Numbers and Their Operations — Operations on Rational Numbers

About this lesson

This unit focuses on operations with rational numbers. It begins by defining rational numbers as numbers that can be expressed as a/b where a and b are integers and b is not zero, and notes that counting numbers, natural numbers, and integers are subsets of rational numbers. The unit then covers converting rational numbers to percentages, finite decimals, and recurring decimals, and vice versa. The main operations taught are addition, subtraction, multiplication, and division of rational numbers, including cases with equal and different denominators. Properties of addition (closure, commutative, associative, additive identity, additive inverse) and multiplication (closure, commutative, associative, multiplicative identity, multiplicative inverse, distributive) are explained and applied. Real-life contexts include a diver's depth, a tree root, a dolphin's dive, stock price changes, a shark's position, a plumber cutting a pipe, a mountaineer climbing a mountain, and dividing a fabric roll. By the end, students should be able to perform all four operations on rational numbers, apply properties to simplify calculations, and solve word problems involving rational numbers.