What Does A Negative And A Positive Make

What does a negative and a positive make? When a negative number and a positive number are added, the result can be positive, negative, or zero. The outcome depends on their absolute values: the number farther from zero determines the sign of the answer, while the difference between the two values gives its size. If the numbers are multiplied or divided instead, however, a negative and a positive always make a negative result.

Introduction

The expression “a negative and a positive” usually refers to adding two numbers with opposite signs, such as:

• −7 + 4
• 5 + (−8)
• −12 + 20

People often wonder whether the answer must always be negative or positive because the two signs appear to “cancel out.” They can cancel each other completely, but only when their distances from zero are equal. Otherwise, the value with the greater absolute value has more influence on the final result.

To give you an idea, −7 + 4 is not automatically negative because it begins with −7. In real terms, instead, the two values represent opposite amounts, and four units of positive value remove four units of the seven-unit debt. Three units remain, so the answer is −3.

Scientific Explanation

Mathematics uses signed numbers to represent quantities with opposite directions or meanings. Because of that, a positive number may represent money in an account, movement to the right, a rise in temperature, or an increase in height. A negative number may represent debt, movement to the left, a drop in temperature, or a decrease in height.

The absolute value of a number is its distance from zero without considering its sign. For example:

• |−7| = 7
• |4| = 4
• |−12| = 12
• |20| = 20

When a positive and negative number are added, their effects oppose one another. The larger absolute value represents the stronger effect, so its sign appears in the final answer. The smaller effect is subtracted from the larger one Turns out it matters..

This is why −7 + 4 = −3: seven units of negative value are reduced by four units of positive value, leaving three units of negative value That alone is useful..

Steps for Adding a Negative and a Positive

Follow these steps whenever you add numbers with opposite signs:

1. Identify both signs. Determine which number is positive and which is negative.
2. Find the absolute values. Ignore the signs temporarily and compare the numbers as ordinary values.
3. Subtract the smaller absolute value from the larger one. This gives the size of the answer.
4. Use the sign of the number with the larger absolute value. That sign belongs to the final result.

Consider −11 + 6:

• The absolute values are 11 and 6.
• Subtract: 11 − 6 = 5.
• Since 11 belongs to the negative number, use a negative sign.
• So, −11 + 6 = −5.

Now consider 4 + (−9):

• The absolute values are 4 and 9.
• Subtract: 9 − 4 = 5.
• Since 9 belongs to the negative number, the answer is −5.

When the absolute values are equal, such as −6 + 6, the values cancel completely. The result is zero, which has neither a positive nor a negative sign.

Examples With Different Outcomes

Adding a negative and a positive can produce any of the three types of signed result.

A Negative Result

−10 + 3 = −7

The negative number has the larger absolute value, so the answer remains negative The details matter here..

A Positive Result

8 + (−2) = 6

The positive number is farther from zero, so the answer is positive.

A Result of Zero

−5 + 5 = 0

Both numbers have the same absolute value, so they are opposites and cancel each other Easy to understand, harder to ignore..

These examples show why it is incorrect to assume that a negative plus a positive must always be negative. The operation combines both magnitude and direction rather than simply placing the signs side by side Easy to understand, harder to ignore..

Using a Number Line

A number line provides a visual explanation. Start at zero and move according to each number:

• Move right for a positive number.
• Move left for a negative number.

For −4 + 7, begin at zero, move four spaces left to reach −4, and then move seven spaces right. You pass zero and stop at 3. So, −4 + 7 = 3.

For 6 + (−9), begin at zero, move six spaces right, and then move nine spaces left. Consider this: you pass zero and stop at −3. Which means, 6 + (−9) = −3 That's the whole idea..

The number line makes the cancellation clear. Positive movement cancels negative movement, and any remaining distance from zero determines the answer.

Why Subtracting a Negative Becomes Addition

Some learners become confused when a problem contains two minus signs, such