A fraction represents a part of a whole or a part of a group. It consists of a numerator (the top number) and a denominator (the bottom number). The numerator represents the number of parts we have, and the denominator represents the total number of parts that make up the whole or the group.

There are different types of fractions:

**Proper Fraction:**A fraction where the numerator is less than the denominator, e.g., 3/4.**Improper Fraction:**A fraction where the numerator is greater than or equal to the denominator, e.g., 7/4.**Mixed Number:**A whole number combined with a fraction, e.g., 1 3/4.**Equivalent Fractions:**Fractions that represent the same value, e.g., 1/2 and 2/4.

There are four basic operations that can be performed with fractions:

**Addition:**To add fractions, make sure the denominators are the same, then add the numerators together and keep the denominator the same, e.g., 1/3 + 1/6 = (2/6) + (1/6) = 3/6 = 1/2.**Subtraction:**To subtract fractions, make sure the denominators are the same, then subtract the numerators and keep the denominator the same, e.g., 5/8 - 3/8 = 2/8 = 1/4.**Multiplication:**To multiply fractions, simply multiply the numerators together to get the new numerator and the denominators together to get the new denominator, e.g., 2/3 * 3/4 = (2*3)/(3*4) = 6/12 = 1/2.**Division:**To divide fractions, multiply the first fraction by the reciprocal of the second fraction, e.g., 2/3 ÷ 4/5 = 2/3 * 5/4 = (2*5)/(3*4) = 10/12 = 5/6.

When comparing fractions, you can use the following methods:

**Common Denominator:**Make the denominators the same, then compare the numerators.**Cross-Multiplication:**Multiply the numerator of the first fraction by the denominator of the second fraction and compare it with the product of the numerator of the second fraction and the denominator of the first fraction.

Now that you understand fractions, try solving the following practice problems:

- Simplify the fraction 10/15.
- Add the fractions 1/4 and 1/3.
- Multiply the fractions 2/5 and 3/8.
- Compare the fractions 2/3 and 3/4 using a common denominator.

Good luck with your practice! If you need further assistance, feel free to reach out to me.

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.