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Do you remember learning in school about the little sideways signs that look like little arrowheads:< >A lot of us know that these signs mean greater than and less than, but cant seem to remember which sign is which.But first, what do these signs mean?These signs are used when math problems dont have a clear answer, which are also called inequalities. Inequalities compare two things, showing the relationship between them. The word inequality means that two things are not equal.The two signs < and > are signs that are used when youre comparing two things in math. With math, you usually have to solve the problem, but when using the greater than and less than signs, youre showing if a number is greater than or less than another number rather than actually solving a problem.Which sign is which?The > symbol means greater than. It shows that one number or value is larger than another number. For example: 5 > 2If you see the symbol < it means that one number is smaller than the other number. For exam: 2 < 6The symbols look similar and can easily be confused by which symbol is which.Open EndsAn easy way to remember which symbol is which is to remember that the open end of the symbol is always facing the bigger number and the arrow points to the small number.The Alligator MethodAnother way to remember the greater than and less than signs is something that you may remember from grade school: the Alligator Method.Imagine the symbols as an alligator mouth with the numbers on each side being little fish. The alligator will always want to eat a larger number of fish. Whichever number is larger, the alligator mouth is opened towards that number.If you were given 5 and 8 and were told to show which number is greater than or less than, the alligator would open his mouth towards the 8. This shows that 5 is less than 8.The same would work if you were given 10 and 4. The alligator mouth would open towards the 10, showing that the 10 is greater than 4.L MethodLess than sign starts with the letter L. The less than sign also looks like an L and the greater than sign > does not. So because the greater than sign does not look like an L, it can never be less than. Need more math help?Our online math college readiness course offers self-paced lessons, easy-to-follow videos, and diverse practice problems to teach you essential math skills.Click here to find out more about how our math course can help you.More Basic Math Review Tips & Videos | Multiplication Charts and Worksheets | Test Prep Resources: GED, TEAS, ASVAB, GRE lo1kvxu-Dc8 As well as the familiar equals sign (=) it is also very useful to show if something is not equal to (≠) greater than (>) or less than (<) These are the important signs to know: = When two values are equalwe use the equals sign example: 2+2 = 4 ≠ When two values are definitely not equalwe use the not equal to sign example: 2+2 ≠ 9 < When one value is smaller than anotherwe use a less than sign example: 3 < 5 > When one value is bigger than anotherwe use a greater than sign example: 9 > 6 Less Than and Greater Than The less than sign and the greater than sign look like a V on its side, dont they? To remember which way around the < and > signs go, just remember: The small end always points to the smaller number, like this: Greater Than Symbol: BIG > small 10 > 5 10 is greater than 5 Or the other way around: 5 < 10 5 is less than 10 Do you see how the symbol points at the smaller value? ... Or Equal To ... Sometimes we know a value is smaller, but may also be equal to! Example, a jug can hold up to 4 cups of water.So how much water is in it?It could be 4 cups or it could be less than 4 cups: So until we measure it, all we can say is less than or equal to 4 cups. To show this, we add an extra line at the bottom of the less than or greater than symbol like this: The less than or equal to sign: ≤ The greater than or equal to sign: ≥ All The Symbols Here is a summary of all the symbols: Symbol Words Example Use = equals 1 + 1 = 2 ≠ not equal to 1 + 1 ≠ 1 > greater than 5 > 2 < less than 7 < 9 ≥ greater than or equal to marbles ≥ 1 ≤ less than or equal to dogs ≤ 3 Why Use Them? Because there are things we do not know exactly ... ... but can still say something about. So we have ways of saying what we do know (which may be useful!) Example: John had 10 marbles, but lost some. How many has he now? Answer: He must have less than 10: Marbles < 10 If John still has some marbles we can also say he has greater than zero marbles: Marbles > 0 But if we thought John could have lost all his marbles we would say Marbles ≥ 0 In other words, the number of marbles is greater than or equal to zero. Combining We can sometimes say two (or more) things on the one line: Answer: Something greater than $0 and less than $10 (but NOT $0 or $10): What Becky Spends > $0What Becky Spends < $10 This can be written down in just one line: $0 < What Becky Spends < $10 That says that $0 is less than What Becky Spends (in other words What Becky Spends is greater than $0) and what Becky Spends is also less than $10. Notice that > was flipped over to < when we put it before what Becky spends. Always make sure the small end points to the small value. Changing Sides We saw in that previous example that when we change sides we flipped the symbol as well. This: Becky Spends > $0 (Becky spends greater than $0) is the same as this: $0 < Becky Spends ($0 is less than what Becky spends) Just make sure the small end points to the small value! Here is another example using ≥ and ≤: Answer: Something greater than, or possibly equal to, $0 and less than, or possibly equal to, $10: Becky Spends ≥ $0Becky Spends ≤ $10 This can be written down in just one line: $0 ≤ Becky Spends ≤ $10 A Long Example: Cutting Rope Here is an interesting example I thought of: Example: Sam cuts a 10m rope into two. How long is the longer piece? How long is the shorter piece? Answer: Let us call the longer length of rope L, and the shorter length S L must be greater than 0m (otherwise it isnt a piece of rope), and also less than 10m: L > 0L < 10 So: 0 < L < 10 That says that L (the Longer length of rope) is between 0 and 10 (but not 0 or 10) The same thing can be said about the shorter length S: 0 < S < 10 But I did say there was a shorter and longer length, so we also know: S < L (Do you see how neat mathematics is? Instead of saying the shorter length is less than the longer length, we can just write S < L) We can combine all of that like this: 0 < S < L < 10 That says a lot: 0 is less that the short length, the short length is less than the long length, the long length is less than 10. Reading backwards we can also see: 10 is greater than the long length, the long length is greater than the short length, the short length is greater than 0. It also lets us see that S is less than 10 (by jumping over the L), and even that 0<10 (which we know anyway), all in one statement. NOW, I have one more trick. If Sam tried really hard he might be able to cut the rope EXACTLY in half, so each half is 5m, but we know he didnt because we said there was a shorter and longer length, so we also know: S<5 and L>5 We can put that into our very neat statement here: 0 < S < 5 < L < 10 And IF we thought the two lengths MIGHT be exactly 5 we could change that to 0 < S ≤ 5 ≤ L < 10 An Example Using Algebra OK, this example may be complicated if you dont know Algebra, but I thought you might like to see it anyway: If x > 11 , then x+3 > 14 (Imagine that x is the number of people at your party. If there are more than 11 people at your party, and 3 more arrive, then there must be more than 14 people at your party now.) 5250, 5251, 5252, 5253, 5254, 5255, 5256, 5257, 5258, 5259 Copyright © 2021 MathsIsFun.com

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