Reciprocals
The reciprocal of a/b is b/a; their product is 1.
Key idea
The reciprocal of a/b is b/a; their product is 1.
In depth
The reciprocal of a/b is b/a; their product is 1. Dividing by a number is the same as multiplying by its reciprocal. Zero has no reciprocal.
Worked example
Reciprocal of 5 is 1/5; of 2/3 is 3/2; of 1½ (=3/2) is 2/3.
Formula
Real-world uses
- Converting speed to time and flow rates to volumes
- Dividing by a fraction in recipes and engineering
Common mistake
Confusing the reciprocal with the negative (opposite). The opposite makes a sum 0, the reciprocal makes a product 1.
How to learn this
- Read the key idea and say it in your own words.
- Work through the worked example, then try a similar problem.
- Use the interactive lesson’s visual and mini-quiz to check the pattern.
Frequently asked questions
What is Reciprocals?
The reciprocal of a/b is b/a; their product is 1. It is a topic at the intermediate level in Arithmetic & Number Sense.
What is the formula for Reciprocals?
The key formula is a × 1/a = 1.
Where is Reciprocals used in real life?
Real-world examples: Converting speed to time and flow rates to volumes; Dividing by a fraction in recipes and engineering.
What should I learn before Reciprocals?
Make sure you are comfortable with Mixed Numbers, the previous topic in Arithmetic & Number Sense.
What is a common mistake with Reciprocals?
Confusing the reciprocal with the negative (opposite). The opposite makes a sum 0, the reciprocal makes a product 1.
How can I practise Reciprocals?
Open the interactive lesson, play with the visual, then answer the three-question mini-quiz. Getting two right marks the topic complete.
What comes after Reciprocals?
Move on to Decimals next.
Related intermediate topics in Arithmetic & Number Sense
- Long Multiplication – Multiply by each digit of the multiplier, shift by place value, then add partial products.
- Long Division – Divide, multiply, subtract and bring down repeatedly to get the quotient.
- Factors and Multiples – Factors divide a number exactly; multiples are its products with whole numbers.
- Divisibility Rules – Quick tests: by 2 last digit even, by 3 digit-sum divisible by 3, by 5 ends 0/5, by 9 digit-sum divisible by 9.
- Prime Numbers – A prime has exactly two positive divisors: 1 and itself.
- Composite Numbers – Numbers greater than 1 with more than two factors.