Let's have a look...
You know that a reciprocal is a fraction whose numerator and denominator have been reversed. For example:
What is the reciprocal of the fraction \( \frac{18}{11} \)?
Reverse the order of the numerator and denominator. The reciprocal of \( \frac{18}{11} \) is \( \frac{11}{18} \).
Reciprocals have a special relationship when they are multiplied together. If you multiply a fraction by its reciprocal, the product will always be the number 1. For example:
Show that the fractions \( \frac{7}{5} \) and \( \frac{5}{7} \) are reciprocals.
You can show that these two fractions are reciprocals by showing that their product is the number 1.
Set up the multiplication problem. |
\( \frac{7}{5} \cdot \frac{5}{7} \) |
Use cross-cancelation to reduce the fractions before multiplying. |
\( \frac{\overset{1}{\cancel{7}}}{\underset{1}{\cancel{5}}} \cdot \frac{\overset{1}{\cancel{5}}}{\underset{1}{\cancel{7}}} \) |
Multiply the numerators and then multiply the denominators. |
\( \frac{1}{1} \cdot \frac{1}{1} = \frac{1}{1} \) |
Make sure that your answer is in simplest form. |
\( \frac{1}{1} = 1 \ \div\ 1 = 1 \) |
Let's Practice
How well do you understand the concept of a reciprocal fraction? Use the activity below to find out.
If two fractions are each other's reciprocal, what is their product?
- \( \frac{1}{2} \)
- 0
- 1
The product of a fraction and its reciprocal will always be the number 1.
The product of a fraction and its reciprocal will always be the number 1.
The product of a fraction and its reciprocal will always be the number 1.
Is the fraction \( \frac{9}{4} \) the reciprocal of the fraction \( \frac{4}{7} \)?
- No, because the product of \( \frac{9}{4} \) and \( \frac{4}{7} \) is not 0.
- No, because the product of \( \frac{9}{4} \) and \( \frac{4}{7} \) is not 1.
- No, because the product of \( \frac{9}{4} \) and \( \frac{4}{7} \) is not \( \frac{1}{2} \).
The product of a fraction and its reciprocal will always be the number 1.
The product of a fraction and its reciprocal will always be the number 1.
The product of a fraction and its reciprocal will always be the number 1.
Which shows that the fractions \( \frac{5}{3} \) and \( \frac{3}{5} \) are reciprocals?
- \( \frac{5}{3} + \frac{3}{5} = 1 \)
- \( \frac{5}{3} \cdot \frac{3}{5} = 1 \)
- \( \frac{5}{3} \ \div\ \frac{3}{5} = 1 \)
The product of a fraction and its reciprocal will always be the number 1.
The product of a fraction and its reciprocal will always be the number 1.
The product of a fraction and its reciprocal will always be the number 1.
Summary
Questions answered correctly:
Questions answered incorrectly:
Question
Does the number 0 have a reciprocal? Why or why not?
