Reciprocals and multiplicative inverses

Key Notes:

Understanding Reciprocals:

• Definition: The reciprocal of a number a is 1/a It’s the number that, when multiplied by a , gives 1.
• Examples: For example, the reciprocal of 2 is 1/2 ​, because 2 × 12 = 1.

Multiplicative Inverses:

• Definition: The multiplicative inverse of a number a is another number b such that a × b = 1.
• Connection to reciprocals: The multiplicative inverse of a is 1/a​.
• Example: For example, the multiplicative inverse of 3 is 1/3​, because 3 × 1/3 = 1.

Finding Reciprocals and Inverses:

• Practice exercises: Provide examples where students find reciprocals of integers and fractions.
• Checking answers: Emphasize checking by multiplication to ensure correctness (e.g., 1/4 × 4 = 1).

Properties and Applications:

• Reciprocal property: a×1/a=1 for any nonzero number a.
• Solving equations: Use reciprocals to solve equations involving fractions and multiplicative inverses.

Graphical Representation:

• Show reciprocals on a number line.
• Visualize how the product of a number and its reciprocal is always 1.

Real-life Examples:

Applications in everyday life: Discuss scenarios where understanding reciprocals (e.g., cooking recipes, proportions) and multiplicative inverses (e.g., scaling measurements) are important.

Learn with an example

Let’s practice!🖊️