Find Reciprocals
The reciprocal of a fraction is found by flipping the numerator and denominator: the reciprocal of 3/4 is 4/3. For a whole number, write it as a fraction over 1 first: the reciprocal of 5 is 1/5. For a mixed number, convert to an improper fraction first: the reciprocal of 2 and 1/3 (= 7/3) is 3/7. A number times its reciprocal always equals 1. This 6th grade skill from enVision Mathematics Grade 6 is essential for fraction division, which uses the reciprocal to convert division into multiplication.
Key Concepts
Property The reciprocal of the fraction $\frac{a}{b}$ is $\frac{b}{a}$, where $a \neq 0$ and $b \neq 0$. A number and its reciprocal have a product of 1. To find the reciprocal of a fraction, we invert the fraction. Reciprocals must have the same sign. The number zero does not have a reciprocal.
Examples The reciprocal of $\frac{5}{8}$ is $\frac{8}{5}$. Check: $\frac{5}{8} \cdot \frac{8}{5} = \frac{40}{40} = 1$. The reciprocal of $9$ is $\frac{1}{9}$. First, write $9$ as $\frac{9}{1}$, then invert it. Check: $9 \cdot (\frac{1}{9}) = 1$. The reciprocal of $\frac{1}{4}$ is $4$. Check: $\frac{1}{4} \cdot (4) = 1$.
Explanation Finding a reciprocal is like flipping a fraction upside down. The numerator becomes the denominator and the denominator becomes the numerator. When you multiply any number by its reciprocal, the result is always 1. Keep the sign the same!
Common Questions
How do you find the reciprocal of a fraction?
Flip the fraction — exchange the numerator and denominator. The reciprocal of 3/4 is 4/3. The reciprocal of 5/8 is 8/5.
What is the reciprocal of a whole number?
Write the whole number as a fraction over 1, then flip it. The reciprocal of 5 is 5/1 flipped to 1/5. The reciprocal of 3 is 1/3.
What is the reciprocal of a mixed number?
Convert to an improper fraction first, then flip. The reciprocal of 2 and 1/3: 2 and 1/3 = 7/3, so the reciprocal is 3/7.
What grade finds reciprocals?
Finding reciprocals is a 6th grade skill in enVision Mathematics Grade 6, essential for fraction division where you multiply by the reciprocal of the divisor.
Why does a number times its reciprocal equal 1?
Because a/b x b/a = ab/ab = 1. The numerator and denominator are the same, giving a value of 1. This property makes reciprocals the tool for undoing multiplication.
Does 0 have a reciprocal?
No. 0 has no reciprocal because 1/0 is undefined. Division by zero is impossible, so there is no number that, when multiplied by 0, gives 1.