EDEXCEL GCSE FOUNDATION MATHS - What are Reciprocals

Edexcel GCSE Foundation Maths - What are Reciprocals?

What are Reciprocals?

A reciprocal is simply the inverse of a number. To find the reciprocal of a number, you divide 1 by that number.

Example:

• The reciprocal of 2 is 1/2.
• The reciprocal of 5 is 1/5.
• The reciprocal of 10 is 1/10.

Key Points:

• Every number (except 0) has a reciprocal.
• The reciprocal of a fraction is found by flipping the numerator and denominator. For example, the reciprocal of 3/4 is 4/3.
• The product of a number and its reciprocal is always 1. For example, 2 * (1/2) = 1.

How to find reciprocals:

1. Write the number as a fraction. If the number is a whole number, write it as a fraction with 1 as the denominator.
2. Flip the numerator and denominator.
3. Simplify the fraction, if possible.

Examples:

1. Find the reciprocal of 3.

   • 3 can be written as 3/1.
   • Flip the numerator and denominator: 1/3.
   • Therefore, the reciprocal of 3 is 1/3.

2. Find the reciprocal of 1/4.

   • The reciprocal of 1/4 is 4/1.
   • Simplifying, we get 4.

Applications of Reciprocals:

• Dividing by a fraction: Dividing by a fraction is the same as multiplying by its reciprocal.
• Solving equations: Reciprocals are used to isolate variables in equations.

Practice Questions:

1. Find the reciprocals of the following numbers:

   • 4
   • 1/2
   • 7/3
   • 0.5

2. What is the reciprocal of 2.5?

3. Simplify the expression: 3/4 * 4/3.

Answer Key:

1. • 1/4
   • 2
   • 3/7
   • 2
2. 2/5
3. 1