ORN - Operations with Rational Numbers Module Overview

Operations with Rational Numbers Module Overview

Introduction

In 6th grade, students learned to represent signed numbers on a vertical and horizontal number line and to identify the opposite of a number. In grade 7, students will develop an understanding of operations with rational numbers. Building on prior knowledge, this module will explore addition and subtraction of rational numbers using a number line and using properties to solve problems with negative and positive fractions and decimals. This module will show students how to convert between decimals and fractions, and to justify the reasonableness of answers by using estimation. These concepts will lead to more in-depth studies of fractions as they are related to measurement, statistics, and probability.

Essential Questions

How can you represent operations on a number line?
How can you write equivalent expressions using properties?
How do you apply properties to solve rational numbers problems?
How can a negative symbol be written in a fraction?
How do you multiply and divide rational numbers?
How can you solve everyday problems involving the four operations with positive and negative numbers?

Key Terms

The following key terms will help you understand the content in this module.

Additive inverse - The additive inverse is the opposite of a number.

Associative property - The associative property states that for all real numbers a, b, and c, the sum/product is always the same, regardless of their grouping.

Commutative property - The commutative property states that two or more numbers can be added/multiplied in any order without changing the sum/product.

Distributive Property - The distributive property states that for all real numbers, a, b, and c, a(b +c) = ab + ac and a(b - c) = ab - ac.

Identity property of one - The identity property states that the product of 1 and any number is that number.

Identity property of zero - The identity property of zero states that the sum of zero and any number is that number.

Integers - Integers include the set of whole numbers and their opposites

Multiplicative inverse - The multiplicative inverse of a number, $LaTeX: \frac{a}{b},\:where\:b\ne0,$ $\frac{a}{b},\:where\:b\ne0,$ is the reciprocal of the number, $LaTeX: \frac{b}{a}$ $\frac{b}{a}$ . The product of a number and its multiplicative inverse is 1.

Opposites - Opposites consist of two numbers that are an equal distance from zero on a number line also called additive inverse.

Rational Number - A rational number is any number that can be expressed as a ratio of two integers.

Reciprocal - A reciprocal is one of two numbers whose product is 1 also called multiplicative inverse.

IMAGES CREATED BY GAVS