Problem 16 - Algebra A Combined Function

Question

Multiply. (3)(-5)(-2)(0)

Step-by-Step Solution

Answer

The product is zero.

Step 1: Multiply the First Two Numbers

Multiply the first two numbers, which are 3 and -5: \[(3)(-5) = -15\]

Step 2: Multiply the Result with the Next Number

Now take the result from the first two numbers (-15) and multiply it by the next number (-2):\[(-15)(-2) = 30\]

Step 3: Multiply by Zero

Finally, multiply the last result (30) by 0. Since any number multiplied by zero is zero:\[(30)(0) = 0\]

Key Concepts

Zero Property

The zero property of multiplication is a fundamental concept that states any number multiplied by zero equals zero. This principle applies universally, whether the numbers involved are positive, negative, fractions, or even variables.
For instance, in the problem (3)(-5)(-2)(0), the zero is a game-changer. Despite the calculation of earlier steps, once a zero is involved, the final result is automatically zero. This property is so crucial because it simplifies complex calculations without further need for extensive computation.
It's helpful to remember that no matter how big or small a number is, multiplying it by zero will always reduce it to zero. So in any multiplication sequence, if a zero appears, you can conclude the multiplication right there.

Negative Numbers

Understanding negative numbers is essential when dealing with multiplication. Negative numbers are numbers less than zero, often found on the left side of the number line. They represent opposite values to their positive counterparts.
When multiplying negative numbers, remember these key rules:

• A positive times a negative equals a negative.
• A negative times a positive equals a negative.
• A negative times a negative equals a positive.

In our original problem, you're asked to multiply (3)(-5)(-2)(0). First, multiplying 3 by -5 gives you -15, because a positive multiplied by a negative results in a negative. Then, multiplying -15 by -2 yields 30, since multiplying two negatives results in a positive.

Step-by-Step Multiplication

Step-by-step multiplication is a methodical way to solve multiplication problems involving more than two numbers. It involves multiplying two numbers at a time and using their product for the next multiplication.
To illustrate, consider the problem (3)(-5)(-2)(0).

• Step 1: Start with the first two numbers: Multiply 3 by -5 to get -15. This matches the rule of positive times negative equals negative.
• Step 2: Take the result from Step 1 (-15) and multiply it by the next number (-2). Here, since both numbers are negative, the product is positive (30).
• Step 3: Finally, multiply this positive product (30) by the last number, which is zero. The multiplication process ends here with a result of 0, demonstrating the zero property's effect on multiplication.

Breaking down the process into these smaller, manageable steps makes it easier to track operations and ensures accuracy through the calculation.