Questions and Answers
When adding rational numbers, you can add the denominators and then multiply by the numerators.
False
To subtract rational numbers, you need to find a common denominator and then subtract the denominators.
False
The formula for adding rational numbers $(a/b) + (c/d)$ is $(a+c)/(b+d)$.
False
When adding or subtracting rational numbers, it is essential to have a common denominator.
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Simplifying the answer by dividing both numerator and denominator by their greatest common divisor (GCD) is optional.
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The formula for subtracting rational numbers $(a/b) - (c/d)$ is $((a+c)/(b+d))$.
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Study Notes
Adding Rational Numbers
- To add rational numbers, follow these steps:
- Find a common denominator (LCD) for the two fractions.
- Convert both fractions to have the LCD.
- Add the numerators (numbers on top) and keep the same denominator.
- Simplify the answer, if possible.
Example:
(a/b) + (c/d) = ((ad + bc) / bd)
Subtracting Rational Numbers
- To subtract rational numbers, follow these steps:
- Find a common denominator (LCD) for the two fractions.
- Convert both fractions to have the LCD.
- Subtract the numerators (numbers on top) and keep the same denominator.
- Simplify the answer, if possible.
Example:
(a/b) - (c/d) = ((ad - bc) / bd)
Key Points to Remember
- When adding or subtracting rational numbers, it is essential to have a common denominator.
- Simplify the answer by dividing both numerator and denominator by their greatest common divisor (GCD).
- Always check if the result can be simplified further.
Adding Rational Numbers
- To add rational numbers, find a common denominator (LCD) for the two fractions.
- Convert both fractions to have the LCD.
- Add the numerators (numbers on top) and keep the same denominator.
- Simplify the answer, if possible.
- The formula for adding rational numbers is
(a/b) + (c/d) = ((ad + bc) / bd).
Subtracting Rational Numbers
- To subtract rational numbers, find a common denominator (LCD) for the two fractions.
- Convert both fractions to have the LCD.
- Subtract the numerators (numbers on top) and keep the same denominator.
- Simplify the answer, if possible.
- The formula for subtracting rational numbers is
(a/b) - (c/d) = ((ad - bc) / bd).
Key Points to Remember
- A common denominator is essential when adding or subtracting rational numbers.
- Simplify the answer by dividing both numerator and denominator by their greatest common divisor (GCD).
- Always check if the result can be simplified further.
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