Problem 66 - Elementary Algebra

Question

Perform the operations. $$ -5 * 3 /(-15) $$

Step-by-Step Solution

Answer

The result of the operation is 1.

Step 1: Understand the Expression

The given expression is \[-5 \times 3 \div (-15)\]which means you need to multiply \(-5\) by \(3\) and then divide the result by \(-15\).

Step 2: Perform the Multiplication

Multiply \(-5\) by \(3\), which is:\[-5 \times 3 = -15\]

Step 3: Perform the Division

Now take the result from the multiplication, which is \(-15\), and divide it by \(-15\):\[\frac{-15}{-15} = 1\]

Key Concepts

Multiplication

In elementary algebra, multiplication is one of the most basic operations we perform on numbers. When we multiply two numbers, we are essentially adding a number to itself a certain number of times. For example, multiplying \(-5\) by 3 means we are adding \(-5 + (-5) + (-5)\), which equals \(-15\).When dealing with negative numbers in multiplication:

• If both numbers being multiplied are negative, the result is positive (e.g., \(-2 \times -3 = 6\)).
• If one number is negative and the other is positive, the result is negative (e.g., \(-5 \times 3 = -15\)).

In our exercise, \(-5\) and 3 are multiplied, yielding \(-15\), which is straightforward as \(-5\) is repeated 3 times.

Division

Division is the process of determining how many times one number is contained within another. When we perform division, we divide one number (the dividend) by another number (the divisor) to find the quotient.In the given operation \(-15 \div (-15)\), \(-15\) is both the dividend and the divisor. Here's a simple breakdown:

• The dividend is the number to be divided, which is \(-15\).
• The divisor is the number you are dividing by, which in this case is \(-15\).
• The quotient represents the result of the division, which here equals 1 since any number divided by itself equals 1.

In our problem, since the same number is dividing itself, the result is 1, and no negative errors occur because a negative divided by a negative is positive.

Negative Numbers

Understanding negative numbers is crucial as they behave differently than positive numbers in mathematical operations. Negative numbers are indicated by a minus sign \(-\)and can represent opposite directions or a deficit. Consider the basic rules for operations:

• The product of two negative numbers is positive (e.g., \(-4 \times -2 = 8\)).
• The product of a negative number and a positive number is negative (e.g., \(-5 \times 3 = -15\)).
• Dividing a negative by a negative results in a positive (e.g., \(-15 \div -3 = 5\)).
• Dividing a positive by a negative gives a negative (e.g., \(15 \div -3 = -5\)).

In the original exercise, understanding that \(-15 \div -15\) results in +1 is based on these rules, as dividing two negatives always results in a positive outcome. Learning these concepts helps one to navigate through algebraic problems efficiently.