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.

6283 questions
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Why does this innovative method of subtraction from a third grader always work?

My daughter is in year $3$ and she is now working on subtraction up to $1000.$ She came up with a way of solving her simple sums that we (her parents) and her teachers can't understand. Here is an example: $61-17$ Instead of borrowing, making it…
user535429
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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. Multiplication: Multiplicand × Multiplier = Product. Generally,…
trw
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Why is it that if I count years from 2011 to 2014 as intervals I get 3 years, but if I count each year separately I get 4 years?

I'm not a very smart man. I'm trying to count how many years I've been working at my new job. I started in May 2011. If I count the years separately, I get that I've worked 4 years - 2011 (year 1), 2012 (year 2), 2013 (year 3), 2014 (year 4). But if…
bodacydo
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51
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10 answers

Is it possible to simulate a floor() function with elementary arithmetic?

I'm using a "programming language" that only allows basic operations: addition, subtraction, multiplication, and division. Is it possible to emulate a floor function (i.e. drop the decimals a number) by using only those operators? I'm only…
fregante
  • 629
47
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How to round 0.4999... ? Is it 0 or 1?

If you want to round the repeating decimal 0.4999... to a whole number what is the right answer? Is it 0 or 1? On the one hand you only look at the first digit when you round numbers which in this case is 4 so the answer should be 0. On the other…
vonjd
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4 answers

How to get the aspect ratio of an image?

I have an image that is: 320 original width 407 original height I want to let users resize the image via a form I am building on a webpage. They can adjust either the width or height. When they do the other dimension should auto adjust to maintain…
JakeRow123
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9 answers

'Bee flying between two trains' problem

There is a famous arithmetic question : Two trains $150$ miles apart are traveling toward each other along the same track. The first train goes $60$ miles per hour; the second train rushes along at 90 miles per hour. A fly is hovering just above the…
Hailey
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38
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9 answers

Is multiplication not just repeated addition?

If multiplication is not repeated addition, what is it? How do you define multiplication? All of us had to memorize the multiplication table in elementary school, but how did they come up with it if so many people claim that it is wrong to think of…
Curiosity
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Rules for rounding (positive and negative numbers)

I'm looking for clear mathematical rules on rounding a number to $n$ decimal places. Everything seems perfectly clear for positive numbers. Here is for example what I found on math.about.com : Rule One Determine what your rounding digit is and look…
Jérôme
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How to avoid arithmetic mistakes?

When dealing with several numbers and long equations, it's common to make careless arithmetic mistakes that give the wrong answer. I was wondering if anyone had tips to catch these mistakes, or even better avoid them more often. (aside from the…
user26649
29
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16 answers

How did the rule of addition come to be and why does it give the correct answer when compared empirically?

I'm still a high school student and very interested in maths but none of my school books describe these kind of things, and only say how to do it not the whys. My question is very simple, for example: 19 +25 = 44 because the…
bzal
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7 answers

Why does exponentiation have 2 inverses?

I was wondering why addition has one inverse (subtraction), multiplication has one inverse (division), but exponentiation has two (radication and logarithm). After a bit of thinking, I thought it might have something to do with the fact that…
The_Animator
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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 borrowing method of subtraction. I have a: 1) I'm trying…
magna_nz
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What is a square root?

If adding is the sum of two numbers, Subtraction is the removal of a number from another. Multiplication is $x$ lots of $y$. Division is splitting $x$ between $y$. Powers are multiplying a value by itself. What is a square root? To be clear, I'm…
Ben Bowen
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Why is $\frac{10}{8.1}$ so weird?

Here's something I came across last night: $$\frac{10}{8.1} = 1.23456790123456790123456790123456...$$ Notice there is no "8" repeating in the decimal. But all the other digits are there, in order: $012345679...$ Why is this? Also I noticed if I took…
DrZ214
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