Percentages are used to express a portion out of 100. Understanding percentages is important in many areas, including finance, science, and everyday life. In mathematics, percentages are often used to compare quantities and to solve problems involving ratios and proportions.

**Percent:**A percent is a ratio that compares a number to 100. It is denoted by the symbol "%". For example, 50% means 50 out of 100.**Converting between Percentages and Decimals:**To convert a percentage to a decimal, divide by 100. For example, 25% is equivalent to 0.25 as a decimal. To convert a decimal to a percentage, multiply by 100. For example, 0.6 is equivalent to 60% as a percentage.**Converting between Percentages and Fractions:**To convert a percentage to a fraction, write the percentage as a fraction with a denominator of 100. For example, 75% is equivalent to 75/100, which simplifies to 3/4. To convert a fraction to a percentage, multiply the fraction by 100 and add a percent sign. For example, 2/5 is equivalent to 40% as a percentage.**Percent Increase and Decrease:**To calculate a percent increase, use the formula: ((New Value - Original Value) / Original Value) * 100. To calculate a percent decrease, use the formula: ((Original Value - New Value) / Original Value) * 100.

1. Convert 0.6 to a percentage.

Answer: 0.6 * 100 = 60%

2. Convert 3/4 to a percentage.

Answer: (3/4) * 100 = 75%

3. Calculate the percent increase if a $50 item is now selling for $65.

Answer: ((65 - 50) / 50) * 100 = 30%

4. Calculate the percent decrease if the temperature drops from 80°F to 68°F.

Answer: ((80 - 68) / 80) * 100 = 15%

Understanding percentages is an essential skill in mathematics. By mastering the conversion between percentages, decimals, and fractions, as well as the calculation of percent increase and decrease, you will be able to apply this knowledge to a wide range of real-world problems.

Study GuideIntroduction to Percent Worksheet/Answer key

Introduction to Percent Worksheet/Answer key

Introduction to Percent Worksheet/Answer key

Introduction to Percent Worksheet/Answer keyIntroduction to Percent

Number and Operations (NCTM)

Understand numbers, ways of representing numbers, relationships among numbers, and number systems.

Work flexibly with fractions, decimals, and percents to solve problems.

Develop meaning for percents greater than 100 and less than 1.

Grade 7 Curriculum Focal Points (NCTM)

Number and Operations and Algebra and Geometry: Developing an understanding of and applying proportionality, including similarity

Students extend their work with ratios to develop an understanding of proportionality that they apply to solve single and multi-step problems in numerous contexts. They use ratio and proportionality to solve a wide variety of percent problems, including problems involving discounts, interest, taxes, tips, and percent increase or decrease. They also solve problems about similar objects (including figures) by using scale factors that relate corresponding lengths of the objects or by using the fact that relationships of lengths within an object are preserved in similar objects. Students graph proportional relationships and identify the unit rate as the slope of the related line. They distinguish proportional relationships (y/x = k, or y = kx) from other relationships, including inverse proportionality (xy = k, or y = k/x).

Number and Operations and Algebra: Developing an understanding of operations on all rational numbers and solving linear equations

Students extend understandings of addition, subtraction, multiplication, and division, together with their properties, to all rational numbers, including negative integers. By applying properties of arithmetic and considering negative numbers in everyday contexts (e.g., situations of owing money or measuring elevations above and below sea level), students explain why the rules for adding, subtracting, multiplying, and dividing with negative numbers make sense. They use the arithmetic of rational numbers as they formulate and solve linear equations in one variable and use these equations to solve problems. Students make strategic choices of procedures to solve linear equations in one variable and implement them efficiently, understanding that when they use the properties of equality to express an equation in a new way, solutions that they obtain for the new equation also solve the original equation.

Connections to the Grade 7 Focal Points (NCTM)

Number and Operations: In grade 4, students used equivalent fractions to determine the decimal representations of fractions that they could represent with terminating decimals. Students now use division to express any fraction as a decimal, including fractions that they must represent with infinite decimals. They find this method useful when working with proportions, especially those involving percents. Students connect their work with dividing fractions to solving equations of the form ax = b, where a and b are fractions. Students continue to develop their understanding of multiplication and division and the structure of numbers by determining if a counting number greater than 1 is a prime, and if it is not, by factoring it into a product of primes.