Is 810 Greater Than 34? The 48 Correct Answer

video transcript

Most of us know the equals sign from the early days of arithmetic. You might see something like 1 plus 1 equals 2. Well, a lot of people might think if they see something like that means equal in some way, give me the answer. 1 plus 1 is the problem. Equal means the answer to me and 1 plus 1 equals 2. That’s not what equal actually means. Equal is really just trying to compare two sizes. When I write 1 plus 1 equals 2, it literally means that what I have on the left side of the equals sign is exactly the same amount as what I have on the right side of the equals sign. I might as well have written 2 equals 1 plus 1. These two things are the same. I could have written 2 equals 2. That is an absolutely true statement. These two things are the same. I could have written 1 plus 1 equals 1 plus 1. I could have written 1 plus 1 minus 1 equals 3 minus 2. These are both the same size. What I have here on the left is 1 plus 1 minus 1 is 1 and this on the right is 1. These are both equal amounts. Now I will introduce you to other ways to compare numbers. The equals sign is when I have exactly the same amount on both sides. Now let’s consider what we can do when we have different amounts on both sides. So let’s say I have number 3 and I have number 1 and I want to compare them. So 3 and 1 are clearly not equal. In fact, I could make that statement with an unequal sign. So I could say that 3 does not equal 1. But let’s say I want to find out which one is bigger and which one is smaller. So if I want to have an icon where I can compare them, where I can say, where I can indicate which one is bigger. And the symbol for that is the greater-than symbol. This would literally be read as 3 is greater than 1. 3 is a larger amount. And if you’re having trouble remembering what that means – greater than – the greater amount is written on the opening. I guess you could think of this as some kind of arrow or some kind of symbol, but that’s the bigger side. Here you have this little tiny dot and here you have the big side, so the bigger amount is on the big side. This would literally be read as 3 is greater than – so let me write that – greater than, 3 is greater than 1. And again, they just don’t have to be numbers like that. I could write an expression. I could write 1 plus 1 plus 1 is greater than, say, just a 1 right over there. That makes a comparison. But what if we had things the other way around. What if I wanted to make a comparison between 5 and, say, 19. So now the greater-than symbol would not apply. It’s not true that 5 is greater than 19. I could say that 5 does not equal 19. So I could still make that statement. But what if I wanted to make a statement about which is larger and which is smaller? Well, as in plain language, I would want to say that 5 is less than 19. So I would want to say — let me write that down — I want to write that 5 is less than 19. That’s what I want to say. And so we just have to think of a mathematical notation for writing “is less than”. Well, if this is greater than then it makes perfect sense that we just swap it. Let’s say again that the dot points to the smaller set and the large side of the symbol points to the larger set. So here 5 is a smaller quantity, so I’ll emphasize the point there. And 19 is a larger amount, so I’ll make it that open. So that would be read as 5 is less than 19. 5 is a smaller quantity than 19. I could also write that as 1 plus 1 is less than 1 plus 1 plus 1. It’s just saying that this statement, this quantity, 1 is plus 1 is less than 1 plus 1 plus 1.

Do you remember at school you learned about the little sideways signs that look like little arrowheads:

< >

Many of us know these characters mean “greater than” and “less than” but can’t seem to remember which character is which.

But first, what do these signs mean?

These signs are used when math problems do not have a definite answer, also known as inequalities. Inequalities compare two things and show the relationship between them. The word “inequality” means that two things are not the same.

The two signs < and > are signs used when you are comparing two things in math. In math, you usually have to solve the problem, but using the greater-than and less-than signs shows whether a number is greater or less than another number, rather than actually solving a problem.

Which sign is what?

The symbol > means “greater than”. It shows that a number or value is greater than another number. For example: 5 > 2

When you see the < symbol, it means that one number is less than the other number. For the exam: 2 < 6 The symbols look similar and it is easy to get confused as to which symbol is which. open ends An easy way to remember which symbol this is is to remember that the open end of the symbol always faces the larger number and the arrow points to the smaller number. The alligator method Another way to memorize the "greater than" and "less than" signs is something you might remember from elementary school: the alligator method. Think of the symbols as an alligator's mouth, with the numbers on either side being small fish. The alligator will always want to eat larger numbers of fish. Regardless of which number is larger, the alligator's mouth will open toward that number. If you were given 5 and 8 and asked to show which number is greater or less than, the alligator would open its mouth towards the 8. This shows that 5 is less than 8. The same would work if you got 10 and 4. The alligator's mouth would open on the 10, showing that the 10 is greater than the 4. L method The less than character starts with the letter L. The less than character also looks like an L and the greater than > doesn’t. So since the greater-than sign doesn’t look like an L, it can never be “less than”.

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“Much greater” is used to indicate a strong inequality, where not only greater than , but much greater (by convention) is denoted by . For an astronomer, “much” might mean a factor of 100 (or even 10), while for a mathematician it might mean a factor of (or even many more).

Euclid used the terminology that if is greater than and greater than then must be much (or far) greater than. In this sense, “far greater than” is equivalent to “greater than” for a dense set of ordered quantities.

What is 20 times greater than 5?

20 times greater than 5 seems easy enough, but is it? Let’s say the answer is = 100 (since 20 x 5 = 100). Shouldn’t this statement then be true?: 100 is greater than 20 x 5. But that’s not true. 100 is no larger than 20 x 5. It’s the same! To make it bigger we could create a formula like (a + 1) b where a = 20 and b = 5 to get this answer: (20 + 1) x 5 = 105 But if that’s the case, why don’t just say “What’s 21 times 5?” Instead of saying “times greater than”, we don’t believe there is a right answer because the question can be misinterpreted. When a lot of people write 20 times greater than 5, they seem to mean 20 times as much as 5, which equals 100. We suggest you ask them what they mean. Go here for our Times Greater Than calculator. Go here for a similar issue that may also interest you.

How to order fractions

In the last lesson you learned to compare fractions.

Let’s use this knowledge to order fractions, which means sorting them from smallest to largest. 👍

Comparative faction overview

There are shortcuts for comparing fractions with equal numerators and equal denominators.

If 2 fractions have the same numerator, just compare the denominators.

The larger the denominator, the smaller the fraction.

Remember, the larger the denominator, the more parts the whole is divided into, making each part smaller.

If 2 fractions have the same denominator, just compare the numerators.

The larger the numerator, the larger the fraction.

When fractions don’t have the same numerator or denominator, find equivalent fractions that have either the same numerator or denominator.

Order fractions with equal numerators

When ordering fractions with the same numerators, look at the denominators and compare them by 2.

👉 The fraction with the largest denominator is the smallest.

Let’s look at an example.

Order these fractions from smallest to largest:

The fractions have the same numerators, so all you have to do is compare their denominators.

1/6 has the highest denominator.

This means that 1/6 is the smallest fraction. 👍

The larger the denominator, the smaller the fraction.

We rearranged the fractions from smallest to largest.

Order fractions with the same denominator

When ordering fractions with the same denominator, look at the numerators and compare them by 2.

👉 The fraction with the smallest numerator is the smallest.

Let’s look at an example.

Order these fractions from smallest to largest:

These fractions have the same denominators, so all you have to do is compare their numerators.

3/8 has the smallest numerator.

This means that 3/8 is the smallest fraction. 👍

Here’s how we order these fractions from smallest to largest:

Order fractions with different numerators and denominators

When ordering fractions with different numerators and denominators, write the fractions as equivalent fractions with the same denominator.

Tip: Same means “same”. Different means “different”.

Let’s look at an example.

Order these fractions from smallest to largest:

👉 First find some equivalent fractions for each fraction by multiplication.

👉 Next, select the equivalent fractions that have the same denominator for all three fractions.

Be careful when choosing the equivalent fractions to compare!

Make sure they all have the same denominator.

8/12, 6/12 and 9/12 have the same denominator.

Now that we’ve found equivalent fractions with matching denominators, it’s easy to compare them!

Just look at the counters:

👉 The fraction with the smallest numerator is the smallest.

Can you order these fractions from smallest to largest? 🤔

That’s correct!

Written in order from smallest to largest, you have 6/12 < 8/12 < 9/12. Now we know that... Great job learning how to order fractions! Now complete the exercise to master sorting fractions yourself. 💪

What is 10 times greater than 20?

10 times bigger than 20 seems easy enough, but is it? Let’s say the answer is = 200 (since 10 x 20 = 200). Shouldn’t this statement then be true?:200 is greater than 10 x 20. But that’s not true. 200 is no larger than 10 x 20. It’s the same! To make it bigger we could create a formula like (a + 1) b where a = 10 and b = 20 to get this answer: (10 + 1) x 20 = 220 But if that’s the case, why don’t just say, “What’s 11 times 20?” Instead of saying “times greater than”, we don’t believe there is a right answer because the question can be misinterpreted. When many people write 10 times greater than 20, they seem to mean 10 times as much as 20, which equals 200. We suggest you ask them what they mean. Go here for our Times Greater Than calculator. Go here for a similar issue that may also interest you.

What is 40 times greater than 4?

40 times bigger than 4 seems easy enough, but is it? Let’s say the answer is = 160 (since 40 x 4 = 160). Shouldn’t this statement then be true?:160 is greater than 40 x 4. But that’s not true. 160 is no larger than 40 x 4. It’s the same thing! To make it bigger we could create a formula like (a + 1) b where a = 40 and b = 4 to get this answer: (40 + 1) x 4 = 164 But if that’s the case, why don’t just say, “What’s 41 times 4?” Instead of saying “times greater than”, we don’t believe there is a right answer because the question can be misinterpreted. When a lot of people write 40 times greater than 4, they seem to mean 40 times as much as 4, which equals 160. We encourage you to ask them what they mean. Go here for our Times Greater Than calculator. Go here for a similar issue that may also interest you.

For general comparisons, note the following(1):

five times the size, not five times the size

Is it wrong to say “five times larger”? The former sounds more “same” to me, meaning no more or less than five times.

googol. It’s a big number, unimaginably big. It’s easy to write in exponential format: 10100, an extremely compact way to easily represent the largest numbers (as well as the smallest numbers). With the least amount of effort, you can also display it in full format: a “one” followed by a hundred “zeros”. However, in its exponential format, it is easy to read; In the full format, you might lose the number of times you need to use the term “billion” in “tens of billions of billions of billions of billions…”. etc.” In any case, we can’t even begin to estimate the magnitude. Even with just one googol, we’re faced with a number larger than anything we use to describe the universe we understand. Our galaxy, for example, consists of approximately hundred billion stars. In exponential form about 1011 stars. The mass of the sun is 2×1033 grams. Using this measurement as the average star mass, we can calculate that the (visible) mass of our galaxy is therefore about 1045 grams. Within the universe there is a few hundred billion galaxies, a number comparable to the number of stars in our galaxy.So together we have collected about 1056-1057 grams of matter.This matter consists mainly of baryons (protons and neutrons) which are mixed with the nuclei of Atoms are connected that, from hydrogen to uranium (among others), make up part of our universe In terms of mass, the electrons, which weigh about one two-thousandth that of nucleons, can easily be neglected. Considering that the mass of a proton (and neutron) is 1.7 x 10-24 g, we can calculate that the number of baryons present in the Universe is approximately 1080. A large number, but considerably smaller than a googol; a hundredth of a billionth of a billion Googol to be precise. There are more neutrinos and photons, but even their number is much smaller than a googol. To outperform a googol, we must address the largest container we know of and its smallest relative part. The smallest physical length known to us is the Planck length. It corresponds to 1.6 x 10-33 centimeters. In a cubic centimeter there are 2.5 x 1098 cubes whose side measures one Planck length. Not even a tenth googol. So in the entire universe, which has a radius of about 1028 cm, there are about 10184 Planck cubes. This number – the number of Planck cubes in the universe – is probably the largest number we can give to a being within the physical world. Leaving physical quantity aside and staying in the realm of mathematical abstraction, we know of a few Mersenne primes that exceed the Googol, starting with 2521 – 1 (which includes 157 digits) and ending with 243,112,609 – 1, which is 13 million comprises numbers and is believed to be the largest of the known Mersenne primes (though no doubt we will discover more in the future). We managed to outperform a googol, but we’re still dealing with small numbers compared to a googolplex.

A googolplex is actually equal to 10 googol and can only be written in exponential format. A googol equal to 10100 can also be written as 1010^2; The Planck cube number contained in the universe can also be written as 1010^2.27, but a googolplex is 1010^100! Not only would the paper or ink not suffice, there is not enough space or time to be able to write a Googolplex in its full format. Even if you were to write each figure using miniature characters small enough to fit in a Planck cube, there would not be enough space in the entire universe, which, as we have seen, contains at most enough space to fill the first 10184 write numbers. However, we need a lot more numbers! In turn, a googolplex, although larger than a googol by 1098, can be considered a smaller number, for example, compared to the largest number ever used in a mathematical context, known as G, Graham’s number. This number, whose relative number is unknown, is not easily written even in exponential format, and it is necessary to resort to new formats such as tetration and subsequent exponential loops that allow its development: addition – multiplication – exponentiation – tetration and so on. Tetration is indicated by two upward pointing arrows between the factors. Subsequent calculations are indicated by an increasing number of arrows. So 3↑3 = 33 = 3x3x3. Then 3↑↑3 = 3↑(3↑3) (hence 33^3) and 3↑↑↑3 = 3↑↑(3↑↑3) – which equals (33^3)^(33^3) is )^(33^3). Finally 3↑↑↑↑3 = 3↑↑↑(3↑↑↑3). This represents the starting point to arrive at Graham’s number, which we shall denote as g1. Step 2 is g2 = 3↑↑…↑↑3, where the number of arrows is equal to g1. The next step is g3 = 3↑↑↑↑…↑↑↑↑3, where this time the number of arrows is equal to one g2. And so forth. This continues up to the 64th degree, where we reach g64 = G, Graham’s number, an obviously unimaginable number. It is possible, even easy, to devise operations that would take us to larger numbers: it is possible to go from simple +1 to an exponential calculus with terms even larger than those defining Graham’s number (g65). , or the higher include factors (e.g. 4 instead of 3).

However, that is not the point. It’s about finding numbers that serve a purpose, have a specific meaning, numbers that result from operations, from mental logic problems, or that cannot be expressed in smaller numbers like prime numbers. In this light, both googol and googolplex are simply two powers of 10 that have been named, are well known, and appear in dictionaries, encyclopedias, documentation, and excerpts. Quite differently, Graham’s number represents an upper limit (but not necessarily the smallest) of the “smallest number of dimensions necessary” to work out the properties of a hypercube (a geometric figure with four or more spatial dimensions). Because of this, it has been called the largest number among those with the same meaning. I’m going to end with some strange information about Graham’s number. Their primes remain unknown, and we have good reason to believe they’ll never be discovered, since they’re computed from scratch (I don’t want to make the same arrogant mistake I wrote about recently, though, so best is “never never to say”). The last numbers are known (at the last count, 500 were calculated and this number keeps increasing). In terms of G, which is simply a annihilated sequence of multiplications of the number 3, there is 7. To put Graham’s number in perspective, let’s not forget that all numbers are relative to the infinite numbers, which is the ratio between Describing the length and diameter of a perimeter or even the ratio between length, alms is the diagonal of the square and its side (although we are now talking about numbers “after the decimal point”, which will not change the size of the number significantly.) But itself when we speak of infinities, we must keep in mind that both larger and smaller exist…

Extract from: Le Stelle No. 107, June 2012

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The order relation $x

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Greater Than and Less Than

It can be difficult to remember which inequality sign or symbol to use in a number comparison, but we have a simple memory trick that can help!

Notice how the inequality symbol has a wide end and a narrow end?

The wide end opens to the larger value and the narrow end points to the smaller value. If we describe the image below from left to right, it reads that all spider people are bigger (or taller) than just a spider ham.

If we flip things around, we can still read it left-to-right, but now it reads like one Spider-Ham is smaller (or smaller) than all of the Spider People.

wide end

open for

larger number

How do we find the larger number? 🕵🏿‍♀️

The larger digit is farther from 0 on the number line. When we compare numbers, we compare place values ​​from left to right. The number that has the first place value with a on the number line. The number furthest to the right on the number line is the larger number. − 4 − 3 − 2 − 1 0 1 2 3 4 Move left Move right Remember that numbers are larger further to the right, by imagining a phone’s signal bars – the bars get bigger and stronger the further we go go right. This also means that any positive number is greater than any negative number 💡. Why is a larger negative number smaller than a smaller negative number? 🤔 Remember that as we move right on the number line, the numbers get bigger. For negative numbers, you can think of “greater than” as meaning “which number is less negative (or more positive)”. − 7 − 2 0 − 2 > − 7 Since −2 is further to the right than −7, −2 is greater than −7. Calculator Calculator Lesson Practice Practice Check out our or the and sections to learn more about comparing numbers, fractions and decimals and test your understanding. Explore Calculator

We can apply the same concept to comparing numbers. The sign should always be that

Comparing Fractions Calculator

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Showing the work Using the given inputs: Rewriting these inputs as decimal numbers: Comparing the decimal values ​​we have: Hence the comparison shows:

use calculator

Compare fractions to find out which fraction is larger and which smaller. You can also use this calculator to compare mixed numbers, compare decimals, compare whole numbers, and compare improper fractions.

How to compare fractions

To compare fractions with different denominators, convert them into equivalent fractions with the same denominator.

If you have mixed numbers, convert them to improper fractions. Find the lowest common denominator (LCD) for the fractions. Convert each fraction to its equivalent using the LCD in the denominator. Compare fractions: If the denominators are the same, you can compare the numerators. The fraction with the larger numerator is the larger fraction.

Example:

Compare 5/6 and 3/8.

Find the LCD: The multiples of 6 are 6, 12, 18, 24, 30, etc. The multiples of 8 are 8, 16, 24, 32, etc. The least common multiple is 24, so we’ll use that as the least common multiple Denominator.

Convert each fraction to its corresponding fraction using the LCD.

For 5/6 numerator and denominator, multiply by 4 to have LCD = 24 in the denominator.

\( \dfrac{5}{6} \times \dfrac{4}{4} = \dfrac{20}{24} \)

For 3/8 numerator and denominator, multiply by 3 to have LCD = 24 in the denominator.

\( \dfrac{3}{8} \times \dfrac{3}{3} = \dfrac{9}{24} \)

Compare the fractions. Since there are equal denominators, you can compare the numerators. 20 is greater than 9, so:

Since \( \dfrac{20}{24} > \dfrac{9}{24} \) we conclude \( \dfrac{5}{6} > \dfrac{3}{8} \)

For more help with fractions, see our Fractions Calculator, Simplified Fractions Calculator, and Mixed Numbers Calculator.

References: Help with Fractions Finding the lowest common denominator.

Comparing and Identifying Fractions on a Number Line

Instructions: Using the digits 1 through 9 exactly once, put a digit in each box to form 4 fractions and place them in the correct order on the number line. (Break B & C are the same)

Note The sum of equivalent fractions is greater than half and greater than a quarter separately. How do you know if two fractions are equivalent? How do you know if fractions are smaller or larger than another fraction?

Answer There are many possible answers. Here are a few: A=1/7, B=3/8, C=9/24, D=5/6; Another possibility is A = 1/5, B = 3/9, C = 8/24, D = 6/7; yet another possibility is A = 5/8, B = 3/4, C = 9/12 and D = 6/7. (or D could be 7/6)

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