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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5
votes
2answers
215 views

Find $x;y$ such that: $\frac{x^2+y^3}{xy-1} \in \mathbb{Z}$ [closed]

Let $x,y \in \mathbb{Z}$ such that: $$\frac{x^2+y^3}{xy-1} \in \mathbb{Z}$$ Find $x,y$ I don't have any ideas about this problem.
2
votes
1answer
47 views

Speeding up integer division if only certain bits in result are needed

Let's say I need to divide two integers $x$ and $y$, but I only care about the lowest 8 bits of the answer, i.e. I'm calculating: $$r = \frac{x}{y}\,\,\%\,\,256$$where % is the modulus operator. Is ...
0
votes
1answer
32 views

Subtraction of trigonometric functions

I was working on a problem booklet and came across the following equation. $$\sqrt2\sin(2x)-\cos(2x)=\sqrt3\sin(2x-a)$$ $a \in \mathbb{R}$ is a specific value that I'm supposed to find, but I don't ...
0
votes
1answer
24 views

Find the lower and upper bounds

I'm stuck with this question: $-2 < x < 6$ and $-4<y<-2$ What are the bounds of $x^2-y^2$? I thought that they are $(-2)^2-(-4)^2 = -12$ and $6^2-(-2)^2 = 32$, but apparently they are ...
1
vote
1answer
123 views

Why is $\sqrt{X}\times\sqrt{X}=X$?

Today I was solving the limit $(\ln(x))/(2*(x^{1/2})$ but then faced the step after applying the derivation that ended up with $(1/x)/(1/x^{1/2})$ and the result of that was $1/x^{1/2}$. When I asked ...
0
votes
4answers
679 views

Dividing fractions in real life scenario / application

First of all sorry if this question sounds too stupid or offends anyone. One apple divide by two you get half an apple. $\large{\frac{1}{2} = 0.5}$ I couldn't get my head around with dividing ...
0
votes
3answers
85 views

Cube roots of complex numbers [closed]

I need help with finding the cube roots of the complex number 27... I know that the obvious answer is three, but what is the less simple method to solving this?
4
votes
0answers
74 views

$d$ and $d+1$ both dividing certain integers

\begin{align} & 1\cdot 72 \\ & 2\cdot 36 \\ & 3\cdot 24 \\ & 4\cdot 18 \\ & 6\cdot 12 \\ & 8\cdot 9 \end{align} When the divisors of a number are listed in this way, let us ...
1
vote
2answers
48 views

Proving that $a \dot{-} (b+1) = (a \dot{-} b) \dot{-} 1$

This should be an easy exercise from Hodel's Introduction to Mathematical Logic, but for some reason I'm not getting it right. Define $a \dot{-} b$ as $a-b$ if $a \geq b$ and as $0$ otherwise. ...
13
votes
2answers
1k views

How to avoid stupid mistakes in calculus exams without checking the whole process?

Few days ago I failed my Calculus exams. And again it was mostly due to simple mistakes such as forgetting about minus in front of fraction, switching y coordinates of two points etc. The assignments ...
0
votes
1answer
23 views

How many rows & columns do 1,028 equal spaces create…

I have a board that is 17.5" wide and 67" long. I need to divide this board into 1,028 equal spaces. How many rows and how many columns will this equate to?
1
vote
4answers
120 views

Find all numbers divisible by 25, that begin with 6.

please, help me solve this problem: Find all numbers divisible by 25, that begin with 6. Regards.
0
votes
2answers
110 views

Cone mensuration sum

I am a tenth grade student. I am normally good in mensuration, but a question stumped me. The height of a cone is 30 cm. A small cone is cut off at the top by a plane parallel to it's base. If ...
4
votes
3answers
53 views

Find all 4 digits numbers that $ABCD=(CD)^2$

Please help me to solve following problem: Find all 4 digits numbers such that $ABCD=(CD)^2$.(any of $A,B,C,D$ is a digit!) I know one of solutions is $5776=(76)^2$.
0
votes
1answer
59 views

How to calculate the number of combinations of $x$ integers, each with a value between $y$ and $z$?

For example, if I have 4 integers, and each can be between 0 and 36, how many combinations are there? If the numbers have appeared before, but in a new order, then this still counts as a new ...
4
votes
2answers
96 views

Are $+, -,\times,\div$ the “base” calculations?

My friend told me that every equation possible with modern mathematical notation boils down to only $+, -,\times,\div$ What that means is that you can take any function and if you dive deep enough ...
4
votes
6answers
491 views

Is $15/52$ equal to $17/59$?

Is $\frac{15}{52} = \frac{17}{59}$? I typed it into the calculator and found: $$\frac{15}{52} = 0.2884615 $$ $$\frac{17}{59} = 0.2881356 $$ So I thought they were different. But then my friend said ...
2
votes
2answers
72 views

How to understand the principles of the rule of three? By the way, who invented it?

I'm looking to learn all the basic math now, because now I'm an adult math looks much more interesting and easier than ever! As I saw no exact answer for my doubt here on Math SE I resolved to ask ...
-3
votes
2answers
68 views

problem of arithmetic [duplicate]

You can only use the numbers $1,3,5,7,9,11,13,15$. You can also repeat the numbers. Fill in the blanks: ____ $+$ ____ $+$ ____ $=30$
23
votes
5answers
2k views

Is there any explanation for the repetitions after decimal point on divisions like 24/7

I was trying to divide 24 by 7 using a pen and a paper. After I had no more space on my checkerboard paper, I decided to put it on a calculator. The calculator returned 3.428571428571429 and I ...
6
votes
3answers
113 views

How to get all the decimals on a division with decimal point and without remainder?

I divided 4.18 by 5 by hand, like this: As you see I removed the decimal point since I was dividing by a whole number, then I put the decimal point back and got 0.83 as result. It's correct, the ...
1
vote
0answers
217 views

Arithmetic progression Find first term and common difference when sum of 10 terms and the 8th term is given

Sigma is a car company that sell cars. Sigma sells $x$ cars in the first month and its sales increase constantly by $y$ cars every subsequent month. It sells $96$ cars in the $8^{th}$ month and the ...
7
votes
2answers
138 views

Prove: if $n\mid 7^n+6^n$ and $n>1$, then $13\mid n$

Prove: if $n\mid 7^n+6^n$ and $n>1$, then $13\mid n$ Let $p$ be the least prime number such that $p\mid n$. And I want to show that $p=13$ Let $d$ be the least number such that: $14^d\equiv 0 ...
2
votes
1answer
58 views

How prove this fact about consecutive square numbers?

I saw somewhere that the sum of three consecutive squares minus $2$ is divisible by $3$. For example, $$2^2+3^2+4^2-2=4+9+16-2=27=3\cdot 9$$ But, I'm not sure how to give proof for this "property" of ...
1
vote
1answer
52 views

MLE of Integer Valued Normal Distribution

If Z is a normal random variable on $\mathbb{R}^d$ with parameters $(\mu,\Sigma)$ and we know that $\mu\in \mathbb{Z}^d$ and $\Sigma \in \mathbb{Z}^{d+}$; then how can we solve this MLE problem for ...
3
votes
5answers
141 views

How does 9 mod -7 = -5?

Forgive me if this question does not belong on this site for it is simplistic and this is my first post, however I do not seem to understand the modulo function when it comes to negative numbers. I'd ...
0
votes
2answers
104 views

An infinite square arithmetic progression? [duplicate]

How to prove that there does not exist and infinite arithmetic sequence that all of it's terms are distinct squares of integers?
0
votes
1answer
249 views

Time And Distance (Train Journey)

The average speed of a train in the onward journey is 25% more than that in the return journey. The train halts for one hour on reaching the destination. The total time taken for the complete to and ...
2
votes
5answers
134 views

Solving $ \sqrt{x - 4} + \sqrt{x - 7} = 1 $.

I have the equation $ \sqrt{x - 4} + \sqrt{x - 7} = 1 $. I tried to square both sides, but then I got a more difficult equation: $$ 2 x - 11 + 2 \sqrt{x^{2} - 11 x - 28} = 1. $$ Can someone tell me ...
1
vote
2answers
106 views

Time, Speed and Distance

A walks around a circular field at the rate of one round per hour while B runs around it at the rate of six rounds per hour. They start in the same direction from the same point at 7.30 a.m. They ...
0
votes
0answers
23 views

Percentage Increase and Dates

Suppose we have the following data: ...
45
votes
11answers
8k views

What exactly IS a square root?

It's come to my attention that I don't actually understand what a square root really is (the operation). The only way I know of to take square roots (or nth root, for that matter) it to know the ...
4
votes
3answers
241 views

Calculate fractional part of square root without taking square root

Let's say I have a number $x>0$ and I need to calculate the fractional part of its square root: $$f(x) = \sqrt x-\lfloor\sqrt x\rfloor$$ If I have $\lfloor\sqrt x\rfloor$ available, is there a ...
1
vote
0answers
56 views

Solving a (tricky) arithmetic congruence equation in the general case

Out of sheer curiosity, I am looking for the solutions of the congruence equation : $n^{n+km} \equiv n$ mod m for every k natural integer where $k,n,m \in N$ where m=$p_1^{\alpha_1}p_2^{\alpha_2} . ...
1
vote
1answer
18 views

A rescaled inner product inequality

I was wondering if the following inequality is true: Let $\xi_1,...,\xi_n$ be vectors in a Hilbert space $H$ and let $x_{i,j}$ be complex numbers such that $\prod x_{i,j}$ is real and $$\prod ...
2
votes
2answers
205 views

Parameterization of Natural Numbers

Suppose we have 4 positive integers $a<b<c<d$ such that $a+d=b+c=n$, i.e. $a,d$ and $b,c$ have the same average. Does there exist $p,q,r,s \in \mathbb Z$ such that \begin{equation*} ...
0
votes
1answer
45 views

Incommensurable units as ratios

I am having a bit of trouble understanding the concept of an incommensurable unit. From what I have gathered so far, it is simply a magnitude that cannot be expressed as the ratio of two natural ...
0
votes
0answers
53 views

Calculate shifted unit circle values

I have the black unit circle and I need to shift it by x degrees getting the red unit circle. How do I shift it, because just subtracting x degrees from the original black circle doesn't work. ...
0
votes
1answer
26 views

Find $f^{-1}(g(x))$ if $f(x) = 2x + 1$ and $g(x) = x^{2}$

Question: Let $f$ and $g$ be defined as: $$f(x) = 2x + 1, ~~~~x \in \mathbb{R}$$ $$g(x) = x^{2}, ~~~~~~~~~~~~x \in \mathbb{R}$$ Find a) $~~f^{-1}(x)$ b) $~~f(g(x))$ c) $~~g(f(x))$ d) ...
2
votes
1answer
73 views

Making the segment with given length $\sqrt[3]{2}$?

Using Pythagoras' Theorem we can make the segment with given length of Square root of natural numbers. For example the segment of given length The square root of 2 is equal to the length of the ...
1
vote
3answers
57 views

If I have the value of $\sqrt{1.3}$ could it be possible to find other square roots from that value? using the manipulation of surds?

If I have the value of $\sqrt{1.3}$ could it be possible to find other square roots from that value? using the manipulation of surds?
25
votes
11answers
2k views

Is there any way to define arithmetical multiplication as other thing than repeated addition?

Is there any way to define arithmetical multiplication as other thing than repeated addition? For example, how could you define $a\cdot b$ as other thing than $\underbrace{a+a+\cdots+a}_{b ...
0
votes
1answer
103 views

How to convert an interval to different one

I have a variable x in the interval [-30; 30]. I need to convert this interval so x would be in the interval [0; 1]. What I mean is like this: ...
0
votes
5answers
74 views

canceling double fractions how?

I had this example: $$ \frac{\frac{11}{5}}{2} = \frac{11}{10} $$ then: $$ \frac{2\frac{1}{5}}{2} = \frac{11}{10} $$ $$ \frac{1}{5} \not= \frac{11}{10} $$ is this right canceling of double ...
0
votes
1answer
33 views

Combinations in Arithmetic progression?

My question actually come from this: Intuitively understanding $\sum_{i=1}^ni={n+1\choose2}$ I was once examining the sum of an A.P series with first term $a$ and common difference $d$ . And this ...
0
votes
1answer
23 views

Dust coating a length of road that is 1.25 miles long.

A length of road is 1.25 miles. 8 landowners along the road would like to split the cost of dust coating the road. The cost of dust coating is at $53 per 100 feet. The county will reimburse the ...
12
votes
4answers
8k views

Subtraction when second number is bigger than first number

I'm a bit new to this. I'm trying to figure out how subtraction works pen and paper wise. I have a bit of a program where I can't seem to find any answers online. What I want to do is use the ...
9
votes
2answers
514 views

Continuum between addition, multiplication and exponentiation?

I noticed this old post which attempts to find the shades of grey between a linear and log scale where results are between zero and one. However, I was looking for the more general case where we find ...
-1
votes
1answer
50 views

Proof that $a^n \ne b^{n+1}, (a, b) \in \mathbb{Z}$ [closed]

I was wondering if there exists a proof that: $$a^n \ne b^{n+1},$$ $$a, b \in \mathbb{Z}$$ It would really help with a project that I am working on. Thank you very much!
3
votes
1answer
74 views

What is meant by “decimal adjustment” in this problem?

I know how to do addition in different bases, and I know how to convert between bases, but I have never heard of "adjustments" between bases while adding. I would solve this by simply getting a ...