Algebra: Writing Expressions, Equations & Inequalities
Email this Mix
Slide 1 - Introduction to Algebra
- Writing Expressions, Equations & Inequalities
Slide 2 - What is algebra?
- Al · ge · bra
- (noun) the part of mathematics in which letters and other general symbols are used to represent numbers and quantities.
Slide 3 - Vocabulary
Slide 4 - Variables & Constants
- Variables: a quantity that could change (or vary) during the calculations. In this class, a variable can be represented by any lower case letter (but it’s best to avoid o and l)
- Constant: a quantity that will not change (is constant) during the calculations. This shows up as a number.
Slide 5 - Coefficients & Operators
- Coefficients: constants that come before a variable. They tell us how many of that variable are present. For example “four x’s” is written 4x
- Operators: mathematical symbols that represent operations to be performed (adding, subtracting, etc.)
Slide 6 - Expressions & Equations
- Expressions and equations are like mathematical sentences.
- An expression has no equals sign, but an equation does…
- For example:
- “Four of a number added to 10”
- 4n + 10 this is an expression
- Another example:
- “Four of a number added to 10 is 30”
- 4n + 10 = 30 this is an equation
- Notice that “a number” is shown as a variable in the examples. We don’t know what that number is yet, so we write is as a variable. When we read an expression or equation, we say “a number” outloud.
Slide 7 - Equations & Inequalities
- An equation has an equal sign. An inequality has an inequality sign.
- ≥ “greater than or equal to”
- > “greater than” (but not equal to)
- ≠ “not equal to”
- < “less than” (but not equal to)
- ≤ “less than or equal to”
- Read from left to right:
- “a number is greater than five”
- Notice that the larger part of the sign points to the larger amount (or “the alligator eats the bigger meal”)
Slide 9 - Evaluating Expressions
- When we are given an expression and a solution, we can evaluate that expression for the given solution.
Slide 11 - Mentally Solving Equations
- Equations can be solved mentally use “try, check, revise”.
- Step 1. Read aloud: “12 minus a number is 10”
- Step 2. Estimate a solution and try it: “Two? 12 minus 2 is 10” CHECK!
Slide 13 - Mentally Solving Inequalities
- Inequalities can also be solved mentally use “try, check, revise”.
- Step 1. Read aloud: “A number is less than 20”
- Step 2. Estimate a solution and try it: “Fifteen? 15 is less than 20?” CHECK!