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Chapter 10: Problem 9

Subtract. $$ 12-16 $$

Short Answer

Expert verified
-4

Step by step solution

01

Understand the Problem

You need to subtract 16 from 12. This means starting at 12 and counting back 16 units.
02

Identify that the Subtraction Leads to a Negative Result

Since 16 is larger than 12, you will end up with a negative number for the result.
03

Subtract the Numbers

Perform the subtraction by calculating \[ 12 - 16 = -4 \] .

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Key Concepts

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

Negative Numbers
Negative numbers are numbers less than zero. They are represented with a minus sign (-) in front of the number. For example, -5, -12, and -20 are all negative numbers. Negative numbers are the opposite of positive numbers, which are greater than zero.

When working with negative numbers, it's important to understand they represent a value below zero. In real life, negative numbers are used to represent things like debt or temperatures below freezing.

In the exercise given, the result of subtracting 16 from 12 is -4. Since 16 is larger than 12, we end up in the negative range. This tells us that moving 16 units back from 12 overshoots zero and lands us at -4.
Integer Operations
Integers are whole numbers that can be positive, negative, or zero. When performing operations with integers, like subtraction, there are specific rules to follow:
  • Subtracting a larger positive number from a smaller positive number results in a negative number.
  • Subtracting any number from a negative number makes it even more negative.
  • Subtracting a negative number from another number is the same as adding the absolute values.


For example,

14 - 5 = 9 (positive result because the first integer is larger)
7 - 12 = -5 (negative result because the second integer is larger)
-8 - 3 = -11 (negative result because a positive number is subtracted from an already negative number)
-4 - (-6) = -4 + 6 = 2 (positive result because subtracting a negative is like adding a positive)

In the provided exercise, 12 - 16 = -4 follows the rule that subtracting a larger number from a smaller one results in a negative integer.
Subtraction Process
Subtraction is one of the four basic arithmetic operations. In subtraction, the order of the numbers matters a lot.

To subtract b from a we perform a - b. In this operation, is called the 'minuend' and is the 'subtrahend'.

The subtraction process can be visualized on a number line:
  • Start at the first number (minuend).
  • Move to the left by the second number (subtrahend).
  • Land on the result.
In our exercise, we start at 12 and subtract 16, moving 16 units left.
Since 16 is larger than 12, we move past zero, ending at -4.

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Most popular questions from this chapter

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Multiply. \(-3 \cdot(-4) \cdot(-5)\)

Divide. $$ \frac{-11}{-13} $$

Subtract and simplify. \(9 \frac{3}{4}-1 \frac{2}{3}\)
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