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Multiplication can often seem intimidating, but when you multiply by 1, there's nothing to worry about! The number stays exactly the same.
Let's take a number, we'll call it \( x \). When you multiply \( x \) by 1: \[ x \times 1 = x \]
The value of \( x \) doesn't change at all. It’s like having a mirror that reflects the same image back at you. This works with any number. Whether you multiply 2, 100, or even 3567 by 1, the result will always be the same number.

• This property is called the identity property of multiplication.
• It helps us understand that multiplying by 1 retains the original value.

Remember: Multiplying by 1 keeps everything constant. It’s like a friendly reminder that no changes are happening!

Division might sound tricky, but dividing by 1 is quite simple.
Just like with multiplication, when we divide by 1, the number stays the same. Consider a number \( x \). When you divide \( x \) by 1: \[ \frac{x}{1} = x \]
This shows that the value of \( x \) remains unchanged. It’s similar to slicing a cake into just one piece; you still have the entire cake.

• Division by 1 retains the original number's value.
• It reinforces the identity property of division.

So whenever you divide by 1, remember: your number stays exactly where it started!

What does it mean for a number to have a constant value? Simply put, it means the number doesn’t change under specific operations. When you multiply or divide by 1, the number remains fixed.
Let’s recap:

• When \( x \) is multiplied by 1: \x \times 1 = x
• When \( x \) is divided by 1: \frac{x}{1} = x\

The value of \( x \) does not change. This stability is called a constant value.
Understanding this helps in simplifying many mathematical problems. When you know that multiplying or dividing by 1 will keep the number constant, you can focus on other parts of the equation.
In essence, both operations leave the value untouched, reinforcing the identity properties of both multiplication and division by 1. So, when you see these operations, you can feel confident knowing that the number remains the same!