The number that undoes a fraction
2/5 is on the board. What do you multiply it by to get 1?
Step 1 of 4
- 2/5.
- Swap the top and bottom.
- That gives 5/2.
- 2/5 × 5/2 = 10/10 = 1.
Turn it upside down
Multiply by 5/2. Then 2/5 × 5/2 = 1.
Swap the two numbers of 2/5 and you get 5/2. Multiply 2/5 by 5/2. On top, 2 × 5 = 10. On the bottom, 5 × 2 = 10. That is 10/10, which is one whole.
The swapped fraction is the reciprocal. Every fraction above zero has one. The pair always multiplies to 1.
- 3/4's reciprocal is 4/3. Check: 3 × 4 = 12 and 4 × 3 = 12.
- A whole number is a fraction over 1. So 6 is 6/1, and its reciprocal is 1/6.
Zero has no reciprocal. Flipping 0/1 gives 1/0. You cannot cut a whole into zero parts.
Watch out!
"1 1/2 flips to 1 2/1" is wrong. Do not flip a mixed number as it is. Turn it into an improper fraction first: 1 1/2 is 3/2. The reciprocal of 3/2 is 2/3.
Slide the top and the bottom in the lab. Make the product exactly 1.
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