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

learn more… | top users | synonyms (1)

0
votes
3answers
29 views

Sum formula for geometric series

I solved this equation something like this, as shown in the photo: Is it correct? If I put $x=2$ I get weird results!
1
vote
0answers
8 views

Arithmetic encoding - probaility

I'm trying to understand how AC works. The thing that bugs me the most is how is probability chosen or calculated. In the given example message abcde produced the ...
0
votes
2answers
37 views

A man bought three tables for rs. $2500$, then find the prices of the individual tables?

Problem A man bought three tables for rs. $2500$. He sell the first at $5 $ % loss, second at $5 $ % profit and the third at $10$% profit. Find the cost price of each table if on the whole he ...
1
vote
1answer
54 views

Two expressions using three-digit floating point arithmetic with rounding?

What is the result of evaluating the following two expressions using three-digit floating point arithmetic with rounding? $(113. + -111.) + 7.51$ $113. + (-111. + 7.51)$ $9.51$ and $10.0$ ...
1
vote
1answer
20 views

Reduce a trigonometric expression 2.0

By what trigonometric trick does \begin{align} \sin\alpha\Bigg[\cos(\omega t + \varphi)+\frac{\cos\alpha\sin(\omega t + ...
0
votes
2answers
35 views

Negative exponents on a quantity in scientific notation considering significant figures

Are there rules that apply to negative exponents with regard to scientific notation? The specific problem is: $$\left(6.3\times10^{2}\right)^{-6}$$ I believe the following is correct: ...
0
votes
1answer
31 views

How to multiply Roman numerals?

How to multiply Roman numerals? I need an algorithm of multiplication of numbers written in Roman numbers. Help me please.
0
votes
2answers
29 views

Water volume sum

Let's start by quoting the question. Water flows at the rate of 10 m per minute through a cylindrical pipe of diameter 5mm. How much time would it take for it to fill a conical vessel of diameter ...
-6
votes
2answers
54 views

Can you get 21 with 9 and 10? [closed]

Okay, so everyone knows the joke that has been going on. "What's 9 + 10? 21". Yeah, so I was wonderning an you get 21 with 9 and 10 at all, this means any mathematical aspect can be used.
1
vote
3answers
92 views

Does the order of operations matter with just addition and subtraction?

Had a debate on whether you could do addition/subtraction in any order you want. Specifically, for the following: $9 - 4 + 3$ We both agree that the answer is 8. I argue that, by giving addition a ...
3
votes
0answers
18 views

Absolute convergence of ordinary Dirichlet series

I am currently reading Serre's 'A course in Arithmetic' and I have a question about proposition 8 of section 2.4 (but I think the question can be answered without knowing the book.) The proposition ...
0
votes
1answer
42 views

A cat chases a rat. For every $5$ leaps of the rat , the cat takes $3$ leaps

problem A cat chases a rat. For every $5$ leaps of the rat , the cat takes $3$ leaps, but the $2$ leaps of the cat are the same as $3$ leaps of the rat. Compare the speeds of the cat and the rat ...
5
votes
4answers
101 views

If $x$ is a positive integer such that $x(x+1)(x+2)(x+3)+1=379^2$, find $x$

If $x$ is a positive integer such that $x(x+1)(x+2)(x+3)+1=379^2$, find $x$ This is a 1989 ARML problem. One, ugly way to solve this is: What's a nicer way? Hint
1
vote
2answers
35 views

Algebra logic on simplification

I've been self studying algebra for some time alone and a common problem I bump into that always throws me off is something like this (Complete idiots guide to algebra, if you know a better book ...
2
votes
2answers
44 views

Silly question about properties of operations

This is a very frivolous question about basic arithmetic. In a precalculus book I'm going through substraction and division are informally defined as the "opposites" of addition and multiplication, ...
0
votes
1answer
35 views

Calculating Lower and Upper Bounds of 100 to 2 Significant Figures

I'm trying to help my daughter with the concept of lower and upper bounds of a number when given a specific accuracy, but I'm starting to realise how many holes there are in my own knowledge! For a ...
3
votes
2answers
20 views

If $(k,l) = 1$, show that $(b_2k-b_1l, a_1l-a_2k) = 1$ for $a_1b_2-a_2b_1=1$

Problem: If $(k,l) = 1$, show that $(b_2k-b_1l, a_1l-a_2k) = 1$ for $a_1b_2-a_2b_1=1$ Note: ($a_1, a_2,b_1,b_2,k,l \in \mathbb{Z}$) Also note that the actual (bigger) problem is: If $m = ...
1
vote
1answer
37 views

Propagation of Uncertainties [closed]

I have five values for the volume of sodium hydroxide needed to neutralise a fixed quantity of hydrochloric acid, each trial with an uncertainty of 0.05 mL. If I take the average of these five values, ...
2
votes
1answer
52 views

Prove that $(a+b, a-b) \ge (a, b)$

Note: $(x,y) := \gcd(x, y)$ Problem: Prove that $$(a+b, a-b) \ge (a,b)$$ for $a,b \in \mathbb{Z}$ Method: I used this method which failed. $$(a+b, a-b) = \min \{(a+b)x+(a - b)y | x,y \in ...
0
votes
1answer
27 views

Explanation of this (strong) induction statement

This might seem pretty simple and stupid to some but I am really not able to get it.... I was reading the proof that $\sqrt{2}$ is irrational (using induction) here. I could understand most of it ...
2
votes
1answer
18 views

Arithmetic Precedence

I stumbled upon an answer in another Stack Exchange site which is : $x = cx + r \times \cos a$ $y = cy + r \times \sin a$ With the above example, a degree of 76 would be: $x = 115 + ...
3
votes
1answer
85 views

Angle between the minute hand and hour hand of a clock?

At what time between $6$ a. m. and $7$ a. m. will the minute hand and hour hand of a clock make an angle closest to $60°$? $ 6: 22$ a.m. $6: 27$ a.m. $ 6: 38$ a.m. $ 6: 45$ a.m. My attempt : ...
0
votes
1answer
27 views

evaluating expressions in modulo 15 system

Hi !! I tried to find information and examples to solve this modulo arithematic problem but couldn't find it.. This is my preparation questions for exam and not assignment.Could someone explain the ...
1
vote
2answers
25 views

$\mathbb{Q}$: Unique operation s.t. $1\star q=q$ and right distributivity hold?

Given $\mathbb{Q}$ and the usual addition $+$ on it, do we have unicity of a binary operation $\star$ such that \begin{align*} \tag{1}1\star q&=q\\ \tag{2}(q+r)\star s&=q\star s+r\star s ...
0
votes
1answer
22 views

Given $n$ natural numbers, there are two or more of them that sum up to a multiple of $n$

Given $n$ natural numbers $m_1, ..., m_n$, of which none is divisible by $n$, I want to prove that there exist an $i \in \{2, ..., n\}, k \in \mathbb{N}$, so that the sum of exactly $i$ of the given ...
39
votes
0answers
4k views

Explaining to a kid why a negative × negative = positive? [duplicate]

My son's just turning 8 this year and has just started to learn some of the basics of multiplications, including multiplication signs. However, he's started asking me why a negative multiplied by ...
0
votes
0answers
15 views

How to add two negative binary numbers

Solve the following using two's complement binary numbers: $ (-111)_{10}-(110)_{10}=?$ $(-111)_{10}=(10010001)_2$ with 2s complement $-(110)_{10}=(10010010)_2$ with 2s complement But ...
2
votes
3answers
75 views

How to find the value of this expression?

I just saw this question in one exam. Please help me solve it. I am not able to find any clue on where to begin. (ignore that tick it might be wrong)
3
votes
0answers
26 views

Does anyone know of a Mental Math Game for blind students?

I'm looking for any computer game made for blind students where the math exercises are asked through a computer's speaker and answered through a microphone by the student. Unlike normal math games, ...
2
votes
2answers
25 views

Why is an equation that originally had a division through 0, still not defined in that point - after it was removed

Relearning the basics. When I have the equation: $$2x^2+2x+2=2x^2+2x+2$$ $$0=0.$$ I can say that x is any number. But when i simplify this equation from the following one: $$2x(x+1+ ...
0
votes
2answers
35 views

Arithmetic and Geometric Sequences, Requested term

c. Find the first four terms, with a1 as the first term, AND the requested term: an= 24 + 5n, a7 d. Find the first four terms, with a1 as the first term, AND the requested term: an= 24 - 9n, a5 ...
0
votes
0answers
17 views

What is Brijesh salary in $2004$ given the following conditions?

In 2003,Brijesh paid a tax of $20$% of his salary.In 2004,his salary increased by $325$/$400$ and the tax scheme changed.Under the new tax scheme he had to pay a fixed sum of Rs $1000$. and an ...
0
votes
1answer
26 views

Find the Total no of votes polled in lakhs given the following conditions?

In a election among $3$ candidates P,Q and R.P gets $120$% more votes than Q.P beats R by 3,50,000 votes.Q beats R by 5% of the total votes.Find the total no of votes polled in lakhs. MyApproach P ...
0
votes
1answer
21 views

How many boys have passed given the following conditions?

A School has $2000$ students,out of which $40$% of the students are in higher secondary.Out of the students in the higher secondary, $28$% are girls and $50$% of them passed.The overall pass ...
0
votes
0answers
26 views

Which is the default Standard Deviation Formula

I have to implement a test from research paper which says: As for testing criteria, standard deviation or min-to-90th percentile ( ) of large packets (1500 B) can be effectively used to find the ...
0
votes
2answers
36 views

For each $x,y∈\mathbb N$, if $x≤y$ and $y≤x$, then $x=y$ [duplicate]

Proof: For each $x,y∈\mathbb{N}$, if $x≤y$ and $y≤x$, then $x=y$ By definition of order, $x≤y$ if and only if $x<y$ or $x=y$ By definition of order, $x<y$ if there exist a $K∈\mathbb{N}$ such ...
1
vote
2answers
41 views

For each $x,y,z∈\mathbb N$, if $x<y$ then $x+z<y+z$

For each $x,y,z∈\mathbb{N}$, if $x<y$ then $x+z<y+z$ I know how to solve this if it was $x=y$ then $x+z=y+z$ (which my professor said I need to do) Is there a definition that says I can change ...
1
vote
1answer
24 views

How do I create an index where a low number equals a high score, as below?

Can you help? If $0.6 = 10$ and $30 = 1$, what does $3.3$ equal and what does $1.62$ equal? Is there a formula to this and if so what is it, please? This would enable me to calculate any number ...
2
votes
0answers
71 views

Prove if $x<y$ then $x+z<y+z$ [duplicate]

Note I am looking a proof using Peano's axiom as I am working on the Natural Numbers, not the Real Numbers. I need help proving "For each x,y,z in N, if $x<y$ then $x+z<y+z$ This must be done ...
1
vote
0answers
19 views

Proof of Antisymmetry [duplicate]

I am stuck with proving antisymmetry under the natural numbers. Prove "For each x,y E N, if x <= y and y <= x, then x=y. I am not really sure where to start with this proof. Im assuming I will ...
0
votes
1answer
72 views

$a_n = S_{n-1}$, arithmetic progression

I have an arithmetic progression. $$a = -27, -19, -11, ...$$ The question asks me to find a term in the progression where the term is equal to the sum of the terms behind him. Therefore: I need to ...
1
vote
3answers
29 views

How to find the smallest integer X where the Remainder of X / Y = 0

I am writing a grocery shopping program. I want to calculate the smallest number of items I have to buy to reach the smallest whole dollar amount. For example: Candies cost 0.11. You need 100 ...
1
vote
2answers
43 views

Tips and tricks for speedy mental division with harder fractions

I'm looking for a strategy to solve these kind of questions rapidly. Do you guys have any suggestions? $$\frac{\frac{15}{25}}{X}=\frac{14}{35}.$$ A. $\frac{3}{5}$ B. $\frac{63}{30}$ C. ...
-2
votes
4answers
80 views

What is the value of $0.7\overline{54}+0.69\overline{2}$?

What is the value of $0.7\overline{54}$ +$0.69\overline2$? (a) $\frac{1813}{900}$ (b) $\frac{1783}{910}$ (c) $\frac{14323}{9900} (d) \frac{13243}{9900}$ I get @edit $$754-7/990 + ...
0
votes
1answer
36 views

Justification for an Algebraic Expression

I have been struggling for the past few days trying to figure out an algebraic expression and solving it. The question consists of a kid spending ${$}20$ on pens and the options are ${$}4$ , ...
-1
votes
2answers
64 views

Property about $a+b=0$

We know well that $$ab=0\iff a=0 \vee b=0.$$ Is there any property that says about $a+b=0$? What about $$a+b=0 \stackrel{?}\iff a=0\wedge b=0.$$ Note that I do not deny that there are many solutions ...
0
votes
2answers
22 views

Average score for the remaining people [closed]

If 1000 people have an average (mean) score of 3.92, and we know that 450 people had a score of 1, how do we calculate the average score of the remaining 550 people? Can we even? My head says yes ...
21
votes
6answers
2k views

Which of the following powers is bigger: $2^{41}$ or $3^{24}$?

Calculate the maximum between the given numbers $$ \max(2^{41},3^{24})\text{.}$$ I got stuck when I tried to decompose the exponent as $41$ is a prime number.
0
votes
1answer
39 views

How does $a^2-4b(a-b)$ simplify to $(a-2b)^2$? [closed]

Please explain, step by step. I'm really stuck with this.
3
votes
3answers
142 views

Prove that between any two rational numbers, there are two irrational numbers whose difference is rational

I've gone through how to prove that there is an irrational between any two rational numbers but this is somehow stumping me