Problem 52 - Elementary Algebra

Question

Perform the operations. \(7(0) \div(-15)\)

Step-by-Step Solution

Answer

The result is 0.

Step 1: Calculate the Multiplication

First, perform the multiplication operation in the expression: \(7(0)\). Since any number multiplied by zero is zero, this results in: \(7 \times 0 = 0\).

Step 2: Division of Zero by a Number

Now, take the result from Step 1 and divide it by \(-15\), so we have:\(0 \div (-15)\). Dividing zero by any non-zero number yields zero. Therefore, the calculation becomes:\(0 \div (-15) = 0\).

Key Concepts

Understanding Multiplication

Multiplication is a fundamental arithmetic operation that involves taking one number and adding it to itself a specific number of times as determined by another number. Think of it as repeated addition. For example, multiplying 7 by 3 (7 x 3) is the same as adding 7, three times: 7 + 7 + 7 = 21. However, there's an important aspect of multiplication known as the zero property, which states that any number multiplied by zero equals zero.

• This means that regardless of how large or small a number might be, multiplying it by zero results in zero.
• In the exercise example, 7 multiplied by 0 gives 0.

This zero property can often simplify complex multiplications by instantly reducing the product to zero. Remember, any number times zero is always zero!

Exploring Division

Division is the process of dividing one number by another to find out how many times the divisor fits into the dividend, or how the dividend can be distributed evenly into the divisor. It's like splitting a pizza into equal slices. For instance, dividing 20 by 4 (20 ÷ 4) gives you 5 slices.

• In mathematical terms, the dividend is the number being divided, and the divisor is the number by which you divide.
• The result of a division is called the quotient.

In the original exercise, after the multiplication, we divide zero by the negative number -15. When zero is divided by any non-zero number, the result is always zero. Why? Because zero pieces of pizza divided among any number of people still leaves everyone with zero slices!

Zero Property in Arithmetic

The zero property is a fascinating principle in mathematics that applies to both multiplication and addition, although it shows its power specifically in multiplication when you get zero as the product.

• For multiplication, zero property makes calculations often straightforward, because any number times zero is zero.
• In addition, zero is the identity element, meaning any number plus zero is the number itself.

In arithmetic, this property helps simplify problems and prevent errors in calculations. In our exercise example, the zero property quickly determined that the product of 7 and 0 is zero, making subsequent calculations straightforward. Understanding and remembering these properties can greatly enhance your math skills and speed up your problem-solving process.