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

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1answer
24 views

binary addition

Can any direct me to any resources online that teach how to approach binary addition such as this/ working with more complex binary arithmetic? I know the basics of binary addition and carrying the ...
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0answers
24 views

Subtracting negative deicmals [on hold]

How do you subtract? I keep getting $-1.5$ as the answer but the calculator and internet says it's $-0.5$? How do you subtract correctly? $\to$ $26.5 -27.0$
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2answers
18 views

Square root and principal square root confusion

A few months ago I asked a question about the $\pm$ symbol because I was confused about it... I still carry the same confusion (which really bugs me) but I think the real confusion has to do with the ...
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3answers
34 views

Numerical problems [on hold]

Arrange the following in ascending order 3 to the power 34, 2 to the power 51, 7 to the power 17. How? Also, please explain.
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1answer
32 views

is this set closed under addition?

I have some revision questions in my maths books and I'm a bit stuck on this one. Is $S=\{n^2:n \in \mathbb{Z}\}$ closed under the usual addition. I know that for it to be closed the sum of any 2 ...
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1answer
39 views

Origin or author of 'Japanese Multiplication Method'

What is the origin or author of the method 1 shown in the following image? Notes Also known as Japanese Multiplication Method for Kids.
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1answer
17 views

Appreciating the Distributive Law

I'm going to introduce my middle school students to the distributive law in arithmetic, in a meaningful way so that they understand its importance and value. I need some interesting examples and ...
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0answers
12 views

What are different ways to do the partial-quotients method?

I've seen this method in a math book and I was probably obsessed with it. To cut to the chase, I need to know the different ways to do this. Now, what are some specific ways you have?
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1answer
73 views

Integral solutions of $x^5-27y^3=2x$

Find all integers $x$ and $y$ such that $x^5-27y^3=2x$.
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2answers
90 views

Two math professors problem

My friend asks me a question from internet. The question is as follows Two math professors, professor Uno and professor Dos, play chess at the park while reminiscing about their past. Prof. ...
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6answers
57 views

How to know a number is divisible by a given number without using a calculator?

My question is simple and comes from my curiousity during studying math. How to know a number is divisible by $7$ or $13$ without using a calculator? For example, how do we decide intuitively that ...
1
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1answer
26 views

what are the set of integers that verify this congruence equation please. [on hold]

for which integers does 3^(n+3) - 4^(n+4) ≡ 0 (mod 11) or in other terms for which integers is 3^(n+3) - 4^(n+4) a multiple of 11 thank you.
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2answers
37 views

solve this congruence please.

$7^{n+1} -(n+1)\times 7^{n} -1 ≡ 0 $ (mod 4) with the variable n as an exponent you can't use a modulo 4 table, which is why it bothers me a bit.i tried messing around with it and i got that this ...
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1answer
23 views

Calculating the Growth of A Small Population After 1000 Years [on hold]

Assuming you wish to start a colony with 100 people as the base population. Each person will have 3 children at 25 and will die at 75. How would you go about calculating the population size after 1000 ...
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0answers
21 views

Why can it be hard to divide with fractions or an integer for the dividend and a fraction for the divisor and no reciprocal of the divisor used? [on hold]

For example, if I had a division problem with fractions like $${3\over 5}/{10\over 14} $$ or a division problem with an integer in the dividend and a fraction in the divisor like $$3/{12\over 19}$$ ...
1
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1answer
15 views

reducing the modulus of a Dirichlet character

Let $\chi$ be a Dirichlet character modulo $N$. Let $M$ be a positive divisor of $N$ such that $$\text{radical}(N)=\text{radical}(M).$$ Is $\chi$ be a character modulo $M$? Best regards.
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1answer
20 views

if $p=(a+ib)(c+id)$ and $p^2 = a^2 + b^2$ then $p\mid a$ & $p\mid b$

We're working on Gauss integers... p is an odd prime such that $p \not\equiv 1 \pmod 4$. We want to prove that if there is $(a,b,c,d) \in \mathbb{Z}^4$ such that $$p = (a+ib)(c+id) \text{ ...
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1answer
9 views

how to calculate gross salary when net salary and percentage of deduction is known

When net salary is 10350 and 13.75% pf deducted how gross amount is calculated.. For eg: If gross salary is 12000, pf is 13.75% then net salary= 12000* 13.75% = 10350 But how to ...
11
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4answers
214 views

$\lim_{n\to\infty}\sqrt{6}^{\ n}\underbrace{\sqrt{3-\sqrt{6+\sqrt{6+\dotsb+\sqrt{6}}}}}_{n\text{ square root signs}}$

We have the following representation of pi: $$\pi=\lim_{n\to\infty}2^n \underbrace{\sqrt{2-\sqrt{2+\sqrt{2+\sqrt{2+\sqrt{2+\dotsb+\sqrt{2+\sqrt{2+\sqrt{2+\sqrt{2}}}}}}}}}}_{n\text{ square root ...
2
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2answers
35 views

Proving arithmetical properties for non-natural numbers

Sorry if my question is dumb but here it is: I know how to prove all of the arithmetical properties such as $(a^{m})^{n}=a^{mn}$ and $a^{m}a^{n}=a^{m+n}$ and $a(b+c)=ab+ac$ etc. For numbers that ...
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0answers
7 views

How do you track each investor's equity stake when the total amount changes?

Let's say there's a casino with a bankroll of $0. User1 invests $100 and now owns $100/100. User2 invests ...
4
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1answer
324 views

Need help with GRE question

I encountered a question while preparing for GRE and am stuck. In an examination paper of 5 Questions, 5 percent of the candidates answered all of them and 5 percent none. Of the rest, 25% ...
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1answer
23 views

Converting double precision IEEE 754 hex to base 10 with repeating decimals

The number is 0x4001 8CCC CCCC CCCC. So far I have the stored exponent as 1000000000 which equals ...
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5answers
220 views

How do I solve this fraction addition problem?

$4\frac{2}{9} + -9\frac{1}{2}$ yeilds result of $-5\frac{13}{18}$ but WolframAlpha says the answer is $-5\frac{5}{18}$ fixed.
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1answer
8 views

Calculate Hourly vacation accrual

I'm try to calculate vacation accrual for 40 hour week for an employee who is allowed 15 days vacation per yer.if the number of business hours per year is 2080,that means his accrual rate is 40/2080= ...
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2answers
22 views

How to round “correctly” (to certain level of accuracy)

Say I have the number 0.73992 and I'm rounding to 3 decimal places. My instinct would be to write 0.740 (3dp). But surely that ...
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0answers
12 views

What mechanism can be used to solve these tasks given to a 5th grader?

Basically this table has to be filled with numbers so the expressions in each column and row would be equal to the last element of that column or row, which is given. Is there some mechanism that ...
2
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3answers
48 views

How to prove that $\gcd(2n+3, 3n+1)$ divides $7$?

How can I start proving that gcd(2n+3, 3n+1) | 7? EDIT: It is $\gcd(2n+3, 3n+1)$ divides $7$. My bad. Thanks paw88789.
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1answer
52 views

Arithmetic progression with common difference 2061

If there are 30 consequent members of an arithmetic progression with CD of 2061, show that among them are at most 20 squares of natural numbers. I wrote out $a_1$ through $a_{30}$ and tried to find ...
0
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1answer
18 views

Division of number of days to get a year

Assuming a year has $360$ days and $12$ months of $30$ days each. I can say that adding $5$ days $2$ months and $15$ years to $17/10/2014 (dd/mm/yyyy)$, is $22$ days $12$ months and $2029$ years ...
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1answer
48 views

Show that $\displaystyle 2<(1+x)(1+y)(1+z)<\frac{64}{ 27}$

If $x,y,z>0$ and $x+y+z=1$ then show that $\displaystyle2<(1+x)(1+y)(1+z)<\frac{64}{27}$. I have solved the right hand first using AM-GM inequality, $\displaystyle\frac{1+x+1+y+1+z}{3} ...
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0answers
24 views

find other sums similarly under sum

In the under sum there exists all number 1,...,9. Similarly write at least 10 sums other. $$659+214=873.$$ For example we can write $259+614=873$ or $619+254=873$ or $596+142=738$. Do there exists a ...
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4answers
801 views

Solved to be 7 after arithmetic

I recently made a blunder while trying to explain a question asked to me in an interview, The question was Think of $X$ Add $X$ to itself ($X+X = y$) Times the result by $3$ ($y\times 3 = z$) ...
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7answers
2k views

Why do we stop at exponentiation stage in arithmetic of natural numbers?

In natural numbers the unary successor operator $S$ is the most natural function which maps each number to the next one. Furthermore we may consider the binary relation $+$ as an iteration of $S$. ...
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4answers
68 views

How do you add two fractions?

I have a fraction I am trying to solve. I know the answer already, as Wolfram says it is $\frac{143}{300}$. The fraction is: $$\frac{5}{12} + \frac{3}{50} = \space ?$$ Please explain why and how your ...
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2answers
56 views

How do you solve this fraction?

The problem is : $ \frac{2}{3} + \frac{-1}{16} $ The answer I got was $ \frac{1}{48} $ . I believe it to be incorrect. Three does not divide into $16,$ so I cross multiplied. What am I doing wrong? ...
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1answer
34 views

Why does increasing a number by 15% and then decreasing it by 15% fail to produce the original number?

I start with number: $.425$ and I want to add $15\%$ to get a new number. $.425 \times 1.15 = .489$ However, when I reduce $.489$ by $15\%$ I don't arrive back at $.425$. $.489 \times .85 = .416$. I ...
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3answers
33 views

How to compute Final Grade with assignment weightings?

I have just finished the Final for my Computer Hardware course, and I'm trying to figure out where my grade currently stands. The way the class is broken up is 50% weight for the homework, 25% for the ...
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2answers
39 views

Base 4 Mathematics

I have an homework question but I'm having hard time to understand the context. Here is the question: Assume that you are using 3-digit number system with base r = 4 (and n = 3). Assume also ...
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3answers
89 views

Why is Division harder than Multiplication?

Both conceptually and computationally it feels easier to see that: $ 6 \cdot 3.7 = 22.2$ than it is to see that $ 22.2 \div 6 = 3.7 $. Thoughts about the roots of this asymmetry? An analogous ...
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0answers
21 views

Sum of two sets with combination

I'm a beginner in mathematics, so, I may be confusing with the vectors... Is there a name and definite operator for this operation ? Two sets A and B : $$A = \{ a_0, a_1 \} \\ B = \{ b_0, b_1, b_2 ...
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1answer
38 views

What are the 'best of the best' textbooks to help me learn math from the ground up?

After 20 years of being a locksmith, I have decided that I want to get a college degree and I'll be starting next year! As part of my degree, I will be doing two math courses - one in calculus and the ...
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1answer
42 views

zero divided by zero is undetermined but why multiplied by zero is defined? [closed]

We consider this multiplication: $$2×0=0$$ this multiplication has two division part: $$0÷2 \quad \textrm{and} \quad 0÷0$$ when we do $0÷2$ then we found $0$, it's ok, but we don't found only ...
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2answers
51 views

Show that $\gcd(3n,3n+ 2) = 1$ when $n$ is odd

I would like to know why $\gcd(3n,3n+ 2) = 1$ when $n$ is odd. I tried to use the Euclidean Algorithm, but I got confused: $$ 3n+2 = 3n + 2$$ $$3n = \ ? $$ Thanks!
2
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1answer
24 views

What are the formal names of operands and results for basic operations?

I'm trying to mentally summarize the names of the operands for basic operations. I've got this so far: Addition: Augend + Addend = Sum. Subtraction: Minuend - Subtrahend = Difference. ...
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4answers
140 views

How do you find the number of multiples of a given range of numbers?

I know this sounds a bit stupid but this question always confounds me. Say that you are given a range of numbers like $20$-$300$. And it asks you to find how many multiples of $5$ are given in that ...
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1answer
23 views

Solving a arithmetic sequence problem

Irene deposited \$200 in a bank on 1st January and on the first day of each of the following months. At the end of June, when the interest was calculated, he found that his account balance was ...
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1answer
26 views

Arithmetic Sequences Problems

Find the sum $S$ defined by $$S = \sum_{n=1}^{20} \left(3n-\frac{ 1}{2}\right).$$ I have $$S = 3 \sum_{n=1}^{20} n- \sum_{n=1}^{20}\frac{ 1}{2} = 3(210) - 10 = 620,$$ but the answer is supposed to ...
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0answers
35 views

How to know if the equation has no solution? E_p (x!)= α

How to know if the equation has no solution? Ep (x!)= α What is the value of x? Knowing if p and α p is a prime number. Ep is the highest power of the prime p contained in X! Given the number α ...
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4answers
73 views

Does a number get destroyed when it is multiplied by zero?

We consider following subtraction- $$3-1=2$$ If we subtract 1 from 3 than result is 2. in This operation 1 is not destroyed but only replaced from 3 now we consider following equation- ...