To reduce a rational number, we need to simplify or express it in its simplest form. This means that the numerator and denominator of the rational number should have no common factors other than 1.
To determine if the numerator and denominator have any common factors, we need to check for their divisibility. Divisibility refers to the ability of a number to be divided evenly by another number. In other words, if one number is divisible by another, then the remainder of the division is equal to zero.
Let's use an example to illustrate this process. Consider the rational number 12/18.
First, we look at the numerator, which is 12. We can find the factors of 12 by listing all the numbers that divide evenly into 12: 1, 2, 3, 4, 6, and 12.
Next, we examine the denominator, which is 18. Similarly, we list the factors of 18: 1, 2, 3, 6, 9, and 18.
By comparing the lists of factors, we see that both 12 and 18 have common factors of 1, 2, 3, and 6. Since the denominator has other factors apart from 1, we can simplify the rational number.
To reduce the rational number 12/18, we divide both the numerator and denominator by their greatest common factor (GCF), which in this case is 6. So, we divide 12 by 6 to get 2, and we divide 18 by 6 to get 3.
Therefore, the reduced form of 12/18 is 2/3, where the numerator and denominator have no common factors other than 1.
Explain how you would reduce a rational number. In your explanation, you may include the vocabulary "divisibility" and "factors". Use an example to help illustrate your explanation. (2 points)
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