Introduction to Percent

Percent is a way of expressing a number as a fraction of 100. It is denoted by the symbol "%". Understanding percentages is important for a variety of real-life applications, such as calculating sales tax, finding discounts, and understanding statistics.

Converting Between Percentages and Decimals

To convert a percentage to a decimal, divide the percentage by 100. For example, to convert 25% to a decimal, divide 25 by 100 to get 0.25.

To convert a decimal to a percentage, multiply the decimal by 100. For example, to convert 0.75 to a percentage, multiply 0.75 by 100 to get 75%.

Converting Between Percentages and Fractions

To convert a percentage to a fraction, write the percentage as a fraction with a denominator of 100, and then simplify if possible. For example, 60% can be written as 60/100, which simplifies to 3/5.

To convert a fraction to a percentage, divide the numerator by the denominator and then multiply by 100. For example, to convert 3/4 to a percentage, divide 3 by 4 to get 0.75, then multiply by 100 to get 75%.

Calculating Percentages

To calculate a percentage of a number, multiply the number by the percentage as a decimal. For example, to find 20% of 80, multiply 80 by 0.20 to get 16.

To find the original amount when given the percentage increase or decrease, divide the new amount by 1 plus (for increase) or minus (for decrease) the percentage as a decimal. For example, if an item increased by 25% to $125, divide 125 by 1.25 to find the original amount of $100.

Study Guide

Here are some key concepts to focus on when studying percent:

Converting between percentages and decimals
Converting between percentages and fractions
Calculating percentages of numbers
Finding the original amount when given a percentage increase or decrease

Practice converting between percentages, decimals, and fractions, and work on solving word problems involving percentages. Understanding percentages will help in various real-world situations, such as shopping, budgeting, and understanding data.

◂Math Worksheets and Study Guides Seventh Grade. Introduction to Percent

Study Guide

Introduction to Percent

Worksheet/Answer key

Introduction to Percent

Worksheet/Answer key

Introduction to Percent

Worksheet/Answer key

Introduction to Percent

Worksheet/Answer key

Introduction to Percent

The resources above cover the following skills:

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.