Mathematics
Grade 8
15 min
Write variable expressions
Write variable expressions
Tutorial Preview
1
Introduction & Learning Objectives
Learning Objectives
Identify keywords and phrases that indicate mathematical operations.
Define and identify variables, constants, and coefficients in algebraic expressions.
Translate simple verbal phrases into algebraic expressions.
Translate complex verbal phrases involving multiple operations into algebraic expressions, using appropriate grouping symbols.
Differentiate between expressions that require parentheses and those that do not.
Write variable expressions to represent real-world scenarios.
Correctly interpret phrases involving 'less than' and 'subtracted from'.
Ever wonder how mathematicians turn everyday language into powerful equations? 🤯 It all starts with writing variable expressions!
In this lesson, you'll learn how to translate wo...
2
Key Concepts & Vocabulary
TermDefinitionExample
VariableA symbol, usually a letter, that represents an unknown or changing quantity.In the expression $x + 5$, 'x' is the variable.
Algebraic ExpressionA mathematical phrase that contains numbers, variables, and at least one operation symbol, but no equality sign.$3y - 7$ is an algebraic expression.
TermThe parts of an algebraic expression that are separated by addition or subtraction signs.In $2x + 5y - 3$, the terms are $2x$, $5y$, and $3$.
CoefficientThe numerical factor that multiplies a variable in a term.In $4a$, $4$ is the coefficient. In $b$, the coefficient is $1$.
ConstantA term in an algebraic expression that does not contain a variable; its value does not change.In $2x + 9$, $9$ is the constant.
Operation KeywordsWords or phrases that indicate s...
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Core Formulas
Translation Rule for Addition
Keywords like 'sum', 'plus', 'increased by', 'more than', 'total of' translate to addition: $a + b$
When you see these words, place a plus sign between the numbers or variables involved. For 'more than', the order is usually reversed from the verbal phrase (e.g., '5 more than a number' is $n+5$).
Translation Rule for Subtraction
Keywords like 'difference', 'minus', 'decreased by', 'less than', 'subtracted from' translate to subtraction: $a - b$
Be careful with 'less than' and 'subtracted from'. The number or variable *after* these phrases comes *first* in the algebraic expression (e.g., '7 less than a n...
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Challenging
A group of 'f' friends agrees to split the cost of a pizza, which costs $22, and an online ordering fee of $3. One of the friends has a coupon for $5 off the entire order. Which expression represents the cost per friend?
A.(22 + 3 - 5) / f
B.22/f + 3 - 5
C.(22 + 3) / f - 5
D.22 + 3 + 5 - f
Challenging
Which option correctly distinguishes between '8 less than the quotient of a number and 3' and 'the quotient of 8 less than a number and 3'?
A.Both are (n/3) - 8
B.First is 8 - n/3; Second is (n-8)/3
C.First is (n/3) - 8; Second is (n-8)/3
D.First is (n/3) - 8; Second is 3/(n-8)
Challenging
From the sum of a number 'x' and its square, subtract twice the number.
A.x + x² - 2x
B.x + 2x - x²
C.2x - (x + x²)
D.(x + x²) / 2x
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