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

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0
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1answer
24 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 ...
3
votes
2answers
55 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 ...
3
votes
6answers
316 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
50 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
45 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: ____ $+$ ____ $+$ ____ $=30$
21
votes
4answers
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 ...
5
votes
3answers
63 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
33 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 ...
3
votes
0answers
78 views

Looking for handy arithmetic tricks [on hold]

A few days ago my grandfather taught me a trick to make it easier to calculate squares of quintuples in decimal numbers. What he told can be expressed in this way: $$ (10n+5)^ 2\quad = \quad ...
-4
votes
0answers
25 views

Advance Algebra sequence ad series [on hold]

A number between 1 and 10000 is randomly selected. What is the sum of all terms which is divisible by 4 ad 5?
7
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2answers
109 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 ...
-9
votes
2answers
43 views

$1$kilogram -$ 200$grams [on hold]

I use 200g out of a 1kg packet of sugar. How many grams of sugar are left?
2
votes
1answer
42 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 ...
0
votes
1answer
30 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 ...
2
votes
5answers
84 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 ...
-4
votes
2answers
29 views

word problem with addition [on hold]

if every 100 points is \$10 and every survey is worth 5 points, how many surveys do I have to take to reach \$200 ?
0
votes
2answers
38 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
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0answers
45 views

Countability of $\mathbb{Q}$ using two sequences. [closed]

I'm trying to prove the countability of $\mathbb{Q}$ using the following problem. For integers $n\ge 1$ , let $a_n=k$ if $3^k$ divides $n$ and $3^{k+1}$ doesn't divide $n$. Let $b_1=2$, and for ...
0
votes
1answer
14 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 ...
0
votes
1answer
34 views

Time And Distance (Gunshots and Train) [on hold]

Two guns were fired from the same place at an interval of 10 minutes and 30 seconds, but a person in the train approaching the place hear the second shot 10 minutes after the first. Speed of sound is ...
0
votes
0answers
26 views

Problem understanding Finance Math question [closed]

A salesman receives a commission of 6% on his Sales for the week. If his income for the week is $746, find the value of his sales for the week, to the nearest dollar. I have no idea how to figure ...
2
votes
5answers
114 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 ...
0
votes
1answer
20 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
19 views

Percentage Increase and Dates

Suppose we have the following data: ...
43
votes
11answers
7k 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
81 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
33 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
12 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
197 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
19 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
26 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. ...
-9
votes
1answer
53 views

Is this method of finding $3\times9$ correct? [closed]

Calculate $3\times9$ : Are there any other methods to solve?
0
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1answer
23 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
54 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
40 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?
21
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
20 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
47 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
17 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
20 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
2k 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 ...
6
votes
2answers
258 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
48 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
33 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 ...
1
vote
7answers
172 views

Why do we invert then multiply when dividing fractions?

I have looked up various sites online. They only explain it in a very basic arithmetic way. Would someone explain to me why is $\displaystyle\frac{x}{\frac{1}{2}}$ is $\displaystyle\frac{2x}{1}$?
8
votes
2answers
878 views

Find P + Q + R?

I was doing questions from previous year exam paper and I'm stuck on this question. It seems easy but I am not getting the point from where I should start. Suppose $P, Q, R$ are positive integer, ...
1
vote
2answers
28 views

Simple Adding and Subtracting algorithm to get a current amount

So this is my first post and its probably a really dumb question but I cannot get my head around a proper algorithm to handle the following situation. I have a dataset that contains employees who ...
0
votes
1answer
20 views

Figure out attendance needed for remaining days to reach attendance goal

Trying to come up with attendance percentage needed to reach a goal. To simplify a student to date has gone to school 140 of the 150 days and therefore their current attendance is .93 There are 70 ...
2
votes
1answer
30 views

Weighted mean of an object (Centers of mass)

I am having trouble understanding the concept. Usually when I calculate the center of mass of an object when given area and dimensions I'd multiply corresponding distances with areas etc then ...
2
votes
1answer
36 views

How to find square and cubes

I want to find the smallest positive integer A in which $$10A$$ is a perfect square and $$6A$$ is a perfect cube Thanks for the hint, I can see now I just needed $$2^5,3^2 , 5^3$$