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)
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.
To reduce a rational number, you need to simplify it by dividing both the numerator and denominator by their greatest common divisor. The greatest common divisor is the largest number that divides evenly into both the numerator and the denominator.
Let's take an example to illustrate this process. Consider the rational number 12/36.
Step 1: Find the greatest common divisor (GCD) of the numerator and denominator. The factors of 12 are 1, 2, 3, 4, 6, and 12. The factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, and 36. The common factors are 1, 2, 3, 4, 6, and 12. The largest common factor is 12.
Step 2: Divide both the numerator and the denominator by the GCD. In this example, both 12 and 36 are divisible by 12.
12 ÷ 12 = 1
36 ÷ 12 = 3
So, the reduced form of 12/36 is 1/3.
In summary, reducing a rational number involves finding the greatest common divisor of the numerator and denominator and dividing both by this value. This process simplifies the fraction to its lowest terms.
To reduce a rational number, we need to simplify it by dividing both the numerator and the denominator by their greatest common divisor (GCD). This process ensures that the resulting fraction is in its simplest form.
To find the GCD, we look for the largest number that evenly divides both the numerator and the denominator. This concept is tied to the notion of divisibility and factors. A factor of a number is a number that divides into it exactly without leaving a remainder.
Let's use an example to illustrate the process of reducing a rational number. Consider the fraction 24/36.
Step 1: Find the GCD:
To determine the GCD of 24 and 36, we examine the factors of both numbers. The factors of 24 are 1, 2, 3, 4, 6, 8, 12, and 24. The factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, and 36. By observing the common factors, we find that the largest factor shared by both 24 and 36 is 12.
Step 2: Divide both numerator and denominator by the GCD:
Now we divide both the numerator (24) and the denominator (36) by the GCD, which is 12.
24 ÷ 12 = 2
36 ÷ 12 = 3
The resulting simplified fraction is 2/3.
By reducing the fraction 24/36, we simplified it to the simplest form, which is 2/3.
In summary, to reduce a rational number:
1. Determine the GCD by finding the largest common factor between the numerator and the denominator.
2. Divide both the numerator and denominator by the GCD to simplify the fraction.
This process ensures that our fractions are in their simplest form and makes it easier to compare and perform calculations with rational numbers.