Reciprocal of a fraction
The partner that multiplies a fraction to give 1.
A number that makes 1
Dividing 1 by 23 asks: 23 × ? = 1. Let us start with an easier one: which number, multiplied by a whole number, gives 1?
What number multiplied by 4 gives 1?
What this lesson covers
The idea
The reciprocal of a fraction a/b is b/a, the fraction with its numerator and denominator interchanged; multiplying a fraction by its reciprocal gives 1.
A number that makes 1
Dividing 1 by 2/3 asks: 2/3 × ? = 1. Let us start with an easier one: which number, multiplied by a whole number, gives 1?
What number multiplied by 4 gives 1?
- 1/4
- 4
- 3
Find the partner
Every fraction has a partner that makes 1. Use the buttons to set the partner. The lower bar shows the fraction times its partner. It must end exactly at 1.
The partner is the fraction turned upside down
The partner of a/b is b/a: swap the numerator and the denominator. This partner is called the reciprocal. A fraction times its reciprocal is always 1.
Why 1? The top is a × b and the bottom is b × a. They are the same number, so the fraction is a whole 1.
The reciprocal of a fraction a/b is b/a. When we multiply a fraction by its reciprocal, we get 1.
- Fraction | Reciprocal | Product
- 2/3 | 3/2 | 1
- 3/5 | 5/3 | 1
- 5 | 1/5 | 1
Notes
The reciprocal of a fraction a/b is b/a. When we multiply a fraction by its reciprocal, we get 1.
Check yourself
What is the reciprocal of 7/4? Type a fraction like 2/9.
Answer: 4/7
The reciprocal of 7/4 is 4/7. Check: 7/4 × 4/7 = 28/28 = 1.
Which pair of numbers has the product 1?
2/9 × ? = 1. What is the missing number? Type a fraction like 3/7.
Answer: 9/2
2/9 × 9/2 = 18/18 = 1, so the missing number is 9/2.
Maya says: “The reciprocal of 6/11 is 6/11 itself, because multiplying by it gives 1.” Is she right?
- 3/4 and 4/5. Not quite: 3/4 × 4/5 = 12/20 = 3/5. The partner of 3/4 is 4/3, not 4/5.
- 2/3 and 3/2 — correct. Yes! 2/3 × 3/2 = 6/6 = 1.
- 5/6 and 6/7. Not quite: 5/6 × 6/7 = 30/42 = 5/7. The partner of 5/6 is 6/5.
- Yes. A fraction is its own reciprocal.. Check: 6/11 × 6/11 = 36/121, which is not 1.
- No. The reciprocal is 5/11, one less than the numerator.. Check: 6/11 × 5/11 = 30/121, which is not 1.
- No. The reciprocal is 11/6, and 6/11 × 11/6 = 1. — correct. Yes! The numerator and the denominator must be swapped.