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Questions tagged [arithmetic]

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. Questions about number theory (sometimes called "arithmetic") should not use this tag and should instead use (number-theory) or (elementary-number-theory).

Arithmetic is defined as operations upon numbers using $4$ main operations along with many others:

addition - the sum of two numbers

subtraction - the difference of two numbers also defined as the addition of negative numbers

multiplication - the area of a rectangle with sides of lengths equal to the two operands

division - the number of times one number can be subtracted from another before equaling zero. Sometimes it will allow decimals and in other cases there will be a remainder left over when a number doesn't go into another evenly

See Arithmetic.

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simplifying formula $\frac{(k-1)(k-1 +1) (2(k-1)+1)}6$

I'm trying to understand my textbook's example (it's part of a mathematical induction problem) and I just don't get how the author managed to simplify this formula: $$\frac{(k-1)(k-1 +1) (2(k-1)+1)}6 = \frac{(k-1) k(2k - 1)}6$$ Could anyone…
limony
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Commutative and Associative Properties for Addition

I am trying to find out the difference between Commutative and Associative Properties for Addition. I got this from a elementary school kid, sadly I was unable to answer his question. basically his question is, What is the addition property for…
CoolArchTek
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How to perform operations on numbers with tolerances?

If I have 1±0.04 + 1±0.04 what would the tolerance of that equal? What if we change it for a - or * or /? I read somewhere that you should square the tolerances, add them together and then square root them. Which doesn't make sense because if I have…
Aequitas
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Compound interest question

A property is mortgaged over $20$ years at an interest rate of $5.6$% per annum compounded annually. If the mortgage is £$120,000$, what are the annual repayments if payments are made at the end of the year? Just trying to help someone out with…
snowman
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Solving proportion problems involving three quantities

How do you solve proportion if 3 variables are given? I have looked in this site but i could not undertand it completely http://www.beatthegmat.com/ratio-proportion-3-variables-t34902.html 15 robots can make a train in 6 days working 5 hours a day.…
shadow
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Given a time, calculate the angle between the hour and minute hands

I cannot understand the solution to the following programming problem. I will be very thankful for you help! Given a time, calculate the angle between the hour and minute hands Solution: • Angle between the minute hand and 12 o'clock: 360 * m / 60 •…
ShockWaveMonster
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How to check that numbers "a" and " b", a digit at a position "i" from number "b" is less or equal than the digit at position "i" at number "a"?

How to check that for given natural numbers "a" and " b", a digit at a position "i" from number "b" is less than the digit at position "i" at number "a" without iterating digit by digit? e.g. for : a = 22222 b = 10001 is ok but b= 10030 is not…
Clyde
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How to evolve an expression with two denominators

The task is to simplify the expression: $\displaystyle\frac{f(x+h)-f(x)}{h}$ when $\displaystyle f(x) =\frac{1}{x}$. I don't know how to do this since I get to the step $\displaystyle\frac{\frac{1}{x+h} - \frac{1}{x}}{h}$ which gives me two…
addde
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Does $k\cdot x < y$ imply that $x \ne y$?

Sorry if the question is trivial, but I have trouble getting my head around it. To keep short, does $\forall k \in \mathbb Z^*, \forall (x, y) \in \mathbb Z^2, k\cdot x < y \implies x \neq y$? ($\mathbb Z^* = \mathbb Z - \{0\}$) I work in $\mathbb…
scand1sk
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Not sure how to do binary division

I saw this question in my textbook: https://i.stack.imgur.com/82luA.png It doesn't look right. From what I understand: 110101 into 101000110100000. 110101 can't go into 101000, so you extend it by one, then do 110101 into 1010001, no? I'm…
soju
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Maximize a possible "sure bet".

I've posted a similar question some days ago: Maximize a welcome bonus. , but I didn't specify some details that turn this in a different question (maybe). (If this has the same answer of the previous one I'll edit that question). A betting website…
KingBOB
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Saving should start early

This is a very interesting word problem that I came across in an old textbook of mine. So I know its got something to do with compound interest, but other than that, the textbook gave no hints really and I'm really not sure about how to approach it.…
anonymous
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Maximize a welcome bonus.

Let's consider a sport betting website that offer to refund the first bet to new users (up to $20). What's the best way to extract the maximum value from it? In a 2 outcomes event, I can easily consider it a "sure bet": if I have 1 outcome refunded…
KingBOB
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Am I going nuts or does this seem right?

Just wondering, it's been a long time since high school math for me. The the expression below make sense? I have my doubts because I remember the laws of radicals saying something about division that contradicts the below. $$ \sqrt{x} \cdot…
Zoltan
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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.
TomDavies92
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