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

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1answer
27 views

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

yesterday got a SMS, and can any one explain it.... ...
0
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2answers
50 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
43 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 $\large\frac{nb}{pa}=\frac{nd}{pc}$ , ...
1
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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
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0answers
86 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 ...
1
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3answers
44 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
38 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
71 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
58 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 $)
0
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2answers
60 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 ...
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3answers
45 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 ...
1
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3answers
84 views

Evaluate $\sqrt{2x} \cdot \sqrt x$

So I have this problem: $\sqrt{2x} \cdot \sqrt x =\ldots$ I already have the answer which is $x\sqrt2$, but I just can't understand it. Someone that could help?
0
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1answer
15 views

Able to adjust a Function/Formula with Weighted Variables to correct for changes in a variable?

I apologize for the somewhat cryptic title as I don't quite know how to word it. I have a somewhat abstract question that may have a simple answer. But I am wracking my mind all over this! So ...
17
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12answers
3k views

Why is $\frac{1}{\frac{1}{X}}=X$?

Can someone help me understand in basic terms why $$\frac{1}{\frac{1}{X}} = X$$ And my book says that "to simplify the reciprocal of a fraction, invert the fraction"...I don't get this because isn't ...
1
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4answers
64 views

How can I determine the function for summing a series of integers? [duplicate]

I want to sum a series of integers, say from 1 to 5, but I want to generalise this function. I have seen that the function is: $$ \text{sum} = \frac{n(n+1)}{2} $$ where $n$ is the number to sum up ...
1
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2answers
46 views

Division with Remainder

When I divide 48/12 by hand, it's 0 Remainder 12. But when I divide it in a calculator, it's .25. Why is this? How does 0R12 turn into .25? Thanks. ANSWER (system won't let me answer my own ...
3
votes
4answers
129 views

Diophantine equation abc + abd + acd + bcd= 1

Is there a reference which classifies or at least gives an infinite family of integer solutions to the above equation? A solution to the problem would also be great obviously.
0
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2answers
46 views

Why 3 is a multiplicative inverse of 7 in modular arithmetic?

why is 3 a multiplicative inverse of 7 in modular arithmetic of 5 ? I'm not able to understand how this is true. PS: I know 3*7-1 % 5 = 0. I'm not able to make sense of inverses in modular ...
3
votes
1answer
53 views

Simplify $\frac {\sqrt5}{\sqrt3+1} - \sqrt\frac{30}{8} + \frac {\sqrt {45}}{2}$

I am trying to find the value of: $$\frac {\sqrt5}{\sqrt3+1} - \sqrt\frac{30}{8} + \frac {\sqrt {45}}{2}$$ I have the key with the answer $\sqrt 5$ but am wondering how I can easily get to that ...
0
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1answer
72 views

Finding how many times one number fits into the other

Is there a way to tell - for example - how many $60$s are there in a number that cannot be divided by $60$, like $183$? I know that we should remove all numbers after the decimal point but how can we ...
0
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1answer
43 views

Change of the average when a number is removed

The average of 21 members is 30. The largest number is 50. If we remove the largest number then the average of remaining numbers will be?
105
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18answers
10k views

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

So I'm tutoring at the library and an elementary or pre K student shows me a sheet with one problem on it: Put 9 pigs into 4 pens so that there are an odd number of pigs in each pen. I tried to ...
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1answer
34 views

Two conversions to base three yield different results

How are there two different conversion results for the same bases? Am I doing something wrong?
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2answers
158 views

In which part of the history the man jumped from the intuitive concepts to the most complex ones? [duplicate]

This question explains better what this one tried: Understanding the intuition behind math In the history mathematics we always see how the numbers were created and for what purpose. Like ...
0
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0answers
27 views

What are the patterns in the number of divisors $d(n)$ of the highly composite numbers?

I am trying to understand the patterns in the number of divisors $d(n)$ of the highly composite numbers. The numbers marked with an asterisk are the superior highly composite numbers. The first ...
0
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1answer
45 views

Factorization of rational powers of rational numbers

If I am not wrong, rational powers of rational numbers can be factorized in an unique way as product of rational powers of different prime numbers: $10^{1/2} = 2^{1/2} \cdot 5^{1/2}$ $(8/9)^{1/6} = ...
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votes
3answers
72 views

Multiplication of 1 to n numbers

Let's say I want to find multiplication of 1,2,3...10 then Do I need to do 1*2*3.10 Manually or is there a easier way to do it? something like we can do for summation for 1 to n like this ...
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1answer
52 views

How to calculate the number of lattice points in the interior and on the boundary of these figures with vertices as lattice points?

We define a point $(x,y)$ in the plane to be a lattice point if both $x$ and $y$ are integers. Now let $$S\colon= \{ (x,y) \ | \ 0 \leq x \leq m, \ 0 \leq y \leq \frac{nx}{m} \}, $$ where $m$ and ...
4
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2answers
77 views

How prove that $ \sqrt[3]{\frac{1}{9}}+\sqrt[3]{-\frac{2}{9}}+\sqrt[3]{\frac{4}{9}}=\sqrt[3]{\sqrt[3]2-1} $

How check that $ \sqrt[3]{\frac{1}{9}}+\sqrt[3]{-\frac{2}{9}}+\sqrt[3]{\frac{4}{9}}=\sqrt[3]{\sqrt[3]2-1} $?
6
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1answer
83 views

About translating subsets of $\Bbb Z.$

This is a continuation of About translating subsets of R2. Is it possible to find a pair of sets $A,B\subseteq\Bbb Z$ such that A is a union of translated (only translations are allowed) copies of ...
1
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0answers
92 views

Given $m^k\le n <m^{k+1}$ find $x$ and $y$ such that $x\cdot m^k+y=n$

Let $n,m,k\in\mathbb{N}$. Assume $m^k\le n <m^{k+1}$. Find $x,y\in\mathbb{N}$ such that (1) $x\cdot m^k+y=n$ (2) $0<x<m$ (3) $0\le y<m^k$ My question: does there exist a general ...
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2answers
92 views

What is the value of $(72^2 - 64^2) : (44^2 - 24^2)$ [closed]

What is the value of $(72^2 - 64^2) : (44^2 - 24^2)$ How to calculate this without calculator?
0
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4answers
55 views

How to work out the percentage?

I'm not exactly sure how to do this. I know the answer is $£64,000$ but whatever I try, nothing is working. i.e. $£80,000$ x $25%$ $= 2,000,000$ devided by $100$ $=$ $20,000$ $£80,000 - £20,000 = ...
0
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4answers
97 views

How does this sum work?

It seems if base number $a$ is a natural number and the exponent $n$ is an odd number greater than or equal to $3$, then: $f(a, n) =\displaystyle\sum_{i=1}^{a^{n-(n+1)/2}}{(2ai-a)}=a^n$ Such as ...
0
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1answer
265 views

Irrational inequalities question: $\sqrt { -3x+1 } + \sqrt {6x+1} < \sqrt {3x+4}$ and $\sqrt { -6x+10 } + \sqrt {-x+2} \gt \sqrt {4x+5}$

Consider the following inequalities: $\sqrt { -3x+1 } + \sqrt {6x+1} \lt \sqrt {3x+4}$ $\sqrt { -6x+10 } + \sqrt {-x+2} \gt \sqrt {4x+5}$ Attempt at a solution; after performing all the ...
0
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1answer
34 views

Help with finding the arithmetic mean of all the radii from the center to the edge of an ellipse?

So far I approached this problem computationally, I decided to take all the radii add them up, by distance formula, then divide by the number of radaii. To make the distribution even, I rotated the ...
0
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1answer
52 views

How is this definition of a constant divided by zero called?

I divide a constant by zero. One example is the following: 2/0 My father told me he learned at school earlier that the result is "not defined". If I enter this arithmetic problem in Wolfram Alpha, I ...
2
votes
3answers
164 views

How can this equality be established by elementary algebraic means?

Let $x \geq 1$. Then is it true that $2x^3 - 3x^2 + 2 \geq 1$? If so, how can I show this using only elementary ideas such as factorisation? Of course, I can demonstrate this using the methods of ...
4
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2answers
66 views

How to turn arbitrary fractions into arbitrary egyptian fractions?

I am reading Stillwell's Numbers and Geometry. There is an exercise about Egyptian fractions which is the following: I've tried to do it in the following way - Expressing an arbitrary fraction ...
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1answer
34 views

Euler product of Dirichlet series

Let $f$ be an arithmetic function such $f(n_1n_2)=f(n_1)f(n_2)$ for all $n_1,n_2 \in \mathbb{N}$ with $\gcd(n_1,n_2)=1$. Suppose we know that the Dirichlet series $$F(s) = \sum_{n=1}^{\infty}f ...
0
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1answer
23 views

How to calculate component amounts so their individual additives equal 3%

I have a list of chemical formulas that are each comprised of a number of base components. Two of the base components contain an additive, $X$. This additive needs to exist in each formula at a ...
1
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1answer
43 views

Why aren't my % Changes additive?

I'm struggling conceptually with the fact that I have a variable C that is the product of 2 other variables, A and B yet the annual change as a % in C is not the annual change % of A + B. e.g As ...
2
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4answers
124 views

How addition and multiplication works

Lets say i am doing 12 + 13 by using the addition method that we know. i mean first we write 13 below 12, then we do 2+3 and then 1+1. The result can be validated as 25 (or true) by doing the counting ...
0
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3answers
47 views

When a fraction is raised to a negative exponent, do you normally transform it to 1 over the fraction, or invert the fraction?

My text shows that $$\left(\frac{3a^2}{4b}\right)^{-3}=\frac{1}{\left(\frac{3a^2}{4b}\right)^{3}}.$$ It also shows that $$\frac{1}{\frac{144}{b}}=\frac{b}{144}.$$ In the first equation, it seems ...
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4answers
1k views

Clock Synchronization [closed]

There is a clock at the bottom of the hill and a clock at the top of the hill. The clock at the bottom of the hill works fine but the clock at the top doesn't. How will you synchronize the two clocks. ...
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2answers
78 views

Why does $(3^{1/2})(10^{1/2})=30^{1/2}$ but $(3a^2)(10a^2)=30a^4$?

$(3a^2)(10a^2)=30a^4$? In that equation the exponents are added. Why does $(3^{1/2})(10^{1/2})=30^{1/2}$. In that equation the exponents are not added. Why?
2
votes
2answers
44 views

Square root each term (clarification on polynomials?)

So I'm in Algebra 2, and right now we're learning about conic sections (circles/ellipse/etc). I thought some problems in the workbook looked weird, like this one: ...
0
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1answer
35 views

What do you call this arithmetical property and how do you prove it?

I think I can prove this property only when exponents are integers. But here is my example: $a(x-b)^{1/2} = (a^2x-a^2b)^{1/2}$ This type of foiling is weird and I wish to see a proof of this. ...