When you evaluate it, you reduce it down to a single number:
10
And now, you can make an equation by connecting the expression and the number with an equal sign:
1 + 2 + 3 + 4 = 10
About This Article
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- Pre-Algebra ,
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Evaluating an algebraic expression means to calculate the expression given a certain variable. Sometimes a problem will ask you to do this; most of the time, however, you will want to evaluate an expression to check your own algebra work. As long as you understand the basic terms and rules of algebra, evaluating an expression is a simple process.
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Identify the parts of an algebraic expression. An algebraic expression is a set of numbers and letters combined by mathematical operations, such as addition, subtraction, division, and multiplication. The numbers in the expression are called constants or coefficients, depending on their function. The letters are called variables.[1]
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Understand what a variable is. A variable is a letter that represents any number. Therefore, variables are often used to represent unknown numbers. [2] In algebra, you are usually trying to find the value of the variable. In order to evaluate an algebraic expression, however, you need to be given the variable’s value.
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Determine how to evaluate the expression. Evaluate means to simplify an expression. When you are asked to evaluate an algebraic expression, you need to plug a given value for the variable into the expression and solve.[3]
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Identify the variable and its value. This information should be given to you. Usually you will be told to evaluate the expression "when" or "where" the variable is equal to a certain value. If you are not given the variable’s value, you cannot evaluate the expression.
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Substitute the given value for the variable. To do this, plug the given value into the expression wherever you see the variable. If the variable has a coefficient (a number you need to multiply its value by), make sure to put the value in parentheses.
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Complete the necessary calculations. Remember to follow the order of operations when solving an expression. When you complete your calculations rewrite the expression as an equation.
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Evaluate an expression with Two Variables. To do this, follow the same steps as you do for evaluating an expression with one variable, except plug in the values for both variables into the equation. These values should be given.
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Evaluate the following expression when : .
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Evaluate the following polynomial when : .
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Question
How do I evaluate 10 and -7 ?
10 + (-7) = 10 - 7 = 3.
Question
If x can have only values -3, 0, and 2, and y can have only the values -4, 2, and 3, what is the greatest possible value for 2x + y^2?
Use 2, the highest positive value of x, and -4, the highest absolute value of y (because it's squared), and evaluate the expression.
Question
How do I write the sum of a, b and c?
a + b + c.
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