Questions and Answers
What does the term 'proportions' refer to?
What is represented by the equation a/b = c/d?
A proportion
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 ______.
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What is the process of 'distribute'?
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What does it mean to 'isolate' a variable?
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What is the purpose of 'simplify' in algebra?
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What is a fraction?
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What is the 'numerator' in a fraction?
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What is the 'denominator' in a fraction?
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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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Description
This quiz focuses on essential vocabulary related to solving proportions in Algebra 1. It includes key definitions and concepts, such as cross multiplying and setting ratios equal to each other. Perfect for reinforcing understanding of ratios and their applications in algebra.
