RECIPROCAL
Definition Of Reciprocal
If the product of two numbers is 1, then the two numbers are said to be reciprocals of each other.
In other words, a reciprocal is the multiplicative inverse of a number.
The reciprocal of ‘a’ is 
Examples of Reciprocal
The real part of a complex number Z is denoted as Re (Z).
Consider 9x 1/9 = 1
9 is the reciprocal of 1/9
1/9 is the reciprocal of 9.
The following are few examples of reciprocals
3.2, 1/32
√6, 1/√6
Video Examples: What Is Reciprocal Math
Solved Example on Reciprocal
Ques: Find the reciprocal of 2/5
Choices:
A. 5/2
B. 2/5
C. 5x 2
D. 1
Correct Answer: A
Solution:
Step 1: The reciprocal of 2/5 is 5/2. [Interchange numerator and denominator of 2/5]
Quick Summary
- The reciprocal of a number is 1 divided by that number.
- To find the reciprocal of a fraction, interchange the numerator and denominator.
⚠️ Common Mistakes
- Confusing reciprocals with additive inverses (negatives).
- Thinking the reciprocal of a whole number is the same whole number.
🌍 Real-World Uses
- Scaling recipes: If a recipe calls for 1/2 cup of flour, and you want to double the recipe, you multiply the amount by 2 (the reciprocal of 1/2).
- Gear ratios: In mechanics, the gear ratio is the reciprocal of the ratio of the number of teeth on the two gears. This determines the speed and torque of the system.
- Currency exchange rates: If 1 US dollar buys 0.8 British pounds, then 1 British pound buys 1/0.8 = 1.25 US dollars (approximately).
📋 Standards Alignment
CCSS.MATH.CONTENT.7.NS.A.2.C
🔗 Related Links
🍎 Teacher Insights
Use visual aids like fraction bars to demonstrate reciprocals. Relate the concept to dividing fractions, as dividing by a fraction is the same as multiplying by its reciprocal.🎓 Prerequisites
- Fractions
- Multiplication
- Division
Check Your Knowledge
Q1: What is the reciprocal of 2/5?
Q2: What is the reciprocal of 7?
Frequently Asked Questions
Q: What is the reciprocal of 0?
A: Zero does not have a reciprocal because division by zero is undefined.
Q: How do I find the reciprocal of a mixed number?
A: First, convert the mixed number to an improper fraction, then flip the numerator and denominator.