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This is the Number Line:
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: numbers/images/number-line-add.js?sub=n Let us think about numbers as balloons (positive) and weights (negative): This basket has balloons and weights tied to it:
Adding positive numbers is just simple addition. We can add balloons (we are adding positive value) the basket gets pulled upwards (positive)
is 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)
is really saying "Positive 6 minus Positive 3 equals Positive 3" We could write it as (+6) − (+3) = (+3) Now 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)
is 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) 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 Subtracting a negative ...
Subtracting a Negative is the same as Adding 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
+(−) are unlike signs (they are not the same), so they become a negative sign. 5+(−2) = 5 − 2 = 3
−(−) 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:
+(+) 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
+(−) 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 Example
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). If you are naughty, we take away 3 points (−3). When you reach 30 Points you get a toy."
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 or add negative points, you still end up losing 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 Copyright © 2021 MathsIsFun.com |