## The Rules of Using Positive and Negative Integers

Illustration by Hugo Lin. ThoughtCo.

- Math Tutorials
- Pre Algebra & Algebra
- Exponential Decay
- Worksheets By Grade

Whole numbers, figures that do not have fractions or decimals, are also called integers . They can have one of two values: positive or negative.

- Positive integers have values greater than zero.
- Negative integers have values less than zero.
- Zero is neither positive nor negative.

The rules of how to work with positive and negative numbers are important because you'll encounter them in daily life, such as in balancing a bank account, calculating weight, or preparing recipes.

## Tips for Success

- Context can help you make sense of unfamiliar concepts. Try and think of a practical application like keeping score when you're practicing.
- Using a number line showing both sides of zero is very helpful to help develop the understanding of working with positive and negative numbers/integers.
- It's easier to keep track of the negative numbers if you enclose them in brackets .

If you're calculating the sum of two negative integers, it looks like this:

## Subtraction

## Multiplication

Dividing one negative integer and one positive integer results in a negative number:

## Sciencing_Icons_Science SCIENCE

## Math Problems With Positives and Negatives

## How to Make a Negative Sign With the TI-84 Plus

## Temperature

## Modeling With Chips

## Related Articles

- Math Beyond School: Applications of Integers
- Math Guide: Operations on Integers
- Math Goodies: Integers

Ryan McVay/Photodisc/Getty Images

## Find Your Next Great Science Fair Project! GO

We Have More Great Sciencing Articles!

## How to Add and Subtract Positive and Negative Numbers

Numbers can be positive or negative.

## No Sign Means Positive

If a number has no sign it usually means that it is a positive number.

## Play with it!

On the Number Line positive goes to the right and negative to the left.

Try the sliders below and see what happens:

## Balloons and Weights

Let us think about numbers as balloons (positive) and weights (negative):

This basket has balloons and weights tied to it:

## Adding a Positive Number

Adding positive numbers is just simple addition.

We can add balloons (we are adding positive value)

the basket gets pulled upwards (positive)

## Example: 2 + 3 = 5

"Positive 2 plus Positive 3 equals Positive 5"

We could write it as (+2) + (+3) = (+5)

## Subtracting A Positive Number

Subtracting positive numbers is just simple subtraction.

We can take away balloons (we are subtracting positive value)

the basket gets pulled downwards (negative)

## Example: 6 − 3 = 3

"Positive 6 minus Positive 3 equals Positive 3"

We could write it as (+6) − (+3) = (+3)

## Adding A Negative Number

Now let's see what adding and subtracting negative numbers looks like:

We can add weights (we are adding negative values)

## Example: 6 + (−3) = 3

"Positive 6 plus Negative 3 equals Positive 3"

We could write it as (+6) + (−3) = (+3)

So these have the same result :

In other words subtracting a positive is the same as adding a negative .

## Subtracting A Negative Number

Lastly, we can take away weights (we are subtracting negative values)

## Example: What is 6 − (−3) ?

Yes indeed! Subtracting a Negative is the same as adding!

## What Did We Find?

## Example: What is 5 + (−7) ?

## Subtracting a negative ...

It can all be put into two rules :

They are "like signs" when they are like each other (in other words: the same).

So, all you have to remember is:

Two like signs become a positive sign

Two unlike signs become a negative sign

## Example: What is 5+(−2) ?

+(−) are unlike signs (they are not the same), so they become a negative sign .

## Example: What is 25−(−4) ?

−(−) are like signs, so they become a positive sign .

## Starting Negative

What if we start with a negative number?

Using The Number Line can help:

## Example: What is −3+(+2) ?

+(+) are like signs, so they become a positive sign .

## Example: What is −3+(−2) ?

+(−) are unlike signs, so they become a negative sign .

## Now Play With It!

And there is a "common sense" explanation:

If I say "Eat!" I am encouraging you to eat (positive)

If I say "Do not eat!" I am saying the opposite (negative).

So, two negatives make a positive, and if that satisfies you, then you are done!

## Another Common Sense Explanation

## A Bank Example

Example: last year the bank subtracted $10 from your account by mistake, and they want to fix it..

So the bank must take away a negative $10 .

Let's say your current balance is $80, so you will then have:

So you get $10 more in your account.

## A Long Example You Might Like

Ally can be naughty or nice. So Ally's parents have said

So when we subtract a negative, we gain points (i.e. the same as adding points).

See: both " 15 − (+3) " and " 15 + (−3) " result in 12.

## Try These Exercises ...

Now try This Worksheet , and see how you go.

- Words with Friends Cheat
- Wordle Solver
- Word Unscrambler
- Scrabble Dictionary
- Anagram Solver
- Wordscapes Answers

Sign up for our weekly newsletters and get:

By signing in, you agree to our Terms and Conditions and Privacy Policy .

We'll see you in your inbox soon.

## Basic Rules for Positive and Negative Numbers

- DESCRIPTION rules for adding and subtracting two numbers positive and negative
- SOURCE Created by Karina Goto for YourDictionary
- PERMISSION Owned by YourDictionary, Copyright YourDictionary

## Rules for Signed Numbers

## Addition: Same Signs, Add the Numbers

## Addition: Different Signs, Subtract the Numbers

## Subtraction: Switch to Addition

- -3 - (+5) becomes -3 + (-5) = -8
- 9 - (-7) becomes 9 + (+7) = 16
- -14 - (+8) becomes -14 + (-8) = -22
- 25 - (-90) becomes 25 + (+90) = 115

## Multiplication and Division: Same Sign, Positive Result

- DESCRIPTION rules for multiplying and dividing two numbers positive and negative
- PERMISSION Owned by YourDictionary, Copyright YourDictionary

## Multiplication and Division: Opposite Sign, Negative Result

## Like and Unlike Signs in Addition and Subtraction

- 7 + (+2) = 9 (++ are like signs, so the equation is addition)
- 9 + (-8) = 1 (+- are unlike signs, so the equation is subtraction)
- 11 - (+13) = 2 (-+ are unlike signs, so the equation is subtraction)
- 15 - (-10) = 25 (-- are like signs, so the equation is addition)

## Understanding Math Foundations

## Broad topic: The Number System and Place Value

- Comparing and ordering numbers 73
- Complex numbers 22
- Counting 94
- Integers 33
- Number bases 25
- Place value 126
- Positive and negative numbers 22
- Rational and irrational numbers 23
- Reading, writing and representing numbers 33
- Standard index form/Scientific notation 5
- Register for our mailing list

The home of mathematics education in New Zealand.

Solve addition and subtraction problems with integers (positive and negative numbers).

## 6 Minus 8 Does Work!

Bucket balance, chilly heights.

solve addition and subtraction problems involving integers

## Disappearing Dollars

add and subtract integers using money context

## Dollars and Bills

Dropping and rising temperatures.

add and subtract with integers

## Hills and Dales

## Integer Slam

Integer zap, it's a try, learning to drive.

add and subtract integers that are multiples of ten

## Lifting Weights

Money matters, number in statistics.

## Shifty Subtraction

## Strategic Solving Part III

The volcanoes erupt, using integer tiles, video viewing, walking the plank.

- Arts & Music
- English Language Arts
- World Language
- Social Studies - History
- Holidays / Seasonal
- Independent Work Packet
- Easel by TPT
- Google Apps

## Interactive resources you can assign in your digital classroom from TPT.

## Easel Activities

## Easel Assessments

Unlock access to 4 million resources — at no cost to you — with a school-funded subscription..

positive and negative integers word problems

## All Formats

Resource types, all resource types, results for positive and negative integers word problems.

## Positive and Negative Integer Word Problem Task Cards

## Integer (Positive and Negative!) Word Problems - Worksheet & Task Cards

## Positive and Negative Integers Operations and Word Problems

Also included in: Middle School Math Worksheets and PowerPoint Bundle

## Adding and subtracting positive and negative integers word problems

## Positive and Negative Integers Word Problems Activity

## Adding & Subtracting Positive/Negative Integers with Chip Models & Number Lines

Also included in: INTEGER ADDITION & SUBTRACTION - Positives & Negatives Bundle :D

## Integers Unit - Subtracting, Adding, Dividing, Multiplying, Word Problems

## INTEGERS & COORDINATE PLANE Homework Worksheets: Skills Practice & Word Problems

Also included in: 6th Grade Math Assessments, Warm-Ups, Task Cards, Worksheets BUNDLE

## Adding and Subtracting Integer Word Problems

## Inequalities - Notes and Practice (Includes Word Problems!)

Also included in: Inequalities Bundle (Writing, Solving and Graphing)

## Integer Operations Word Problems

Also included in: Integer Operations BUNDLE with stations, notebook page, and word problems

## Integers Unit - Adding Subtracting Multiplying & Dividing Integers

## INTEGERS & COORDINATE PLANE Error Analysis, Word Problems, HW Practice BUNDLE

## Positive and Negative Integers Game - Writing Integers on a Number Line Activity

Also included in: 6th Grade Math Review Games for the Entire Year BUNDLE - Math Activities

## Adding and Subtracting Integers: Who is Correct? Word Problems

## INTEGERS & the COORDINATE PLANE Word Problems - Error Analysis (Find the Error)

## Positive and Negative Integer Word Vocabulary Activity

## Integers Worksheets & Absolute Value Word Problems + Fun Game | 6.NS.5, TEK 6.2C

Also included in: NUMBEROCK's Ultimate Integers & Absolute Value Bundle | Aligns 6.NS.5 TEK 6.2B

## 6th grade Math Warm-Up Bundle: Daily Spiral Review & Word Problem Solving

## Integers Bundle

## 6.NS.5 Task Cards ✦ Integers | Positive & Negative Numbers For Google Classroom™

Also included in: 6th Grade Math Review Digital Task Cards | Word Problems for Google Classroom™

## Integer Word Problems - Homework Assessment Task Cards - Differentiated!

## Adding and Subtracting Rational Numbers Word Problems Digital Pixel Art Activity

Also included in: 7th Grade Math Pixel Art Activities Growing Bundle

## INTEGERS & the COORDINATE PLANE Word Problems with Graphic Organizer

Also included in: 6th Grade Math WORD PROBLEMS Graphic Organizer BUNDLE

TPT empowers educators to teach at their best.

## Keep in Touch!

## Integers Worksheets

## Most Popular Integers Worksheets this Week

## General Use Printables

General use integers printables including coordinate grid paper and number lines.

## Coordinate grid paper

## Number lines

## Comparing & Ordering Integers Worksheets

Comparing and ordering integers worksheets for learning about ordinality in integers.

## Comparing random pairs of integers

## Comparing pairs of integers in close proximity

## Ordering/Sorting Integers

## Adding & Subtracting Integers Worksheets

## Adding integers worksheets

## Vertically arranged integer addition

## Scaffolded Integer Addition and Subtraction

## Subtracting integers worksheets

## Vertically arranged integer subtraction

## Mixed adding and subtracting integers worksheets

## Multiplying & Dividing Integers Workshets

## Multiplying integers

## Dividing integers

## Mixed Operations with Integers Worksheets

Integers worksheets with a mixture of four operations on the same page.

## IMAGES

## VIDEO

## COMMENTS

As with multiplication, the rules for dividing integers follow the same positive/negative guide. Dividing two negatives or two positives yields

learn the rules of positive and negative numbers.

The symbol (-) is placed in front of negative numbers at all times. The symbol (+) may or may not be placed in front of positive numbers, and

Play with it! On the Number Line positive goes to the right and negative to the left. Try the sliders below and see what happens: 6 + (−2) = 4. integer

To subtract signed numbers (either positive or negative), ... E. Solve the following word problems using positive and negative numbers.

If you're adding positive and negative numbers together, subtract the smaller number from the larger one and use the sign from the larger number. For example: 6

In this problem, we're investigating the number of steps we would climb up or down to get out of or into the swimming pool. How could you number the steps below

Level Four. Number and Algebra. Numeracy activities. Solve addition and subtraction problems with integers (positive and negative numbers). Resource logo

They will draw random positive or negative integer cards for each problem and use the number line and arrow as a manipulative to solve.

In positive minus positive questions, if the subtrahend is greater than the minuend, the answer will be negative. In negative minus negative questions, if the