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

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How long before I (see q.) will have recovered the extra purchase cost?

Standard 100w light bulbs cost 40p each and are expected to last for 2 year in average use. Low power equivalent brightness bulbs cost £10 each, are expected to last 8 years and use only 20W. A 100W ...
0
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1answer
20 views

Weighted average of household size given number of households of each size

I hope this isn't too simple to bother you with, but this calculation is at the center of a dispute at work and I want to make sure I'm on solid ground here. To begin with, we know that the average ...
0
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1answer
19 views

Difference in the number of laps covered by two runners with different speeds

Stuck on this question for my 9-year old (no calculator allowed) - the section the teacher gave was in LCM and HCF - I think it is LCM to be used in this query? The LCM she worked out as 1200 but is ...
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4answers
32 views

Prove that all values $n$ which are odd can be written in one of two forms: $4q+1$, $4q+3$ with a non-negative integer $q$?

How can I prove that all values $n$ which are odd can be written in one of the following two forms: $4q+1$, $4q+3$ with a non-negative integer $q$?
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2answers
104 views

How is division comparable to subtraction? [closed]

I was watching a lecture where the professor was describing the mathematics of the ancient Greeks and said they had division because "that's just fancy subtraction." That line got me thinking because ...
2
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3answers
43 views

Bracket expansion, keeps failing tests.

It's $((a + b)c - bc)a - a^2(c - a)$. I rearrange to make it easier to see: $a(c(a + b) - bc) - a^2(c - a)$ Expand the term on the left: $a(ac + bc) - abc - a^2(c - a)$ Again: $aac + abc - abc - ...
1
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1answer
20 views

Problem with a proof of a statement about the arithmetic root of a rational number

Let $x$, $y$, $n$ be natural numbers and $(x,y)=1$ (the greatest common divisor of $x,y$ is 1). I wish to prove that if $\sqrt[n]\frac{x}{y}$ is a rational number then there are natural numbers $p$, ...
1
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1answer
47 views

divide or multiply if number between 1 and 0

This is a math question in the context of an Excel spreadsheet. I have an Excel spreadsheet with 10 rows, where I am dividing the value in ColumnB by the value in ColumnA to create a new number like ...
6
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3answers
143 views

Understanding the actual meaning of “square root”. [duplicate]

So we were always told at school that the square root of a number is the number you need to square to get back to that number. i.e $\sqrt{4}=2$ because $2^2=4$ Fine, as you then get more invloved in ...
1
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1answer
24 views

Invalid Coin measuring?

Imagine 101 coins in front of you. All of them look the same, but it is known that among them there is a defect one, a coin that doesn't have the same mass as his friends. What is the smallest number ...
2
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1answer
55 views

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

Given $\mathbb{Z}$ and the usual addition $+$ on it, do we have unicity of a binary operation $\star$ such that \begin{align*} \tag{1}1\star m&=m\\ \tag{2}(m+n)\star p&=m\star p+n\star p ...
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0answers
27 views

Calculation of bond's market price

A bond \$100 has semiannual coupons worth \$1.30 each (annual coupon rate is 2.6%), matures in 8 years, and yields 3% annually. What is its market price? I think it is $P=100(1.03)^{-8} ...
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1answer
28 views

Avoiding infinite loop in multi variable polynomial division

I have written an algorithm that can successfully perform some algebraic long division but gets stuck on some problems with multiple variables in the denominator. Here's an example expressed as you ...
-1
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1answer
28 views

$a_n = 4n - 11$, finding $d$ in sequence

I was given the information that the last member of an arithmetic progression is: $$a_n = 4n - 11$$ I need to prove that this is an arithmetic progression and then find the equation for $S_n$ (sum). ...
0
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2answers
49 views

How to prove that $\frac{x}{2}$ is smaller than $x$ for positive $x$

Could someone provide me a valid proof that $\frac{x}{2}$ is smaller than $x$. It seems obvious but i cannot think of a proof. Or just prove that $x+x$ is larger than $x$ for positive $x$.
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2answers
75 views

Why aren't square roots written between vertical bars (absolute value)?

The root of a number $x$ is $y$ and $-y$. So why aren't we writing either $|\sqrt{x}|$ or just $\sqrt{x}$ to determine if someone wants $-x$ or $x$?
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3answers
55 views

Is it possible to find the absolute value of an integer using only elementary arithmetic?

Using only addition, subtraction, multiplication, division, and "remainder" (modulo), can the absolute value of any integer be calculated? To be explicit, I am hoping to find a method that does not ...
0
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1answer
17 views

Multiplication in $\mathbb{N}$ from two simple laws

From Barry Mazur's Imagining Numbers: (particularly the square root of minus fifteen), p. 97: Suppose that you have some unknown operation that allows, as its "input," any two positive whole ...
0
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0answers
15 views

Calculate $\mathcal{A}(t_1)$ and $\mathcal{A}(t_2)$.

In this exercise, I will define you what a $\Box$-term is. A variable $x_i$ with $i\in\mathbb{N}$ is a $\Box$-term. If $t_1$ and $t_2$ are $\Box$-terms, then is $(t_1\Box t_2)$ also a $\Box$-term. ...
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3answers
2k views

subtraction of two irrational numbers to get a rational [duplicate]

Say you have a number like $\pi$ or e. Is it possible to subtract another number from it and end up with a rational number? I mean I guess you could write an equation like $\pi-x=3$ But could there ...
0
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1answer
17 views

Sup-multiplicative function related to sum of two squares

Say that a representation $n=a^2+b^2$ (where $n,a,b$ are integers) is normalized if $0\leq a \leq b$. Among those normalized representations, there is a unique one minimizing $a$ (or equivalently ...
2
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1answer
25 views

Tips on counting length of intervals

I'm studying for an actuarial exam and it always confuses me when I'm trying to count intervals in annuities. For example, if I want to know how many payment periods there are from period 13 to ...
2
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1answer
45 views

Integers Construction without Equivalence Classes?

The typical way of constructing $\mathbb{Z}$ from $\mathbb{N}$ is by defining an equivalence relation $\sim$ on $\mathbb{N}\times\mathbb{N}$ by $$ (a,b)\sim(c,d)\iff a+d=c+b. $$ Then, we define ...
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0answers
68 views

Visual questions for 6th graders

I'm tutoring a 6th grader in math at the moment and because she never has a ton of homework I like to give her some interesting extra problems to do. It seems she really enjoyed a problem I showed ...
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0answers
23 views

Calculate item percentage span across a vertical line that equals to 100%

I have a graph with an Y-axis of 8 numbers: 0, 20, 40, 60, 80, 100, 120, 140% The 8 numbers spread equally across a vertical line that is 100%. That means each ...
0
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1answer
49 views

What is the largest floating point number a so that fl(100 + a) = 100?

What is the largest floating point number a so that fl(100 + a) = 100? Here is how float number is computed. $fl(a ⊙ b) = (a ⊙ b)(1 + δ)$. Where $|δ| ≤ ε$. Furthermore, $ε = 2^{-53}$. My ...
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1answer
37 views

Function for numeric input output series

I am trying to find function which will give me output for corresponding inputs. ...
3
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2answers
55 views

What is the lowest common multiple?

what is the lowest common multiple of 120 and 150? Ive got 240 but I'm pretty sure this is incorrect. could you show me how you work it out please?
4
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3answers
353 views

How do i express 108 as the product of powers of its prime factors?

How do i express $108$ as the product of powers of its prime factors? I've got $2^2 \times 3^3$ is this correct? I need to know please thanks
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1answer
32 views

Equation self-substitution

Let $f(y)=g(x)$ be an equation. I remember my grade school teacher warning students against self-substitution in solving equations, which is the procedure described as follows: Assuming $f(.)$ to ...
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0answers
44 views

floating point subtraction for binary numbers

Consider that I want to do a binary operation on the following floating point numbers: 0.35-0.62 I can reach the end but I can not figure out how the sign bit is ...
2
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1answer
45 views

Square root of continued fraction

Assuming I've been given a number in the form of a continued fraction. Is there a general way to write the square root of that number as continued question? For example, consider $$1+\sqrt{2} = ...
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3answers
32 views

Find the ratio of male teachers to male students

At a school function, the ratio of teachers to students is $5:18$. The ratio of female students to male students is $7:2$. If the ratio of the female teachers to female students is $1:7$, find the ...
4
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2answers
50 views

There is a certain game that people play.

There is a certain game that people play. Player A on average has scored 20 more points than the opponents he has played. Player B on average, has scored 16 less points than his opponents. If Player A ...
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1answer
39 views

Do two negatives really make a positive? [duplicate]

Why does a negative times a negative equal a positive? Does this ever happen in the real world?
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3answers
95 views

Solving $\sqrt{25 - 10x + x^2} = x-5$ [closed]

I need help solving this math question. $$\sqrt{25-10x+x^2}=x-5$$ I got $x=5$, but apparently it is wrong. Please provide an explanation if possible. Thanks.
4
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0answers
108 views

Arithmetic Derivative

In Calculus, whenever we see a constant and want to take the derivative of it, it always is $0$. However in Number Theory, we have something called the arithmetic derivative in which we can ...
3
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1answer
50 views

Last digit of $1234 \cdot 5678$

How to find the last digit of this multiplication $1234\times5678$. It may seem like homework but its not. I can do simple multiplication to get the result but I see some patter here, the digits are ...
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3answers
34 views

Hexadecimal dividing $\frac{17a}{12}$ with remainder

How much is it $\frac{17a}{12}$ (in hexadecimal) I got $15$ with remainder $a$. Can someone confirm its true? Thank you!
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2answers
36 views

About how much faster was Albert than Josh?

Albert ran a race $17.6$ seconds. Josh ran the race in $18.307$ seconds. About how much faster was Albert than Josh? This is homework for a 5th grader. It's subtracting and rounding. There is no ...
0
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3answers
57 views

Why does my calculator show -2^2 as -4

I'm worried that this will be a spanner in the works when I'm using a calculator in an exam , I know that $-2^2= 4$ since $(-2) \cdot (-2) = 4 $. So why does my calculator show it as negative 4 ? Does ...
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votes
3answers
48 views

Adding 1 to a/b?

I've been learning algebra 2 and came across a question telling me to add 1 to $\frac{a}{b}$ by finding the least common multiple of the divisors. So I got $\frac{1b}{1b}+\frac{a}{b}$ that simplified ...
0
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1answer
84 views

Common prime divisors of 2 integers

I was trying to solve the task of checking if 2 numbers have same prime divisors. For example 10 has prime divisors of 2 and 5, 50 has prime divisors of 2 and 5, so they have the same prime divisors. ...
0
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1answer
19 views

How to align elements on Y axis evenly inside a container that is smaller then the sum of the child elements?

How to align elements evenly inside a container (vertically), having the first element positioned top left (container X,Y) and the last right bottom (X,Y). I've been trying different calculations so ...
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2answers
39 views

Which is the greatest possible value of n [closed]

In a number with at least two digits, the last digit was deleted. The resulting number was n times smaller than the previous one. Which is the greatest possible value of n? A).10 B).11 C).19 ...
2
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1answer
48 views

What is the inside of a bracket called?

Here's maybe a simple question about nomenclature. Is there a formal name for the inside of a bracket: $$\left(\Large\text{ inside }\right)$$ in the same manner that parts and terms in usual ...
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0answers
32 views

Calculate Standard Deviation in Multiplication

I have a question that asks to find the result (in sig figs) as well as the standard deviation for the following $$(23\pm 8)\times(99\pm 11)\times(11\pm 3)\times(8\pm 4)$$ I began this question by ...
0
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1answer
23 views

Shared terms in an arithmetic sequence

I have a two arithmetic progressions (or arithmetic sequences): 2, 10, 18, ... 5, 8, 11, ... They say to you that this two arithmetic sequences have 41 shared terms (terms I mean by $a_1$, ...
0
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1answer
26 views

Binary subtraction with borrowing

Consider two number which we are going to subtract: 0x44 - 0x29. How can we subtract using borrowing method. The numbers in () shows the value of the digit in ...
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0answers
40 views

Square root digit recurrence algorithm

I'm reading a book which expose how to compute a square root using the digit recurrence algorithm. Following the book basically it expose a simple case with each step necessary to compute such square ...