# Tagged Questions

Questions on basic arithmetic involving numerical quantities only. Questions involving variable values (other than the result of the operation) should be placed under the (algebra-precalculus) tag.

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### Prove that : $10^{5n+2}+(-1)^{n}\cdot 4 \equiv 0 \pmod {13}$

Prove that : $$10^{5n+2}+(-1)^{n}\cdot 4 \equiv 0 \pmod {13}$$ I don't have enough skills in modular to do it Please help
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### What is the logic of priority of operations?

For example $2+2\times2$ is $6$ not $8$. Actually $+$ and $\times$ are binary operations on $\mathbb Z$. but here there is an triple $(2,2,2)$ which we sent to $2+2\times 2$. So we have to put and ...
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### Mathematics- Time and work

A & B can complete a job in 8 days and B & C can do it in 12 days. A & B commence the work and do it for 4 days, then A leaves. B continues for 2 days and leave. C starts working and ...
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### What is the definition of $n\cdot n\cdot n$?

Intuitively, What does it mean when you multiply numbers? I asked my professor about what does it mean when we multiply $5\cdot 5\cdot 5$. He said there is no definition of this thing in mathematics. ...
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### Characterization of elementary arithmetic operators to explain certain properties in programming languages

In the LISP-like family of programming languages, the four elementary arithmetic operators behave differently: + and * can take ...
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### How do I average two numbers that are already averaged?

$50$ juniors and seniors are tested. $35$ of them average $80%$. $15$ of them average $70%$. What is the average of the class of $50$? We tried $(70+80)/2$ but that was $75$ and the real answer is ...
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### Easier way to divide a fraction by a fraction.

Say this is the problem: $$\frac{3/8}{4/5}$$ As of right now, I would multiply both fractions by $40$ then simplify to get $\frac{15}{32}$ Or I would multiply $\frac{3}{8}$ and $\frac{5}{4}$ to ...
I can solve this type of problem first time so need hint what can I do and where I get such more problem. The Value of $$100\left[\frac{1}{(1)(2)}+\frac{1}{(2)(3)}+ \frac{1}{(3)(4)}+\ldots+\frac{1}{(... 1answer 43 views ### General formula for the numerators? Suppose that a is a natural number. The numerator of \dfrac {1}{a} is 1. The numerator of \dfrac {1}{a} + \dfrac {1}{a+1} is 2a+1 [Note: Here for our purpose we don't cancel common factors ... 1answer 44 views ### Making a “larger than” function with only basic arithmetic Is it possible to make a function using only arithmetic (no logic operators), that can return 1 if it's input x is larger than a given number a, and 0 if it's less than a? If it is, how would one ... 1answer 33 views ### additive integral property There's a common property of definite integrals: \int_a^bf(x) \, dx=\int_a^cf(x)\,dx+\int_c^bf(x)\,dx. I've often seen it said that c must lie in the interval [a,b]. However, is this really the ... 1answer 32 views ### what is the initial temperature of the object? [closed] I have a question and I cant solve it . I'll be thankful if you solve it for me and give your complete solution. We put an object in a freezer which have -17 degrees temperature. After a few minutes ... 1answer 29 views ### Best method to add and subtract (Common Core-ish) What's the best method for adding and subtracting? I have a son in the third grade so as a parent I'm smack dab in the middle of the common core debate (I'm hoping to avoid the Facebook ... 2answers 27 views ### Fractions (Dividing… Maybe?) The question... (With mixed fractions) (3)3/4 is bigger than (1)19/21 How many times bigger? I assume you divide the first fraction by the second but I cant seem to do it, could someone maybe answer ... 2answers 48 views ### Definability of the < order relation on the natural numbers using addition. [closed] Show that the usual order relation < on the natural numbers is definable in the structure (\mathbb{N}, +) with only addition. My teacher has clarified this for me and quantifiers can be used. ... 2answers 16 views ### Calculating a function given a certain x range. I have the function f(x) = x^3 + 1 and I want to calculate the following: f(x) = (\frac{a}{25})^3 + 1  Where "a" is 1,2,3,4,..,50. 1 through 50 Basically I'm adding up f(1) + f(2) + f(3) + ... 0answers 45 views ### Serre mass formula under extension Suppose K_1 is a local field and K_2 is a totally ramified finite Galois extension. Let e be a positive integer with [K_2:K_1]|e. Consider the set of isomorphism classes of K_1 extensions of ... 1answer 3k views ### What is this type of math notation called? (+ 4 5) So I've been looking for a general name of this type of mathematics notation (google hasn't been very useful) so that I can learn more about it. Basically, the symbols are in the form of functions and ... 1answer 19 views ### (Straight line) Gradient for (-4, 0) (0, 2.5) So I changed the question the textbook gave me to (-4,0) (0, 5/2). The question asked me what is the gradient for the X and Y.I was doing the question without a calculator and the answer I got was 8/... 1answer 52 views ### Simple Addition Question [closed] In basic math, when adding there is the notion of carry. For example if you have 9999+9999, since 9+9=18 the 1 is leftover and carried to the top. Is there some formula that gives us the total ... 1answer 60 views ### Inequalities - AM-GM Let H_n = 1 + 1/2 + 1/3 + ... + 1/n Prove that; H_n + n \geq n(n+1)^\frac{1}{n} for n \leq 2 I have tried writing H_n + n = 1/2 + 1/3 +...+ 1/n + (n+1) but am left with an n! in ... 0answers 26 views ### If 1/2 ≤ p/q ≤ 2 , then p-q is representable exactly on the computer I've found the following affirmation in an article. I've been thinking about it but I don't know the way to prove it: It is not hard to prove that if p and q are two of a computer’s floating–... 0answers 67 views ### How do hyperoperations like tetration exist if operations are seperate relations and not repeatitions of each other. I've run into a bit of a conflict in my fundamental understanding of concepts in math. I've always known the arithmetic operation to be extensions of each other. Multiplication is repeated addition, ... 0answers 30 views ### Decrementing one number, incrementing another, while keeping the same relation to one another This is a game development question related to math. Apologies if I shouldn't be asking this here, but I'm not good at math and need help with increasing the speed of my game. I have one number ... 4answers 486 views ### A simple binomial identity Is there a simple way of showing that a prime p must divide the binomial coefficient p^n\choose{k} for all n\geq 1 and 1\leq k\leq p^n-1? 3answers 32 views ### Algebra and brackets opening I'm trying to clarify, how to open brackets. Simple example:$$2a - {4 - [3b -(5a -7 + b)] + 2} = 2a - {4 - 3b +5a +7 - b + 2}$$As you can see, need to change sign. Opened () changed - to + ... 2answers 80 views ### Finding the general formula of a sequence alternating between even and odd So I know how to find the general formula of a simple sequence and sequences involving alternating signs but how would you devise a general formula for sequqences alternating between even and odd ... 4answers 42 views ### Explain equality F(n)=2^{n-1} \cdot 1 \cdot 3 \dots(2n-3)=\frac{(2n-2)!}{(n-1)!} F(n)=2^{n-1} \cdot 1 \cdot 3 \dots(2n-3)=\frac{(2n-2)!}{(n-1)!} Any thouts how to prove this equality? Thanks 0answers 12 views ### Is there any equation to find the number of additions in Multiplication? By seeing this answer that tells "it takes 200 additions for multiplying two 100 digit numbers" I would like to know whether there is any equation to find the number of additions in multiplication. 0answers 30 views ### Method of Complements in Base 17 Given a base 10 number. Given the following table which shows the symbols I am using when representing numbers in base 17. \begin{array}{|c|c|c|c|c|c|c|c|c|c|c|c|c|c|c|c|c|} \hline 0_{10} & 1_{10} & 2_{10} & ... 2answers 34 views ### Order of precedence, multiplication vs. division Recently I had this doubt about the order of precedence of mathematical operations multiplication and division. Given that we have a simple question like this ... 1answer 57 views ### Fill in operators (7 7 7 7 7 7 7 7 = 820) My kid's git the following as his homework - the problem is to fill in arithmetic operators between eight digits 7 to get 820, that is: 7_7_7_7_7_7_7_7=820 This drives me mad, but I myself cannot ... 3answers 104 views ### Mental n-th root of N It has been a while since I started thinking about this problem: a fast method to evaluate (in an approximate way) mentally the n-th root of a number N. I'm talking about great numbers, because ... 2answers 30 views ### Simple existence proofs without bounds Which is/are the most simple proof/s of an existential statement like$$ \exists x P(x) $$or$$ \forall x \exists y P(x,y) $$where the variables rage over the integers, such that the proof doesn't ... 1answer 36 views ### How to square a two digit number without a calculator? [closed] I will put the answer as an answer as if I post it here then the answer section will be pointless also you can answer your own question so why not? 2answers 28 views ### algorithum math problem if x, y and z each represent a different digit from 0 to 9, what is the value of (x)(y)(z)? 4z 27 +x5 ____ y14 I answered it like this: ... 1answer 15 views ### Proportion questions relating with 3 subjects . Eight men can build two houses in 20 days. How man men does it take to build 3 houses in 15 days My workings : 2 houses = 20 days 3 houses = 20.2.3= 120 days 1 men = 2 houses = 1/20 days ... 1answer 43 views ### Three-Terms Ratios. . How to write these ratios X:Y:Z in terms of fraction i.e. either like$$\frac{\frac{X}{Y}}{Z}$$or$$\frac{X}{\frac{Y}{Z}}$$? 2answers 56 views ### Simplifying Fractions involving negative numbers I want to simplify$$\frac{\frac{7}{-10} \times \frac{-15}{6}}{\frac{7}{-19} + \frac{-17}{-8}}$$I really don't understand how to do this, or even how to start? Negative numbers make it even harder ... 3answers 35 views ### Find a fraction of a part that is shaded In the figure , O is the centre of the two circles . The circles are divided into sectors of equal sizes. Given that the area of the shaded portion A is twice of the area of the shaded portion B ... 2answers 48 views ### Is there a way to encode all decimal numbers between 0 and 1 into whole numbers? Is there a way to encode ALL decimal numbers between 0 and 1 into whole numbers with a rationale that supports sum operations between the encoded numbers? so 1=0.1 2=0.2 3=0.3... 1+2 = 3 .. 0.2+0.1 =... 2answers 43 views ### Work and time problem I came up with this problem: 150 workers were employed to do a particular work. On first day, 150 workers worked. On second day, 146.. and each subsequent day, workers kept on decreasing by 4. ... 4answers 49 views ### Numerical property P(n) such that \forall n P(n) is false but a counterexample is difficult to find I would like to find a nontrivial property P(n) for n \in \mathbb N such that \forall n P(n) is false but the first counterexample can be found only for "very high" n (so high that it wouldn't ... 0answers 24 views ### How can we prove that a number is a prime with some limits? [duplicate] A simple python program implemented a simple fact that the number is prime if no numbers within it's square root including the square root and excluding 1 divide it. Empirically analyzing it for some ... 1answer 30 views ### multiplying parentheses with more variables than (a b) * (c d) I want to solve$$ (1 - 2\lambda + \lambda^2)(1 - \lambda) + 2 - 3(1 - \lambda) = 0 $$Eventually I would probably want to factor the polynomial, but I don't know how to multiply the parentheses of ... 2answers 32 views ### Expansion and factorisation I have a little problems with a few questions here and I need help.. Thanks ... Factorise completely$$9x^4 - 4x^2 - 9x^2y^2 + 4y^2 $$My workings ..$$ (3x^2+2x)(3x^2-2x) - y^2 (9x^2-4) = (3x^...
Evaluate the following by algebraic expansion of factorisation . a) $2007^2$ b) $(503)(497)$ c) $20.5^2 - 19.5^2$ I'm not sure what does it mean by "algebraic expansion of factorisation ." Can I ...