Fractions

A fraction represents a part of a whole. It consists of two numbers, one above the other, with a line between them. The number on top is called the numerator, and the number on the bottom is called the denominator.

Types of Fractions

There are several types of fractions:

Proper Fraction: A fraction where the numerator is less than the denominator, e.g., 1/2.
Improper Fraction: A fraction where the numerator is greater than or equal to the denominator, e.g., 5/3.
Mixed Number: A whole number combined with a fraction, e.g., 2 1/4.
Equivalent Fractions: Fractions that have the same value but may look different, e.g., 1/2 and 2/4.

Operations with Fractions

There are four basic operations that can be performed with fractions: addition, subtraction, multiplication, and division.

Addition and Subtraction

When adding or subtracting fractions, the denominators must be the same. If they are not, you need to find a common denominator before performing the operation. Once the denominators are the same, you can add or subtract the numerators and keep the denominator unchanged.

Multiplication

To multiply fractions, simply multiply the numerators together to get the new numerator, and multiply the denominators together to get the new denominator.

Division

To divide fractions, multiply the first fraction by the reciprocal of the second fraction (i.e., flip the second fraction and then multiply).

Study Guide

Here are some tips for studying fractions:

Understand the concept of fractions as parts of a whole.
Practice identifying the numerator and denominator in different fractions.
Learn how to convert between improper fractions and mixed numbers.
Practice finding equivalent fractions for a given fraction.
Work on adding, subtracting, multiplying, and dividing fractions using different examples.

Remember, practicing regularly is key to mastering fractions!

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

Study Guide

Introduction to Algebra

Activity Lesson

Algebraic Expression Cards

Worksheet/Answer key

Introduction to Algebra

Worksheet/Answer key

Introduction to Algebra

Worksheet/Answer key

Introduction to Algebra

Worksheet/Answer key

Algebra Riddles

The resources above cover the following skills:

Algebra (NCTM)

Represent and analyze mathematical situations and structures using algebraic symbols.

Develop an initial conceptual understanding of different uses of variables.

Use symbolic algebra to represent situations and to solve problems, especially those that involve linear relationships.

Recognize and generate equivalent forms for simple algebraic expressions and solve linear equations

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.