A multiple-choice quiz
by AdamM7.
Estimated time: 3 mins.

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Quiz Answer Key and Fun Facts

Answer:
**Commutative**

Addition is commutative, as is multiplication. It is also associative, which means the order is irrelevant no matter how many numbers you add.

For instance, 2+5+25+52 = 52+25+5+2 = 5+52+2+25 etc.

Addition is commutative, as is multiplication. It is also associative, which means the order is irrelevant no matter how many numbers you add.

For instance, 2+5+25+52 = 52+25+5+2 = 5+52+2+25 etc.

Answer:
**Minuend**

In 5−2 = 3, the 5 is called a minuend, the 2 is a subtrahend and the 3 is the difference.

With subtraction of two numbers, the order does matter but changing the order just changes the sign (positive/negative) - their absolute values (distance from 0) are the same. For example, 52−25 = 27, but 25−52 = -27. These numbers (27 and -27) have the same "absolute value", which just means that ignoring the sign, they are both 27.

In 5−2 = 3, the 5 is called a minuend, the 2 is a subtrahend and the 3 is the difference.

With subtraction of two numbers, the order does matter but changing the order just changes the sign (positive/negative) - their absolute values (distance from 0) are the same. For example, 52−25 = 27, but 25−52 = -27. These numbers (27 and -27) have the same "absolute value", which just means that ignoring the sign, they are both 27.

Answer:
**Its prime factors**

Factors are numbers which divide into a bigger number to give a whole number. 10 divided by 5 is 2, and 10 divided by 2 is 5, so 2 and 5 are both factors of 10.

Prime factors are just factors that are also prime numbers (numbers which have no further factors other than one and itself). For instance, the prime factorisation of 52 is 2x2x13 (2^2 x 13).

Factors are numbers which divide into a bigger number to give a whole number. 10 divided by 5 is 2, and 10 divided by 2 is 5, so 2 and 5 are both factors of 10.

Prime factors are just factors that are also prime numbers (numbers which have no further factors other than one and itself). For instance, the prime factorisation of 52 is 2x2x13 (2^2 x 13).

Answer:
**Co-ordinate parentheses**

Two divided by 5 is 0.4 while five divided by 2 is 2.5.

2/5 = 0.4 uses a forward slash to denote division. A "vinculum" is a line, with one number on top of one another, often used to represent fractions. An "obelus" is a line with a dot above and beneath it, which looks like this: ÷

Two divided by 5 is 0.4 while five divided by 2 is 2.5.

2/5 = 0.4 uses a forward slash to denote division. A "vinculum" is a line, with one number on top of one another, often used to represent fractions. An "obelus" is a line with a dot above and beneath it, which looks like this: ÷

Answer:
**Exponentiation**

Exponentiation uses "powers": the power is usually written as a superscript to the right of the base, but on computers the caret (^) symbol can be used.

5^2 ("five squared") = 5x5 = 25

2^5 ("two to the power of five") = 2x2x2x2x2 = 32

So exponentiation is repeated multiplication: a^b means "a multiplied by itself b times". If the power is two, we can call it "_ squared", and if it is three, we can call it "_ cubed". No other powers have their own name, and are said aloud as "_ to the power of _".

Exponentiation uses "powers": the power is usually written as a superscript to the right of the base, but on computers the caret (^) symbol can be used.

5^2 ("five squared") = 5x5 = 25

2^5 ("two to the power of five") = 2x2x2x2x2 = 32

So exponentiation is repeated multiplication: a^b means "a multiplied by itself b times". If the power is two, we can call it "_ squared", and if it is three, we can call it "_ cubed". No other powers have their own name, and are said aloud as "_ to the power of _".

Answer:
**Square root**

Roots are an opposite of exponentiation: 2.236^2 = 5, so 2.236 is the square root of 5.

A radix symbol is used for a square root, but other roots need the degree number superscripted. As with exponentiation, only two and three have their own names: it goes "square root", "cube root", "fourth root" etc.

Using two and five, we can actually make three numbers via roots. The fifth root of 2 is 1.149. Square roots always have two answers: one positive and one negative. Therefore, the square root of 5 can be 2.236 or -2.236.

Roots are an opposite of exponentiation: 2.236^2 = 5, so 2.236 is the square root of 5.

A radix symbol is used for a square root, but other roots need the degree number superscripted. As with exponentiation, only two and three have their own names: it goes "square root", "cube root", "fourth root" etc.

Using two and five, we can actually make three numbers via roots. The fifth root of 2 is 1.149. Square roots always have two answers: one positive and one negative. Therefore, the square root of 5 can be 2.236 or -2.236.

Answer:
**2^2.322 = 5**

Logarithms is the other opposite of exponentiation. A logarithm yields the power of x that will make y.

So, if 2^5 = 32, then the logarithm of 32 to base 2 is 5.

Using 2 and 5 as the base/antilogarithm, we can get two answers: 2.322 or 0.431.

Logarithms is the other opposite of exponentiation. A logarithm yields the power of x that will make y.

So, if 2^5 = 32, then the logarithm of 32 to base 2 is 5.

Using 2 and 5 as the base/antilogarithm, we can get two answers: 2.322 or 0.431.

Answer:
**1**

The modulo operation finds the remainder. If we were doing 5 divided by 2, we would get two and a remainder of 1. Another way of looking at this is that you repeatedly subtract 2 from 5, until you get to a number smaller than the modulo (two): 5−2 = 3; 3−2 = 1, so 1 is the answer.

2 mod 5 is simply 2, as 2 is already smaller than 5.

Time can be thought of in terms of modulo operations. If it is 22:00 on Monday, and we want to know what time it will be in 55 hours, the answer is (22+55) mod 24 (because 24 is the number of hours in a day). 77 mod 24 = 77−3(24) = 5, so it will be 05:00 on Thursday (Monday + 3 days).

The modulo operation finds the remainder. If we were doing 5 divided by 2, we would get two and a remainder of 1. Another way of looking at this is that you repeatedly subtract 2 from 5, until you get to a number smaller than the modulo (two): 5−2 = 3; 3−2 = 1, so 1 is the answer.

2 mod 5 is simply 2, as 2 is already smaller than 5.

Time can be thought of in terms of modulo operations. If it is 22:00 on Monday, and we want to know what time it will be in 55 hours, the answer is (22+55) mod 24 (because 24 is the number of hours in a day). 77 mod 24 = 77−3(24) = 5, so it will be 05:00 on Thursday (Monday + 3 days).

Answer:
**3125**

Tetration is repeated exponentiation, that is to say, if we have x^^2 (x to the tetrated two), that is equal to x^x (x to the power of x).

So 5^^2 = 5^5 = 5x5x5x5x5 = 3125. (You didn't need to work this out fully, as 3125 was the only option ending in "5", and 5 to the power of anything will always end in a 5).

Giving another example, 3^^3 = 3^(3^3) = 3^27 = 7,625,597,484,987. As you can see, tetration gets incredibly large very quickly.

Tetration is repeated exponentiation, that is to say, if we have x^^2 (x to the tetrated two), that is equal to x^x (x to the power of x).

So 5^^2 = 5^5 = 5x5x5x5x5 = 3125. (You didn't need to work this out fully, as 3125 was the only option ending in "5", and 5 to the power of anything will always end in a 5).

Giving another example, 3^^3 = 3^(3^3) = 3^27 = 7,625,597,484,987. As you can see, tetration gets incredibly large very quickly.

Answer:
**101**

We normally use a decimal (base 10) system, which means we have 10 single-digit numbers (0, 1, 2, 3 etc.) In binary, there are only 2 single-digit numbers: 0 and 1.

The last digit (the equivalent of base 10's units column) is worth 1, the second-to-last is worth 2, the anti-penultimate 4, the next 8 etc. If the value in that position is a "1", you add the value of the position. If not, the number doesn't change.

So, in a three-digit number, the digits are worth (from right-to-left) 1, 2 and 4. In "101", the 1 digits are in the 1 and 4 value positions - 1+4 = 5.

Computers use binary, because it is easy to transfer knowledge like this. A "1" can be represent by a pulse or a light or anything, and a "0" is no pulse/light etc. Although it needs more bits of information than decimal systems do, you can still get quite a lot of information across in binary. There are over 1 million combinations of 20-digit binary numbers (2^20 = 1,048,576).

We normally use a decimal (base 10) system, which means we have 10 single-digit numbers (0, 1, 2, 3 etc.) In binary, there are only 2 single-digit numbers: 0 and 1.

The last digit (the equivalent of base 10's units column) is worth 1, the second-to-last is worth 2, the anti-penultimate 4, the next 8 etc. If the value in that position is a "1", you add the value of the position. If not, the number doesn't change.

So, in a three-digit number, the digits are worth (from right-to-left) 1, 2 and 4. In "101", the 1 digits are in the 1 and 4 value positions - 1+4 = 5.

Computers use binary, because it is easy to transfer knowledge like this. A "1" can be represent by a pulse or a light or anything, and a "0" is no pulse/light etc. Although it needs more bits of information than decimal systems do, you can still get quite a lot of information across in binary. There are over 1 million combinations of 20-digit binary numbers (2^20 = 1,048,576).

This quiz was reviewed by FunTrivia editor rossian before going online.

Any errors found in FunTrivia content are routinely corrected through our feedback system.

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