Every number so far is one integer over another
7, −3, 2¼, 65% and 0.375 look different. Here 2¼ means two and a quarter. 65% means 65 out of 100. Are they different kinds of number?
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No. All five can be written as one integer over another.
Write each one as an integer over an integer. An integer is a whole number or its negative: 7, 0, −3. The bottom number is never 0. Dividing by 0 has no answer.
- 7 is 7/1.
- −3 is −3/1.
- 2¼ is 9/4, since 2 × 4 + 1 = 9.
- 65% is 65/100. Cut down (divide top and bottom by 5), it is 13/20.
- 0.375 is 375/1000. Cut down (divide top and bottom by 125), it is 3/8.
A number you can write this way is a rational number. It is a ratio, an integer over a non-zero integer. Write any minus sign on the top.
| As it came | As a pair of integers | Cut down |
|---|---|---|
| 7 | 7/1 | 7/1 |
| −3 | −3/1 | −3/1 |
| 2¼ | 9/4 | 9/4 |
| 65% | 65/100 | 13/20 |
| 0.375 | 375/1000 | 3/8 |
Lowest terms means the top and bottom share no factor above 1. A factor divides a number with nothing left over. Divide both by their highest common factor to reach it.