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Chapter 3: Problem 447

In the following exercises, divide. $$ 56 \div(-8) $$

Short Answer

Expert verified
-7

Step by step solution

01

Identify the numbers

The first step is to identify the numbers involved in the division problem. In this case, we are dividing 56 by -8.
02

Understand the division of positive and negative numbers

When dividing a positive number by a negative number, the result will always be negative. This is because a positive divided by a negative results in a negative.
03

Perform the division

Now, simply divide the absolute values of the numbers \( 56 \div 8 = 7 \). Since we are dividing by a negative number, the result will be \( -7 \).
04

Write the final answer

Putting it all together, the result of dividing 56 by -8 is \( -7 \).

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

dividing positive and negative numbers
When you divide numbers, the sign (positive or negative) matters a lot.
In our example, the division problem is with a positive number (56) and a negative number (-8).
The rule to remember is simple:
  • If the signs are different (one positive and one negative), the result is always negative. For example, 56 divided by -8 gives -7.
  • If the signs are the same (both positive or both negative), the result is always positive. For example, -56 divided by -8 gives +7.
Knowing these rules helps you quickly determine the sign of your answer.
absolute value
Understanding absolute value is key in division, especially when dealing with negative numbers.
The absolute value of a number is its distance from 0 on the number line, regardless of direction.
This means:
  • The absolute value of 56 is 56.
  • The absolute value of -8 is 8.
In other words, you temporarily ignore the signs and work with the positive values.
So, when dividing 56 by -8, you first divide the absolute values: \(56 \div 8 = 7\).
After you get the result, you then apply the correct sign, based on the rules for dividing positive and negative numbers.
integer division
Integer division involves dividing whole numbers.
This is simpler than dividing fractions or decimals. Let's go through our example step by step:
  • Identify the numbers to divide: 56 and -8.
  • Find the absolute values: 56 and 8.
  • Divide the absolute values: \( 56 \div 8 = 7 \).
  • Apply the rules for signs (since we are dividing a positive by a negative, the result is -7).
Integer division is straightforward because it deals only with whole numbers.
And you follow simple rules for positive and negative signs to get your final answer.

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