Explain how to add and subtract rational numbers with common or like denominators. Include in your explanation any relevant vocabulary and rules. Use an example to illustrate your explanation. (2 points)
To add or subtract rational numbers with common or like denominators, you first need to understand what common or like denominators are. Denominators refer to the bottom part of a fraction, which represents the total number of equal parts into which a whole has been divided. Common or like denominators mean that the fractions have the same number on the bottom.
To add or subtract rational numbers with common denominators, you can follow these steps:
1. Write the rational numbers with their common denominators.
2. Add or subtract the numerators (the top part of the fractions) as regular whole numbers.
3. Keep the common denominator the same for the result.
For example, let's say we have two rational numbers: 1/4 and 3/4. Since they have the same denominator (4), we can simply add/subtract the numerators:
1/4 + 3/4 = (1 + 3)/4 = 4/4 = 1
In this case, the common denominator was 4, and by adding the numerators (1 + 3), we get 4. Then we keep the numerator as 4 and the denominator as 4, resulting in a simplified fraction of 4/4, which is equal to 1.
Similarly, if we want to subtract these fractions:
3/4 - 1/4 = (3 - 1)/4 = 2/4 = 1/2
The numerator (3 - 1) gives us 2, and by keeping the common denominator as 4, we get the fraction 2/4. However, it is not fully simplified, so we divide both the numerator and denominator by their greatest common factor (2), resulting in 1/2.
So, the rules to add or subtract rational numbers with common denominators are to add/subtract the numerators while keeping the common denominator the same, and then simplify the resulting fraction, if possible.
To add or subtract rational numbers with common or like denominators, follow these steps:
1. Identify the common denominator: The common or like denominator is the same for both rational numbers. It is the number that appears in the denominator of both fractions.
2. Add or subtract the numerators: For addition, simply add the numerators of the two rational numbers. For subtraction, subtract the numerators of the second rational number from the first rational number.
3. Write the result: Keep the common denominator the same, and write the result as a fraction with the sum or difference as the numerator.
Let's illustrate this with an example:
Suppose we need to add 1/4 and 3/4.
1. The common denominator is 4 since it is the same for both fractions.
2. Add the numerators: 1 + 3 = 4.
3. Write the result: The sum is 4/4.
To simplify the result, we can see that both the numerator and denominator are divisible by 4. So, we divide both numerator and denominator by 4, resulting in 1.
Therefore, 1/4 + 3/4 = 4/4 = 1.
So, when you have rational numbers with common or like denominators, you can simply add or subtract the numerators and keep the denominator the same to get the final result. In this example, the sum of 1/4 and 3/4 is 1.