How to Add and Subtract Positive and Negative NumbersNumbers Can be Positive or NegativeThis is the Number Line: Show
No Sign Means PositiveIf a number has no sign it usually means that it is a positive number. Example: 5 is really +5 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: numbers/images/number-line-add.js?sub=n Balloons and WeightsLet us think about numbers as balloons (positive) and weights (negative): This basket has balloons and weights tied to it:
Adding a Positive NumberAdding positive numbers is just simple addition. We can add balloons (we are adding positive value) the basket gets pulled upwards (positive) Example: 2 + 3 = 5is really saying "Positive 2 plus Positive 3 equals Positive 5" We could write it as (+2) + (+3) = (+5) Subtracting A Positive NumberSubtracting 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 = 3is really saying "Positive 6 minus Positive 3 equals Positive 3" We could write it as (+6) − (+3) = (+3) Adding A Negative NumberNow let's see what adding and subtracting negative numbers looks like: We can add weights (we are adding negative values) the basket gets pulled downwards (negative) Example: 6 + (−3) = 3is really saying "Positive 6 plus Negative 3 equals Positive 3" We could write it as (+6) + (−3) = (+3) The last two examples showed us that taking away balloons (subtracting a positive) or adding weights (adding a negative) both make the basket go down. So these have the same result:
In other words subtracting a positive is the same as adding a negative. Subtracting A Negative NumberLastly, we can take away weights (we are subtracting negative values) the basket gets pulled upwards (positive) Example: What is 6 − (−3) ?6−(−3) = 6 + 3 = 9 Yes indeed! Subtracting a Negative is the same as adding! Two Negatives make a Positive What Did We Find?Adding a positive number is simple addition ...Adding a Positive is Addition Positive and Negative Together ...Subtracting a Positive Example: What is 6 − (+3) ?6−(+3) = 6 − 3 = 3 Example: What is 5 + (−7) ?5+(−7) = 5 − 7 = −2 Subtracting a negative ...Subtracting a Negative is the same as Adding Example: What is 14 − (−4) ?14−(−4) = 14 + 4 = 18 The Rules: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. 5+(−2) = 5 − 2 = 3 Example: What is 25−(−4) ?−(−) are like signs, so they become a positive sign. 25−(−4) = 25+4 = 29 Starting NegativeWhat 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. −3+(+2) = −3 + 2 Start at −3 on the number line, move forward 2 and you end up at −1 −3+(+2) = −3 + 2 = −1 Example: What is −3+(−2) ?+(−) are unlike signs, so they become a negative sign. −3+(−2) = −3 − 2 Start at −3 on the number line, move back 2 and you end up at −5 −3+(−2) = −3 − 2 = −5 Now Play With It!
A Common Sense ExplanationAnd 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). Now if I say "Do NOT not eat!", I am saying I don't want you to starve, so I am back to saying "Eat!" (positive). So, two negatives make a positive, and if that satisfies you, then you are done! Another Common Sense ExplanationA friend is +, an enemy is −
A Bank ExampleExample: 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: $80−(−$10) = $80 + $10 = $90 So you get $10 more in your account. A Long Example You Might LikeAlly's PointsAlly can be naughty or nice. So Ally's parents have said "If you are nice we will add 3 points (+3).
So when we subtract a negative, we gain points So Subtracting a Negative is the same as Adding
See: both "15 − (+3)" and "15 + (−3)" result in 12. So: It doesn't matter if you subtract positive points So
Subtracting a Positive Try These Exercises ...Now try This Worksheet, and see how you go. And also try these questions: 11715, 11716, 11717, 11718, 11719, 11720, 11721, 3445, 3446 What is the rule for subtracting and adding negative and positive 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 + (-5) = 1. -17 + 22 = 5.
What are the rules for positive and negative numbers?The Rules:. Why subtracting negative number is positive?Subtracting a number is the same as adding its opposite. So, subtracting a positive number is like adding a negative; you move to the left on the number line. Subtracting a negative number is like adding a positive; you move to the right on the number line.
|