Reciprocal of a Fraction
This Grade 6 math skill from Pengi Math (Grade 6) teaches students the concept of the reciprocal of a fraction. Students learn that the reciprocal of a fraction a/b is b/a (obtained by flipping numerator and denominator), and that multiplying a fraction by its reciprocal always equals 1. Reciprocals are essential for dividing fractions.
Key Concepts
Property The reciprocal of a non zero fraction $\frac{a}{b}$ is the fraction $\frac{b}{a}$. A number multiplied by its reciprocal always equals 1. $$\frac{a}{b} \times \frac{b}{a} = 1$$.
Examples The reciprocal of $\frac{2}{3}$ is $\frac{3}{2}$. The reciprocal of the whole number $5$ (written as $\frac{5}{1}$) is $\frac{1}{5}$. To find the reciprocal of a mixed number like $1\frac{1}{4}$, first convert it to an improper fraction, $\frac{5}{4}$. The reciprocal is $\frac{4}{5}$.
Explanation The reciprocal of a fraction is what you get when you "flip" the numerator and the denominator. This is also known as the multiplicative inverse. The key property of a reciprocal is that when you multiply a number by its reciprocal, the result is always 1. Understanding reciprocals is the first step to learning how to divide fractions, as division is the same as multiplying by the reciprocal.
Common Questions
What is the reciprocal of a fraction?
The reciprocal of a fraction a/b is b/a—you simply flip the numerator and denominator. For example, the reciprocal of 3/4 is 4/3.
What happens when you multiply a fraction by its reciprocal?
Any fraction multiplied by its reciprocal equals 1. For example, 3/4 × 4/3 = 12/12 = 1.
How are reciprocals used in division of fractions?
To divide by a fraction, multiply by its reciprocal. For example, 2/3 ÷ 4/5 = 2/3 × 5/4 = 10/12 = 5/6.
Does every number have a reciprocal?
Every non-zero number has a reciprocal. Zero has no reciprocal because division by zero is undefined.
Where is the reciprocal of a fraction taught?
Reciprocals are covered in the Grade 6 Pengi Math textbook as a foundational concept for fraction division.