Mathematics Stack Exchange
Mathematics Stack Exchange

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
0
votes
1 answer

How can I get the first (most significant) N digits in a positive integer, without counting the total number of digits in it?

I can calculate the number of digits in $x$: $$M=\Big\lfloor\log_{10}{x}\Big\rfloor+1$$ And then calculate the first $N$ digits in $x$: $$\Big\lfloor\frac{x}{10^{M-N}}\Big\rfloor$$ Is there any trick to achieve that without counting the number of…
bbbbbbbbb
  • 175
  • 6
0
votes
1 answer

Division of number with fixed decimal (sharing monetary fee)

I'm possibly writing a lot of terms incorrectly in this question since I'm kinda lost in how to look for this. The problem I have is, given a monetary value that must be paid (a fee of some sort), and also given that this value comes from multiple…
Diego Venturi
  • 13
0
votes
1 answer

What is the greater number?

I would like to prove that $100^{99}<99^{100}$. My attempt: $\dfrac{100^{99}}{99^{99}}<99$ $\left(\dfrac{100}{99}\right)^{99}<99$ $\left(\dfrac{2^2\cdot5^2}{3^2\cdot11}\right)^{99}<99$ $\dfrac{2^{198}\cdot5^{198}}{3^{198}\cdot11^{99}}<99$ But now I…
Flor
  • 17
0
votes
1 answer

How to convert percentage to 6 points grading system?

In my home country grades start from 4.0 and go up to 10.0. How can I convert percentage of points gotten in a test, to the above grading system? So for example, what grade would 37.4% be?
DjAndGo
  • 3
0
votes
2 answers

The commutative property of addition involving a number and a member of the English alphabet.

I was going over counting and letters with my students by starting at a letter and counting how many moves it takes to get to another. That got me thinking. Could addition between an integer, $x$, and a letter, $Γ$, (in the context of the English…
Eugene Mason IV
  • 47
0
votes
0 answers

Comutative inverse operation question

From pre algebra for Dummies Comutative When the second number is missing in a subtraction or multiplication problem, just switch around the two values that are next to the equal sign (that is, the blank and the equal sign: I can’t understand…
Guilherme Woolley
  • 39
0
votes
0 answers

GCF of a self-made arithmetic function

I'm exploring some arithmetic pattern f(a,b) defines as "the sum of all numbers from 1 to a that are not divisible by b" which goes like this: $$f(4,4) = 1 + 2 + 3 = 6$$ $$f(8,4) = 1 + 2 + 3 + 5 + 6 + 7 = 24$$ $$f(12,4) = 1 + 2 + 3 + 5 + 6 + 7 + 9 +…
Jerwin Ablay
  • 1
0
votes
1 answer

Is my algebra book correct?

Pré álgebra for dummies Brasil edition Fast multiplication with exponents took a job that pays you 1 cent the first day, 2 cents Here's an age-old question that still raises eyebrows: Imagine that you you on the second day, 4 cents on the third day,…
Guilherme Woolley
  • 39
0
votes
0 answers

Absolute value some

Adding signed numbers involves two different rules, both depending on whether the two numbers being added have the same sign or different signs. After determining whether the numbers are the same or different, you use the absolute values ​​of the…
Guilherme Woolley
  • 39
0
votes
0 answers

A Clarification from Algebra 1 for Dummies

From Algebra $1$ For Dummies: Multiplying and dividing numbers with signs Multiplication and division are by far the easiest operations to do with the signs. As long as you can multiply and divide, the rules are simple and are exactly the same for…
Gui
  • 11
0
votes
0 answers

Logic Behind the Convention of the Result of Modulo Operations

Consider the following 4 results 7 % 3 = 1 -7 % 3 = 2 7 % -3 = -2 -7 % -3 = -1 I'm struggling to see why these outputs have been selected as such 7 % 3 is clear. Imagining | as 0, I can chunk up 7 into 3 groups of 3, and I have 1 left over…
doliphin
  • 103
0
votes
1 answer

Beginner confusion about adding a positive number and having $+(+5)$ appear

Forgive me if this is a stupid question but I can't find anywhere else to ask it. Suppose we had, $X + (X+5),$ is it correct to say we can "distribute" the plus sign into the bracket to get $X + X + (+5),$ to get the correct answer of $2X + 5,$ and…
Nav Bhatthal
  • 1,057
0
votes
1 answer

How is the property called that makes $(a\cdot b)/c = (a/c)\cdot b = a\cdot (b/c)$

As far as I know for any rational numbers $a$, $b$ and $c$ the following is true: $(a\cdot b)/c = (a/c)\cdot b = a\cdot (b/c)$. How is this property called?
Bentley4
  • 175
0
votes
1 answer

periodicity of primes inverses decimals in base b

I would like to prove the following: Let b > 1 a natural. Let p a prime number where p ^ b = 1. The decimals of 1/p in base b are infinite and periodic from the first decimal (I've proven that already), let t be that period. Prove that t | p-1
kheorus 7
  • 1
0
votes
2 answers

What is the minimum amount of money Bob can receive (in whole dollars) to ensure he receives more than any other employee?

A certain company has $1,000$ to distribute to Bob and nine other employees, with each to receive at least $ 75$. What is the minimum amount of money Bob can receive (in whole dollars) to ensure he receives more than any other employee? I think…
user1086853
1 2 3
…
99 100