Mathematics
Grade 8
15 min
Evaluate expressions involving rational numbers
Evaluate expressions involving rational numbers
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1
Introduction & Learning Objectives
Learning Objectives
Define rational numbers and identify them within mathematical expressions.
Accurately apply the order of operations (PEMDAS/BODMAS) to expressions containing rational numbers.
Perform addition, subtraction, multiplication, and division of rational numbers (fractions and decimals) within multi-step expressions.
Substitute given rational values for variables into algebraic expressions and evaluate them.
Simplify expressions involving various forms of rational numbers (fractions, decimals, mixed numbers).
Solve multi-step problems that require evaluating expressions with rational numbers.
Understand and apply properties of operations (e.g., distributive property) to simplify expressions before evaluating.
Ever wonder how engineers calculate precise measure...
2
Key Concepts & Vocabulary
TermDefinitionExample
Rational NumberA number that can be expressed as a fraction \( \frac{p}{q} \) where \( p \) and \( q \) are integers and \( q \) is not zero. This includes integers, fractions, and terminating or repeating decimals.\( \frac{1}{2}, -3, 0.75, 2\frac{1}{3} \)
ExpressionA mathematical phrase that contains numbers, variables, and operation symbols, but does not contain an equality sign.\( 3x + 5 \), \( \frac{1}{2}y - 4 \), \( (0.5 + 1.2) \times 3 \)
EvaluateTo find the numerical value of an expression by performing all indicated operations.To evaluate \( 2 + 3 \times 4 \), you find its value, which is 14.
Order of OperationsThe specific sequence in which mathematical operations must be performed to ensure a unique correct answer for any expression (Parentheses/Brackets, E...
3
Core Formulas
Order of Operations (PEMDAS/BODMAS)
1. Parentheses/Brackets
2. Exponents/Orders
3. Multiplication and Division (from left to right)
4. Addition and Subtraction (from left to right)
This fundamental rule dictates the precise sequence for performing mathematical operations to ensure consistent and correct evaluation of any expression. Always work from the innermost parentheses outwards.
Rules for Operations with Rational Numbers
• Addition/Subtraction of Fractions: Find a common denominator, then add/subtract numerators.
• Multiplication of Fractions: Multiply numerators and multiply denominators.
• Division of Fractions: Multiply the first fraction by the reciprocal of the second fraction (Keep, Change, Flip).
• Decimals: Align decimal points for addition/subtraction. For multi...
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Challenging
Evaluate the expression \( \frac{x - y}{z} + xy \) when \( x = \frac{1}{2} \), \( y = -1 \), and \( z = 0.5 \).
A.3.5
B.-1.5
C.2
D.2.5
Challenging
Evaluate the expression: \( \frac{\frac{1}{3} + \frac{1}{6}}{\frac{3}{4} - \frac{1}{2}} \)
A.1/2
B.2
C.4/3
D.3/4
Challenging
Let \( A = -0.5 \times (8 - 2) \). Let \( B = \frac{A}{1/2} \). What is the value of \( B - A \)?
A.-9
B.3
C.-3
D.9
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