Questions on basic arithmetic, e.g. addition, subtraction, multiplication, division, powers, radicals, etc.

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2
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0answers
36 views

Given a set of nonnegative numbers, put $\pm$ between them to minimize the magnitude of the result

Let's say I have a finite set of non-negative numbers. I have to put $+$ or $-$ between the numbers, in order to minimize the absolute sum.(i.e the sum has to be closest to 0) For example: the set: ...
1
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1answer
79 views

Should BODMAS not be BODMSA?

Let me and blindly follow for a second BODMAS. $$ \begin{align*} 1-3+2 &=1-(3+2)\\ &=1-5\\ &=-4 \end{align*} $$ (The brackets are just to make the error clear - I wouldn't write them in ...
2
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2answers
67 views

square root solutions

Is there a specific rule to get square root of any non-negative number?. The main reason why I'm asking this is that my maths teacher told me there is only one solution can be contained for any ...
5
votes
1answer
99 views

Determine if the number $ \sqrt{8+2\sqrt{10+2\sqrt{5}}} - \sqrt{8-2\sqrt{10+2\sqrt{5}}} $ is rational

$ \sqrt{8+2\sqrt{10+2\sqrt{5}}} - \sqrt{8-2\sqrt{10+2\sqrt{5}}} $ I have tried to raising it to the square, but I can't obtain the result. $ \sqrt{8+2\sqrt{10+2\sqrt{5}}} - ...
1
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2answers
33 views

What kind of mathematical operation is used to repeatedly increase a number by a certain percentage?

I am sure that this is an easy question to answer for most of you. I need to take a number, let's say $10$, and then increase it by a percentage, let's do $25\%$. $10 \times 1.25 = 12.5$ Easy ...
1
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1answer
70 views

Prove 1+1=2 in the most complex way possible? [closed]

Best answer goes to the most complex, but this was just out of pure curiosity.
2
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2answers
59 views

Evaluate $\frac{\frac{1}{1}}{\frac{1}{5^{-2}}}$

I solved a question in the Manhattan GRE 5 pound book (specifically the 11th question in the Exponents and Roots section). I evaluated $\frac{\frac{1}{1}}{\frac{1}{5^{-2}}}$ as $5^{-2}$ and then ...
2
votes
1answer
182 views

When the sum of 455 and four times a positive number is subtracted from the square of the number, the result is 117. Find the number.

When the sum of $455$ and four times a positive number is subtracted from the square of the number, the result is $117$. Find the number. Any thoughts on what to do first? How to set up a formula ...
-1
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1answer
60 views

Solving linear inequalities and expressing in interval notation…

I have a set of problems for my algebra class dealing with expressing linear inequalities in interval notation. I get the solution but I'm not sure how to express the infinity, here's an example. ...
0
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2answers
48 views

Find the additive and multiplicative inverse of $-36$

Find the additive and multiplicative inverse of $-36$. I don't remember how to do these problems. If you can help that would be great. thanks!
3
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2answers
65 views

Find a number by the decimal part of its square root [duplicate]

I have a math problem consisting of two questions: can we find a number N knowing only the decimal part of its square root up to a precision (only an approximation of the decimal part because the ...
1
vote
2answers
90 views

What is the name for a number plus itself?

I'm asking out of curiosity more than anything else. A number multiplied by itself is squared, is there a specific mathematical term for a number plus itself? $(n*n = n^2, n+n=?)$
2
votes
2answers
284 views

(PQ)²=RSP, where P,Q,R,S are distinct single digit natural numbers, then R=?

I have a problem I tried to solve, but couldn't because I don't know the method to solve it and I've never come across such problem. Here's the problem. $(PQ)²=RSP$ Where $P, Q, R, S$ are distinct ...
0
votes
1answer
34 views

Calculate total number of matrices of all orders which contain $2013$ elements

Calculate total number of matrices of all orders which contain $2013$ elements My Try:: By Simple Guessing wecan say that there are two matrices of order $(1\times 2013)$ and $(2013 \times 1)$ ...
2
votes
2answers
90 views

How to split the rent if two roommates live there from the beginning and a third one joins in the middle of the month?

I've been thinking over it and I can't figure it out. Consider the rent of the house is $X$. Now there are two roommates from the beginning and a third one joins in the middle of the month. Now ...
1
vote
1answer
62 views

Calculating unique “damage-per-second” for a game

I'm having a little trouble reaching a conclusion I'm happy with. The following is an "ability" for a game, which has a damage output and a "cooldown". The cooldown is how long I must wait before I ...
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5answers
96 views

Mathematical proof for order of operations

I was watching this YouTube video and at around 40:40 the speaker himself states that he does not know why we have the order of operations we have today. This got me thinking and I realize that I ...
0
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1answer
13 views

Greatest possible length to measure given lengths

I was given a question to find a greatest possible length to measure $495$, $900$,$1665$ (in centimetres). The solution is finding GCF or GCD or HCF (highest common factor) of these numbers which is ...
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2answers
70 views

Convert angles from the sexagecimal system to centesimal one

How do you convert angles from the sexagecimal system to centesimal one? For example 63 degrees 14 minutes 51 seconds reduced to centesimal ?? Here's how it's done but I don't understand the ...
1
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1answer
283 views

A question about orders of magnitude

I'm reading a book in which the author compares two pairs of numbers $(0.31, 0.39)$ and $(6.10,0.39)$ and multiplies the second member of each pair by a factor $R_1 = 2$ and $R_2 = 20$ so that both ...
0
votes
1answer
37 views

Can't come up with the correct result.(order of operations) Could you please help?

I have the following exercise: $$2\cdot \{100\cdot 3-3\cdot [100-3\cdot (100-3\cdot 33)]\}$$ I've looked into the text book and the correct answer is $18$ but I keep getting $-99$. Here's how I ...
2
votes
3answers
30 views

Percentages of $\$100,000$

$\$6,200$ is $6.2\%$ of $\$100,000$. That leaves $\$93,800$ as $93.8\%$ of that $\$100,000$. But when I take $\$93,800$. and multiply it by $6.2\%$, I get $\$99,615.60$ instead of $\$100,000$. Why is ...
0
votes
3answers
64 views

What is the smallest number x such that $180\times x$ is a perfect cube?

What is the smallest number x such that $180\times x$ is a perfect cube?
0
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0answers
50 views

Number theory/proof help appreciated! Includes working.

my question concerns number theory and proofs. I have shown my working for the following two questions but I'm not too sure if I am correct - I feel as if this might be a trick question. Any feedback ...
0
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3answers
49 views

How to do long division $1.068 / 40$ without using a calculator?

1.068 divided by 40. 1.068 / 40 = ? How would you do this problem by long division and any other methods to figure this out without using a calculator. Just pencil and paper.
3
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5answers
373 views

How to explain infinty to a $3^{rd}$ grader?

In my country in $3^{rd}$ grade in math kids learn the four basic arithmetic operation (addition, subtraction, multiplication and divison) up to $10 000$. My sister this year goes to $3^{rd}$ grade ...
2
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3answers
75 views

How to put 9 pigs into 4 pens so that there are an even number of pigs in each pen?

Put 9 pigs into 4 pens so that there are an even number of pigs in each pen. Read this for inspiration.
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3answers
62 views

How to round $ 0.03446$ to three decimal places?

What is $ 0.03446 $ rounded to three decimal places? I think it is $0.035$ but someone told me that it should be $0.034$. I think $0.035$ because the $6$ would change the $4$ into a $5$, which ...
1
vote
1answer
100 views

Find the sale price given the 40% markup over wholesale and later 20% discount

A retailer pays $\$86$ to a wholesaler for an article. The retail price is set using a $40\%$ rate of markup on selling price. To increase traffic to his store, the retailer marks the article down ...
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1answer
33 views

How to convert one number range to another? (Prioritizing a list of skills based on current familiarity and usefulness)

I'm trying to come up with a formula to prioritize a list of skills that a learner should tackle based on: current familiarity with the skill, and the usefulness of the skill. Familiarity is a $1$ ...
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4answers
385 views

negative number divided by positive number, what would be remainder?

my question is If $-27$ is divided by $5$, what would be the remainder?
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2answers
211 views

partnership calculation

3 partners are doing business No.1 has 60% partnership no2 has 23% partnership no3 has 17% partnership If No2 partner (23% ) want to leave partnership then how many percent partnership ...
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3answers
189 views

Why sqrt(4) isn't equall to-2? [duplicate]

Possible Duplicate: Square roots — positive and negative $\sqrt{4} = -2$. WolframAlpha says "false"! Now lets take a deeper look to my idea. Well...we know that, $$2^2 = 4 \iff \sqrt{4} ...
45
votes
8answers
3k views

The last digit of $2^{2006}$

My 13 year old son was asked this question in a maths challenge. He correctly guessed 4 on the assumption that the answer was likely to be the last digit of $2^6$. However is there a better ...
71
votes
18answers
7k views

Is there another simpler method to solve this elementary school math problem?

I am teaching an elementary student. He has a homework as follows. There are 16 students who use either bicycles or tricycles. The total number of wheels is 38. Find the number of students using ...
2
votes
4answers
259 views

How do you work out $\sqrt[4]{16^3}$ without a calculator.

$$\sqrt[4]{16^3}$$ I just don't know what to do when I get to $4096$. The original equation was $16^{3/4}$.
4
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1answer
544 views

Simplify $\frac{9}{2}(1 + \sqrt 5)\sqrt{10 - 2\sqrt 5} + 9\sqrt{5 + 2\sqrt 5}$

Simplify $\displaystyle{\frac{9}{2}(1 + \sqrt 5)\sqrt{10 - 2\sqrt 5} + 9\sqrt{5 + 2\sqrt 5}}$. I get this when I was doing another Q, but I don't know how to further simplify it. Can anyone help me, ...
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1answer
29 views

Is this correct - Rs.1 is equal to 1 paisa

yesterday got a SMS, and can any one explain it.... ...
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2answers
52 views

Simplifying Surd Fractions

can someone show me how to simple surd fractions such as: $$\frac{{8\sqrt 3 }}{2}$$ Can someone please help me here?
2
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2answers
48 views

A property of proportions: if $a/b=c/d$, then $(ma+nb)/(pa+qb)$ is equal to $ (mc+nd)/(pc+qd)$

If $\large\frac{a}{b}=\frac{c}{d}$ how we can obtain $\displaystyle{\frac{ma+nb}{pa+qb}=\frac{mc+nd}{pc+qd}}$? I can get $\large\frac{ma}{qb}=\frac{mc}{qd}$ and $\large\frac{nb}{pa}=\frac{nd}{pc}$ , ...
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0answers
76 views

Why does base*height work?

I want to rigorously prove the idea that Base*Height=Area works (I do realise there are shapes which do not satisfy this equation). I think I can see why it works for integer values, but I want ...
4
votes
0answers
90 views

Adding Numbers Pattern

A few nights ago I couldn't sleep and so started doing this: I would take a number and add up all of its digits to get a new number and then add up all of those digits and so on until there was only ...
0
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3answers
45 views

A question on arithmetic progression [closed]

If $a\left(\frac{1}{b} + \frac{1}{c}\right), b\left(\frac{1}{a} + \frac{1}{c}\right),$ and $c\left(\frac{1}{a} + \frac{1}{b}\right)$ are in arithmetic progression, then prove that $a,b,$ and $c$ are ...
2
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2answers
39 views

Definition and decidability of bounded quantifiers

Consider quantifier-free formulas $P(x,y) = Q(x,y)$ of Peano arithmetic. Consider $P(x,y),Q(x,y)$ to be terms composed of variables $x,y, \operatorname{succ}, +, \times$. Note that these are ...
2
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1answer
72 views

Did the ancient Sumerians calculate the square root of two?

This post makes the claim: Not bad you might think, but compare it to the Summerian Kù of 51.85cm of the copper of Nippur and its derived unit SAR of 3600 Kù being 1866.6 meter being only 0.77% ...
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5answers
59 views

Why if $x>2 \sqrt x$, then $\sqrt x > 2$?

I don't understand this step: $$x>2 \sqrt x \Longrightarrow \sqrt x > 2$$ ($x\geq 0 $)
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2answers
61 views

Grade 4 level arithmetic maths problem that I can't work out

My grade 4 son was given this problem as homework, except I can't even seem to work it out! Any help is appreciated. Each student in year 4 was asked to bring a paint tin, a paint brush and glue for ...
0
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3answers
49 views

how to prove $ax + by = cx + dy \implies a = c, b = d$?

Actually the question is in the title. I just have saw such a method $$ ax + by = cx + dy \implies a = c, b = d $$ in my textbook, so I can assume it is true, but I'm very interested on proving ...
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0answers
31 views

Interval arithmetic for open intervals

I found a detailed paper which outlines the rules of interval arithmetic for closed intervals, including unbounded closed intervals, but it makes no mention whatsoever about open intervals. I'm ...
3
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1answer
28 views

Adding repeating decimals

(intimidated newbie here, please be gentle) I got curious about adding repeating decimals while working on a "convert degrees/min/sec to degrees" problem. To convert 5°13'11'' to degrees, I can ...