Final answer:
To do equations with rational numbers, multiply the numerators and denominators for multiplication; for addition or subtraction, get a common denominator. Simplify by canceling common factors. Always check your final answer for reasonableness.
Step-by-step explanation:
When dealing with equations with rational numbers, it's important to understand the basic operation rules. For multiplication of fractions, you simply multiply the numerators (top numbers) together and multiply the denominators (bottom numbers) together. For addition and subtraction, you need a common denominator to combine the fractions.
If we examine Example A.4.1, multiplying 2 by the fraction 15/60, we follow these steps: Multiply the numerators resulting in 30 and multiply denominators resulting in 120. We see many common factors and can simplify to get a final answer of 1/4. Remember that any fraction where numerator and denominator are equal equals 1.
For solving equations, always remember that performing the same operation on both sides of the equals sign keeps the expression as an equality. This means you can simplify, reduce or cancel out terms as long as you do so evenly on both sides. Finally, substitute the known quantities into the equation and simplify. As a last step, always check if the answer makes sense.