key term - Proportion

Definition

Proportion is the relationship between two or more quantities where the ratio between them remains constant. It is a fundamental concept that underlies various mathematical topics, including decimals, fractions, ratios, rates, and percent calculations.

5 Must Know Facts For Your Next Test

1. Proportions are used to represent equivalent fractions, where the ratio between the numerator and denominator is the same.
2. Ratios and rates are special types of proportions, where the relationship between the quantities is constant.
3. Proportions are essential for understanding and solving percent problems, as the part-to-whole relationship can be expressed as a proportion.
4. Solving proportions involves finding an unknown value in the relationship, often using cross-multiplication or other algebraic methods.
5. Proportions are widely used in various applications, such as scale drawings, currency conversions, and recipe adjustments.

Review Questions

• Explain how proportions are used in the context of decimals and fractions.
  • Proportions are fundamental to the relationship between decimals and fractions. A decimal can be expressed as a fraction, where the numerator and denominator form a proportion. For example, the decimal 0.5 can be written as the fraction 5/10, where the ratio between the numerator and denominator is 1:2, or 0.5. This proportional relationship allows for the conversion between decimals and fractions, which is essential for understanding and manipulating these numerical representations.
• Describe the role of proportions in the understanding of ratios and rates.
  • Ratios and rates are specific types of proportions, where the relationship between two or more quantities is constant. A ratio compares two or more quantities of the same unit, such as 3:5 or 3/5, while a rate compares two different units, such as 50 miles per hour. These proportional relationships are fundamental to understanding and working with ratios and rates, as they allow for the comparison, conversion, and application of these concepts in various real-world situations.
• Analyze how proportions are used to solve percent problems and their applications.
  • Proportions are essential for understanding and solving percent problems, as the part-to-whole relationship can be expressed as a proportion. For example, to find 25% of a number, you can set up a proportion where the part (25%) is to the whole (100%) as the unknown value is to the original number. By solving this proportion, you can determine the value that represents 25% of the original number. Proportions are widely used in percent applications, such as currency conversions, tip calculations, and scaling measurements, making them a crucial concept for understanding and applying percent-related problems.

Related terms

Ratio:

A ratio is a comparison of two or more quantities, expressed as a fraction or a rate.

Rate:

A rate is a ratio that compares two different units, such as miles per hour or dollars per pound.

Percent:

Percent is a way of expressing a proportion as a fraction of 100, often used to describe a part-to-whole relationship.