Decimals are a way of expressing parts of a whole. They are a way of writing fractions with denominators of powers of 10. The decimal point separates the whole number part from the fractional part of a number.

Understanding the basic concepts of decimals is crucial. Here are some key points to remember:

**Decimal Place Value:**The value of each digit in a decimal number is based on its position from the decimal point. The positions to the left of the decimal point represent whole numbers, while the positions to the right of the decimal point represent fractions of a whole.**Reading Decimals:**Decimals are read as "and" when the decimal point is spoken. For example, 3.25 is read as "three and twenty-five hundredths."**Comparing Decimals:**When comparing decimals, start from the left and compare the digits in each place value. If the digits are the same, move to the next place value until a difference is found.

Performing operations with decimals is an important skill. Here are the basic operations involving decimals:

**Addition and Subtraction:**When adding or subtracting decimals, it is important to align the decimal points and then perform the operation as if working with whole numbers. The decimal point in the result should be placed directly below the decimal points in the numbers being added or subtracted.**Multiplication:**To multiply decimals, ignore the decimal points and multiply the numbers as if they were whole numbers. The final answer should have the same number of decimal places as the total number of decimal places in the factors.**Division:**When dividing decimals, first move the decimal point in the divisor to make it a whole number. Then move the decimal point in the dividend the same number of places. Perform the division as if working with whole numbers, and place the decimal point in the quotient directly above the decimal point in the dividend.

Decimals are used in various real-life applications, such as money, measurements, and scientific notation. Understanding decimals is essential for handling these everyday situations.

Here are some practice problems to help reinforce your understanding of decimals:

- Perform the following addition: 4.7 + 2.63 =
**Answer: 7.33** - Calculate the product of 3.25 and 1.6 =
**Answer: 5.2** - If a person has $35.75 and spends $18.90, how much money does he have left?
**Answer: $16.85**

Practicing these problems will help solidify your understanding of decimals and improve your skills in working with them.

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.