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

learn more… | top users | synonyms (1)

0
votes
1answer
44 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 ...
0
votes
3answers
55 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 ...
0
votes
2answers
64 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 ...
6
votes
3answers
120 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 ...
0
votes
0answers
23 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 ...
0
votes
1answer
45 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 ...
1
vote
1answer
47 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 ...
2
votes
2answers
54 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
votes
1answer
66 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. ...
1
vote
4answers
239 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 ...
0
votes
1answer
30 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 ...
0
votes
1answer
28 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 ...
1
vote
4answers
76 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- ...
1
vote
1answer
121 views

An impressive fact expressible in presburger arithmetic?

Is there something expressible in presburger arithmetic that would seem impressive to students at an undergraduate level?
-1
votes
1answer
57 views

The number Triangles in this picture [duplicate]

I want a method for find the number triangles in the under image.
0
votes
1answer
14 views

Change formula from EV to Shutter Speed equivalent

I have this formula: $$\mathrm{EV}=\log_2\frac{N^2}t,$$ How can I extract $t$? $t = ?$
0
votes
0answers
17 views

A set of integers for which the sum of any two nos. is unique to the sums of any other pairs of nos?

Is there a set of numbers for which the sum of any two nos. is unique to the sums of any other pairs of nos? I'm trying to keep track of the coincidence of several events, and if each event is ...
1
vote
1answer
30 views

how to find percentage loss

I am passing through a question in which problem is like `I sold a book for $250$ dollars, which resulted in a loss of 50 dollars. So how much loss in percentage. The formula I understand to fit on it ...
0
votes
2answers
46 views

Divisibility rules of 2, 3, 5, 9 and 11

How can I prove this divisibility rules? $b \in \mathbb{Z}^+$ $2\mid b \Longleftrightarrow 2\mid r_0$ $3\mid b \Longleftrightarrow 3\mid(r_0+r_1+\cdots+r_n)$ $5\mid b \Longleftrightarrow 5\mid r_0$ ...
1
vote
1answer
33 views

Conjecture: Substrings of $x^x$

My conjecture: There exists no natural number $x$ for which the following statement holds: The string $x$ occurs $x$ times in the number $x^x$. For example, pretend that $11921192^{11921192}$ ...
0
votes
3answers
67 views

How to simplify $\sqrt[3]{29\sqrt{2}-45}-\sqrt[3]{29\sqrt{2}+45}$

I in trouble simplifying this: $$\sqrt[3]{29\sqrt{2}-45}-\sqrt[3]{29\sqrt{2}+45}$$ couldn't find a solution. Can you help?
0
votes
1answer
20 views

An actuary question but more of an algebraic manipulation

I'm stuck in this actuary question. If $a_{\overline{n|}}=x$ and $a_{\overline{2n|}}=y$, express $d$ as a function of $x$ and $y$ Hints: $a_{\overline{n|}}=\frac{1-v^n}{i} $, $v=\frac{1}{1+i}$, ...
1
vote
3answers
177 views

Find the distance between two towns given train timings

While practicing maths and starting to learning it, I found question this question: A train running between two towns arrives at its destination 10 minutes late when it goes 40 miles per hour and ...
0
votes
1answer
39 views

Sum of numbers in arithmetic series [closed]

I need some help to find the summation of the series of following from $\frac{1}{(n+10)^2}$. I need to get the some from $n=0$ to $n=2280$. can anybody help me find the answer for this. Thanks in ...
0
votes
4answers
41 views

Arithmetic: simple interest question

Alice puts 3400 dollar on her bank account with interest rate 3,7%. How much interest does she receive in the second year? I answered: $3525.8\cdot1.037-3400\cdot1,037=130.5$, but this is the ...
2
votes
2answers
53 views

How to prove that $(p-1)^2$ $\mid$ $(p-1)!$ when $p$ is a prime number and $p>5$?

I say that $p-1$ $\mid$ $(p-1)!$ then I want to prove that $p-1$ $\mid$ $(p-2)!$. I started by saying that $p-1$ is an even number so $2\mid (p-1)$ and that means that $\frac{p-1}{2}$ is an integer. ...
1
vote
1answer
91 views

Is there a simple closed form of $|\alpha(\sqrt{n}-\left\lfloor \sqrt{n} \right \rfloor) + \beta(\sqrt{n}-\left\lfloor \sqrt{n} \right \rfloor)|$?

Let $d_n(x)$ denote the $n$'th digit after the decimal point in $x$. Examples: $d_8(e) = 2,\;d_5(\pi) = 9$ $\alpha(x)$ and $\beta(x)$ are defined this way: $$d_n(\alpha(x)) = \left\{ ...
3
votes
4answers
93 views

Is there an example to demonstrate why $\frac{1}{(1/2)}$ equals $2$?

To explain why $\frac{1}{2}=\frac{2}{4}$ I use slices of pizza and show how eating one slice of a pizza cut in half is the same thing as eating two slices of a pizza cut in quarters. Is there a way ...
0
votes
0answers
21 views

help in simplifying an easy but nasty expression

I would like double check my work, I am trying to simplify the following summation, \begin{align} \sum_{\substack{(i,j) \in \mathcal{S}}} A_i v_i v_j \end{align} with the assumption that $$v_iv_j= c ...
0
votes
1answer
35 views

How to show that$\ \sqrt[3]{ \sqrt{y^2-x}+y}+ \sqrt[3]{-\sqrt{y^2-x}+y} = k \implies y = \frac{k\left(k^2-3 \sqrt[3]{x}\right)}{2}$?

We also have $\ x \ne y $, $\ y > 1$, $\ 0<x<1$,$\ k \ne 0$. I have tried on my own, by canceling out the roots, but they keep on appearing. I guess that is not the right way. Thanks in ...
1
vote
1answer
45 views

The elementary question on sign of Rational numbers

The under picture show that $$+\dfrac{8}{3}=\dfrac{+8}{3}$$ Similarly we can show $-\dfrac{8}{3}=\dfrac{-8}{3}.$ Now How do can show that $$-\dfrac{8}{3}=\dfrac{8}{-3}?$$
0
votes
1answer
18 views

Enumerating the elements of $\mathbb{Z}^n$

The elements of $\mathbb{Z}$ can be enumerated as $0, 1, -1, 2, -2, 3, -3, \ldots$. Similarly, the points of the lattice $\mathbb{Z}^2$ can be enumerated $$(0,0), (1,0), (0,1), (-1,0), (0,-1), ...
0
votes
2answers
35 views

How to solve this age probem - ration using singapore mathematics?

I am new to Singapore mathematics. I could solve this question very easily using algebra. However, I feel that you get a good picture - conceptually when you try to solve questions using singapore ...
2
votes
2answers
53 views

How do I solve an equation with three terms, with the unknown inside a square root, inside a third root, in two of them?

The equation is $$\\ \sqrt[3]{\sqrt{a}+b}+\sqrt[3]{-\sqrt{a}+b}=k.$$ How do I find$\ a$?
0
votes
4answers
142 views

Does the zeroth root exist?

Definition of Nth root: 3rd order inverse group 1 hyperoperation. Division is how many times you can subtract a certain divisor from the dividend before it becomes negative. Likewise Nth root is ...
0
votes
0answers
22 views

Computing composite functions

This may not be strictly a math question but is related. Whenever there is some function that computes more than two elements, is it possible that all elements are computed at once? Or is computing ...
0
votes
1answer
49 views

How many (decimal) digits does $2^{3021 377}$ have?

I was wondering, how many (decimal) digits does $2^{3021377}$ have? We have $2^4=16,\, 2^5=32,\, 2^6=64$ and $2^7=128,\, 2^8=256, \, 2^9=512$ but $2^{10}=1024,\, 2^{11}=2048, \, 2^{12}=4096, \, ...
5
votes
4answers
82 views

Find the limit as x approaches negative infinity for $\sqrt{x^2+x-1} +x$

Find the limit as x approaches negative infinity for $\sqrt{x^2+x-1} +x$ My solution: multiplying by: $\displaystyle\frac{\sqrt{x^2+x-1}-x}{\sqrt{x^2+x-1}-x}$ Which gives us: ...
0
votes
2answers
41 views

Running 3 miles in 20 minutes, how many miles can one run in 50 minutes?

Maria can run 3 miles in 20 minutes. At this rate, how many miles could she run in 50 minutes? I have tried dividing 3 by 20 to get the unit rate.
0
votes
2answers
12 views

Converting units and currency

A supermarket in Japan sells soy milk for 398 yen per liter. If there are 83.35 yen per dollar, then what is the price in dollars per quart? Conversions that were given. Dollars per foreign =0.0120 ...
2
votes
0answers
27 views

Significance of formulas similar to summation formula

We all know formula $n(n+1)/2$ for adding up the numbers from $1$ to $n$. But I would like to know if there is any significance and use of formulas of type $n(n^{p-1}+p-1)/p$, where $p$ is a prime. ...
1
vote
1answer
82 views

Can we solve variable questions without using algebra - for example age problems?

I am not sure on what should be the quick way of approach to solve these kind of questions. As we grow, we can think of other possible ways to solve the same problem. Many genius can solve the algebra ...
1
vote
2answers
44 views

Are there real extensions of the operations of addition, multiplication, exponentiation, etc in the other direction?

We have $\underbrace{a+a+a...+a}_{n\:times}$ which equals $a \times n$, and also $\underbrace{b \times b \times b.... \times b}_{p\: times}$ is $b^p$, so I was wondering if the generalization would ...
3
votes
2answers
157 views

Is it allowed to use “equal to” and “approximately equal to” in the same sentence?

Let's use the following example: $$17! = 16!*17 \approx 2 \cdot 10^{13} * 17 = 3.4 \cdot 10^{14} $$ Are you allowed to do this? I am in doubt whether or not this indicates that $17! = 3.4 \cdot ...
0
votes
1answer
38 views

how many questions did D answer correctly

Each of A, B, C, and D took a test. Each of them answered at least one question correctly, and altogether they answered 67 questions correctly. A had more correct answers than anyone else. B and C ...
-1
votes
2answers
45 views

What is the sum of one + one in a 26 letter number system

A number system based on 26 uses the letters of the alphabet as its digits, with $A = 0, B = 1, C = 2, D = 3, E = 4, . . . , Y = 24,$ and $Z = 25. $ What is the the sum: ONE + ONE = in this system
0
votes
1answer
61 views

x / 3 + y /3 + z / 3 = (x + y + z) / 3?

Is the following equation always true? x / 3 + y /3 + z / 3 = (x + y + z) / 3 I hope this is not too simple of a question. Every example I can think of, this equation is true. However, in a ...
1
vote
1answer
54 views

Is this assertion true or false? $(\exists x)(\exists y)(\forall z)(y \ne x+z \Rightarrow y\lt x)$ Cohn - Classic Algebra P7

$x,y,z\in\mathbb{N}$ with $0$ $(\forall x)(\forall y)(\exists z)(y \geq x \Rightarrow y=x+z)$ Can you help me with trivial thing above? I imagine it is because I am tired, but I can't see if this is ...
0
votes
1answer
25 views

An inequality question involving non-negative integers

I am trying to prove something then I hit a stumbling block in the form of this problem. Let $a,b,c,d$ be non-negative integers such that: $c,d$ are fixed $\max a=d$ $$a\geq b$$ $$c\geq b$$ ...
6
votes
3answers
149 views

What does $23_4$ mean?

I just saw this on a mathematical clock for $11$, i.e $23_4=11$: http://ecx.images-amazon.com/images/I/51nsaGqFoUL.jpg I guess it is some notation from algebra. But since algebra was never my ...