Ratio: A comparison of two quantities expressed as a quotient, typically written as a : b or a/b. It indicates how many times one value contains or is contained within the other.
Ratio notation: The way ratios are written, often using a colon (a : b) or fraction (a/b), to compare quantities directly.
Proportion: An equation stating that two ratios are equivalent, written as a : b = c : d or a/b = c/d. It signifies that the relationship between the first pair is the same as the second pair.
Equivalent ratios: Ratios that express the same relationship, meaning a : b = c : d if and only if a × d = b × c (cross-multiplication).
Cross-multiplication method: A technique to solve proportions by multiplying across the equal sign, transforming the proportion a/b = c/d into a × d = b × c.
Unit rate: The ratio of two quantities where the second quantity is 1, often used to compare per-unit quantities, e.g., miles per hour or price per item.
1. What is a ratio in mathematics?
2. What is the correct method to convert a decimal to a percent?
3. What is the primary function of percent equations in problem-solving?
Ratios — definition?
Comparison of two quantities as a quotient.
Proportion — role?
States two ratios are equivalent.
Cross-multiplication — function?
Solves proportions by multiplying across.
Unit rate — example?
Speed or cost per item.
Fraction to decimal — process?
Divide numerator by denominator.
Decimal to percent — conversion?
Move decimal two places right.
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