Problem 56 - Prealgebra

Question

Divide. $$\frac{72}{-8}$$

Step-by-Step Solution

Answer

-9

Step 1: Identify the Dividend and Divisor

In this division problem, identify the two numbers involved: the dividend 72 and the divisor -8. The expression \( \frac{72}{-8} \) means dividing 72 by -8.

Step 2: Perform Division Ignoring Signs

First, perform the division as if both numbers are positive: divide 72 by 8. Calculate \( 72 \div 8 = 9 \).

Step 3: Determine the Sign of the Result

Next, apply the rules for division of integers: when dividing two numbers with different signs, the result is negative. Therefore, \( 72 \div -8 = -9 \).

Step 4: Write Final Answer

Combining the results from previous steps, the solution to the division \( \frac{72}{-8} \) is -9.

Key Concepts

Integer Division Rules

When you need to divide integers, it's good to remember a few easy rules. They help you find the right sign of the result. Here’s what you should keep in mind:

• Dividing two positive numbers or two negative numbers gives you a positive result.
• Dividing a positive number by a negative number or a negative number by a positive number gives you a negative result.

So, "same signs give a positive, different signs give a negative." This rule is very handy because it helps you know whether your answer should be positive or negative without doing much math. Using these rules, you can easily solve problems like dividing 72 by -8. Since the dividend (72) is positive and the divisor (-8) is negative, the result is a negative number. That's why the final answer is -9.

Negative Numbers

Negative numbers can seem tricky at first, but they're not too bad once you get used to them. These are the numbers with a minus sign in front, like -1, -2, -3, and so on. Here’s a simple way to understand them:

• On a number line, negative numbers are always to the left of zero.
• When you multiply or divide, look at the signs to know if the answer is positive or negative.
• Negative numbers become positive when multiplied or divided by other negative numbers.

In the example, 72 divided by -8 involves a negative divisor. Remember, dividing a positive number by a negative gives a negative result, which is why the answer is -9. Dealing with negative numbers means keeping track of signs and knowing their rules.

Dividend and Divisor Identification

Before you can start dividing, you have to identify your numbers—and they each have a special name. Here's what they are:

• The **dividend** is the number that you are dividing. Think of it as the number being broken down into smaller parts.
• The **divisor** is the number you are dividing by. It tells you the size of the parts you're making.

In the division expression \( \frac{72}{-8} \), 72 is the dividend, and -8 is the divisor. This identification lets you know which number goes inside the division bracket (the dividend) and which number does the work of dividing (the divisor). Knowing what each number is called and what role it plays is crucial for solving division problems accurately.