Inaugurated by IN-SPACe
ISRO Registered Space Tutor
S3-SA4-0422
What is the Multiplicative Inverse of a Rational Number?
Grade Level:
Class 6
AI/ML, Data Science, Physics, Economics, Cryptography, Computer Science, Engineering
Definition
What is it?
The Multiplicative Inverse of a rational number is another rational number that, when multiplied by the original number, gives a product of 1. It's also often called the Reciprocal. Think of it as 'flipping' the fraction.
Simple Example
Quick Example
Imagine you have 2/3 of a yummy samosa. What fraction would you multiply by 2/3 to get a whole samosa (which is 1)? You would multiply it by 3/2. So, the multiplicative inverse of 2/3 is 3/2.
Worked Example
Step-by-Step
Let's find the Multiplicative Inverse of the rational number 5/7.
Step 1: Identify the given rational number. It is 5/7.
---Step 2: To find the multiplicative inverse, we need to 'flip' the fraction. This means the numerator becomes the denominator and the denominator becomes the numerator.
---Step 3: The numerator of 5/7 is 5. The denominator is 7.
---Step 4: Flipping it, the new numerator is 7 and the new denominator is 5.
---Step 5: So, the multiplicative inverse is 7/5.
---Step 6: Let's check: (5/7) * (7/5) = (5*7) / (7*5) = 35/35 = 1.
Answer: The Multiplicative Inverse of 5/7 is 7/5.
Why It Matters
Understanding multiplicative inverses helps us solve equations and divide fractions easily. In fields like Computer Science, it's used in cryptography to secure data, and in Physics, it helps calculate resistances in parallel circuits. Even Data Scientists use it in complex calculations!
Common Mistakes
MISTAKE: Thinking the multiplicative inverse of 2 is -2. | CORRECTION: The multiplicative inverse of 2 (which is 2/1) is 1/2, because 2 * (1/2) = 1. -2 is the additive inverse.
MISTAKE: Forgetting that a whole number like 4 can be written as 4/1 before finding the inverse. | CORRECTION: Always write whole numbers as fractions (e.g., 4 = 4/1) to easily find their inverse (1/4).
MISTAKE: Believing 0 has a multiplicative inverse. | CORRECTION: Zero does NOT have a multiplicative inverse because you cannot divide by zero. Any number multiplied by 0 is 0, never 1.
Practice Questions
Try It Yourself
QUESTION: What is the multiplicative inverse of 3/8? | ANSWER: 8/3
QUESTION: Find the reciprocal of -6. | ANSWER: -1/6
QUESTION: If a number multiplied by 5/4 gives 1, what is that number? | ANSWER: 4/5
MCQ
Quick Quiz
Which of the following numbers is the multiplicative inverse of 9?
-9
2026-01-09T00:00:00.000Z
2026-09-01T00:00:00.000Z
The Correct Answer Is:
B
The multiplicative inverse of 9 (which is 9/1) is 1/9, because 9 multiplied by 1/9 equals 1. Options A, C, and D do not satisfy this condition.
Real World Connection
In the Real World
When you're sharing a pizza and need to figure out how many pieces each person gets, you might implicitly use inverses. Or, imagine you're a shopkeeper calculating how many small packets of spices (say, 1/4 kg each) can be made from a large 1 kg bag. You're essentially finding the inverse of 1/4 (which is 4) to know you can make 4 packets.
Key Vocabulary
Key Terms
RATIONAL NUMBER: A number that can be expressed as a fraction p/q, where p and q are integers and q is not zero. | RECIPROCAL: Another name for the multiplicative inverse. | NUMERATOR: The top number in a fraction. | DENOMINATOR: The bottom number in a fraction. | PRODUCT: The result of multiplying two or more numbers.
What's Next
What to Learn Next
Great job learning about multiplicative inverses! Next, you can explore how to use them when dividing fractions. This will make understanding more complex fraction problems much easier and faster!
