Multiplicative inverses

Learning Objectives Define multiplicative inverse and reciprocal. Find the multiplicative inverse of any non-zero whole number. Find the multiplicative inverse of any non-zero fraction. Find the multiplicative inverse of any non-zero mixed number. Find the multiplicative inverse of any non-zero decimal. Explain why the product of a number and its multiplicative inverse is always 1. Apply the concept of multiplicative inverses to simplify expressions. Ever wonder how to 'undo' multiplication? 🤔 What if you wanted to get back to 1 after multiplying a number? In this lesson, you'll discover multiplicative inverses, also known as reciprocals. These special numbers help us understand division, simplify fractions, and solve equations, making math much clearer an...

TermDefinitionExample Multiplicative InverseA multiplicative inverse of a number is another number that, when multiplied by the first number, results in a product of 1. It 'undoes' the multiplication.The multiplicative inverse of 5 is 1/5, because 5 × (1/5) = 1. ReciprocalReciprocal is another name for the multiplicative inverse. To find the reciprocal of a fraction, you 'flip' it (swap the numerator and denominator).The reciprocal of 2/3 is 3/2. ProductThe result obtained when two or more numbers are multiplied together.In 4 × 3 = 12, the number 12 is the product. Identity Property of MultiplicationThis property states that any number multiplied by 1 remains that same number. The number 1 is called the multiplicative identity.7 × 1 = 7, and 1 × (-3) = -3. Unit Fractio...

Definition of Multiplicative Inverse $a \times \frac{1}{a} = 1 \quad \text{for } a \neq 0$ This rule defines what a multiplicative inverse is: any non-zero number multiplied by its inverse equals 1. This applies to whole numbers, fractions, and decimals. Reciprocal of a Fraction \text{The reciprocal of } \frac{a}{b} \text{ is } \frac{b}{a} \quad \text{for } a, b \neq 0$ To find the reciprocal of a fraction, simply swap its numerator and denominator. This 'flips' the fraction. Reciprocal of a Whole Number \text{The reciprocal of } a \text{ is } \frac{1}{a} \quad \text{for } a \neq 0$ To find the reciprocal of a whole number, write it as a fraction with 1 as the denominator (e.g., $a = a/1$), then flip it.