Imagine numbers as friends that have different characteristics. The number y is like a rational friend who can be expressed as a simple fraction or a ratio. For example, if y is -3, we can write it as -3/-1, which simplifies to 3. This is like saying a piece of a cake is negative 3 out of 1 piece, which is just 3 pieces of cake.
Now, let's meet z, who is our irrational friend. Z is a bit more mysterious and cannot be written as a simple fraction. It's like a never-ending decimal. For example, the square root of 2 is irrational because it goes on and on without a pattern.
So, when we have the number y as rational and negative, like -3, and z as irrational, like the square root of 2, and we add them together, the result can still be rational or irrational.
For example, if we add -3 and the square root of 2, the result is irrational. This is because the irrationality of z overpowers the rationality of y, making the sum irrational as well.
Therefore, when combining a rational negative number with an irrational number, the result can be irrational. It's like mixing a simple fraction friend with a mysterious decimal friend – the result may not always be easy to predict!