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Questions and Answers
What does the term 'proportions' refer to?
What does the term 'proportions' refer to?
- Two ratios set equal to each other (correct)
- A single ratio
- A type of equation
- None of the above
What is represented by the equation a/b = c/d?
What is represented by the equation a/b = c/d?
A proportion
What does 'cross multiply' mean?
What does 'cross multiply' mean?
Multiplying a and d, and b and c
To solve a proportion, you should put all multi-term numbers/denominators in ______.
To solve a proportion, you should put all multi-term numbers/denominators in ______.
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What is the process of 'distribute'?
What is the process of 'distribute'?
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What does it mean to 'isolate' a variable?
What does it mean to 'isolate' a variable?
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What is the purpose of 'simplify' in algebra?
What is the purpose of 'simplify' in algebra?
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What is a fraction?
What is a fraction?
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What is the 'numerator' in a fraction?
What is the 'numerator' in a fraction?
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What is the 'denominator' in a fraction?
What is the 'denominator' in a fraction?
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Give an example of a proportion problem.
Give an example of a proportion problem.
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Study Notes
Proportions
- Proportions consist of two ratios set equal to each other, represented as a fraction.
Mathematical Representation
- A proportion can be expressed as ( a/b = c/d ).
Cross Multiplication
- To solve proportions, apply cross multiplication: multiply the numerator of one ratio by the denominator of the other ratio (e.g., multiply ( a ) by ( d ) and ( b ) by ( c )).
Steps to Solve Proportions
- Begin solving a proportion by grouping multi-term numerators and denominators in parentheses.
- Follow with cross multiplication to form an equation.
- Simplify the equation: distribute, combine like terms, and then isolate the variable by moving terms as needed.
Key Concepts
- Distribute: This process involves multiplying a term across a sum or difference within parentheses.
- Isolate: Focus on getting the variable alone on one side of the equation for easier solutions.
- Simplify: Reduce fractions or expressions to their simplest forms.
Fraction Basics
- A fraction comprises a numerator (the top number) and a denominator (the bottom number).
Example of a Proportion Problem
- When given ( x/3 = 8/12 ), solve for ( x ) by cross multiplying: the equation becomes ( 12x = 24 ), leading to the solution for ( x ) being 2.
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