Introduction to Fractions

A fraction represents a part of a whole. It consists of a numerator (the top number) and a denominator (the bottom number). Fractions are used to represent numbers that are not whole numbers, such as 1/2, 3/4, 5/8, etc.

Adding and Subtracting Fractions

When adding or subtracting fractions, the first step is to make sure the denominators are the same. If they are not, find a common denominator. Once the denominators are the same, add or subtract the numerators and keep the denominator the same.

Example:

Find the sum of 1/3 and 2/5.

First, find a common denominator, which is 15. Then, rewrite the fractions with the common denominator: 1/3 = 5/15 and 2/5 = 6/15 Now, add the fractions: 5/15 + 6/15 = 11/15 So, 1/3 + 2/5 = 11/15

Multiplying and Dividing Fractions

When multiplying fractions, simply multiply the numerators together to get the new numerator, and multiply the denominators together to get the new denominator. When dividing fractions, multiply the first fraction by the reciprocal of the second fraction.

Example:

Find the product of 2/3 and 3/4.

Multiply the numerators and denominators together: 2/3 * 3/4 = (2*3)/(3*4) = 6/12 Simplify the fraction: 6/12 = 1/2 So, 2/3 * 3/4 = 1/2

Practice Problems

Find the sum of 3/4 and 5/6.
Find the difference between 7/8 and 2/3.
Find the product of 2/5 and 3/4.
Find the quotient of 5/6 and 2/3.

Study Tips

Practice finding common denominators for adding and subtracting fractions.
Remember to simplify your answers whenever possible.
When dividing fractions, multiply by the reciprocal of the second fraction.
Use visual representations like fraction bars to help understand fraction operations.

By practicing these operations and study tips, you can improve your skills in working with fractions!

◂Math Worksheets and Study Guides Seventh Grade. Fraction Operations

Create And Print more Fractions worksheets with Comparing Fractions, Equivalent Fractions, and Simplifying Fractions

The resources above cover the following skills:

Number and Operations (NCTM)

Compute fluently and make reasonable estimates.

Develop and analyze algorithms for computing with fractions, decimals, and integers and develop fluency in their use.

Grade 7 Curriculum Focal Points (NCTM)

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.

Fraction Operations: Addition, Subtraction, Multiplication, and Division

Introduction to Fractions

Adding and Subtracting Fractions

Example:

Multiplying and Dividing Fractions

Example:

Practice Problems

Study Tips

[Fraction Operations] Related Worksheets and Study Guides:

◂Math Worksheets and Study Guides Seventh Grade. Fraction Operations

Create And Print more Fractions worksheets with Comparing Fractions, Equivalent Fractions, and Simplifying Fractions

The resources above cover the following skills: