how to do the sums and products of rational numbers quick check
To do the sums and products of rational numbers, follow these steps:
1. Simplify the given rational numbers if necessary by canceling out common factors in the numerator and denominator.
2. Determine the operation to be performed (addition, subtraction, multiplication, or division) based on the problem.
3. For addition or subtraction:
- Find a common denominator by multiplying the denominators of the rational numbers.
- Rewrite each rational number with the common denominator.
- Add or subtract the numerators while keeping the common denominator the same.
- Simplify the resulting fraction if possible.
4. For multiplication:
- Multiply the numerators together to get the new numerator.
- Multiply the denominators together to get the new denominator.
- Simplify the resulting fraction if possible.
5. For division:
- Invert the second rational number (also known as the reciprocal) by swapping the numerator and denominator.
- Multiply the first rational number by the inverted second rational number.
- Simplify the resulting fraction if possible.
After performing the necessary calculations, check your work for accuracy and simplify the final fraction whenever possible.
To do the sums and products of rational numbers, follow these steps:
1. Simplify the fractions: If the fractions are not in their simplest form, simplify them by finding the greatest common divisor (GCD) of the numerator and denominator and dividing both by it.
2. Addition of rational numbers:
a. Find a common denominator: If the fractions have different denominators, find a common denominator by taking the least common multiple (LCM) of the denominators.
b. Add the fractions: Once you have a common denominator, add the numerators of the fractions and keep the denominator the same.
3. Multiplication of rational numbers:
a. Multiply the numerators: Multiply the numerators of the fractions together.
b. Multiply the denominators: Multiply the denominators of the fractions together.
c. Simplify the result: If possible, simplify the resulting fraction by dividing the numerator and denominator by their GCD.
4. Write the final answer in the proper form: Make sure to write the final answer as a simplified fraction, mixed number, or decimal, depending on the question's requirements.
Remember to double-check your calculations and simplify your answers whenever possible to ensure accuracy.