Question

what are the characteristics of ratios?
what do you know about ratios? how can they be compared?
how can ratios be seen? how can ratios be used?
look back in your carnegie learning book if needed.

Explanation:

1. Characteristics of Ratios:

• A ratio is a comparison of two or more quantities (e.g., \(a:b\) or \(\frac{a}{b}\), where \(a\) and \(b\) are non - negative numbers and \(b

eq0\) when written as a fraction).

• Ratios are unit - less when comparing quantities of the same kind (e.g., the ratio of boys to girls in a class has no units as both are counts of people).
• They can be written in different forms: part - to - part (comparing two parts of a whole, like ratio of red marbles to blue marbles) or part - to - whole (comparing a part to the entire whole, like ratio of red marbles to total marbles).

1. What we know about Ratios and Comparison:

• Ratios represent the relative size of two or more quantities. To compare ratios, we can convert them to equivalent forms (e.g., find a common denominator if written as fractions, or find equivalent ratios with the same second term if written as \(a:b\) form). For example, to compare \(2:3\) and \(4:5\), we can find the cross - products: \(2\times5 = 10\) and \(3\times4=12\). Since \(10<12\), \(\frac{2}{3}<\frac{4}{5}\) or \(2:3 < 4:5\).

1. How Ratios can be seen:

• Ratios can be seen in real - life situations such as recipes (ratio of flour to sugar), in maps (ratio of distance on map to actual distance, scale factor), in financial statements (ratio of expenses to revenue), and in demographics (ratio of urban population to rural population).

1. How Ratios can be used:

• In cooking, ratios help in scaling recipes (e.g., if a recipe for 2 people uses 1 cup of flour and we want to make it for 4 people, we use the ratio \(2:4 = 1:2\) to double the amount of flour).
• In business, financial ratios (like current ratio = current assets/current liabilities) are used to analyze the financial health of a company.
• In construction, ratios are used in scale drawings to represent the actual size of buildings or structures on a smaller paper.

Answer:

• Characteristics of Ratios: A ratio compares quantities, is unit - less (for same - kind quantities), and can be part - to - part or part - to - whole, with multiple notation forms (\(a:b\), \(\frac{a}{b}\), \(a\) to \(b\)).
• About Ratios and Comparison: Ratios show relative size. Compare by finding equivalent forms (e.g., common denominator for fraction - form ratios, cross - multiply for \(a:b\) form).
• How Ratios are seen: In recipes, maps, financials, demographics, etc.
• How Ratios are used: Scale recipes, analyze business finances, in construction scale - drawings, etc.