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.

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2
votes
1answer
38 views

Irreducible fraction

Prove that $$ \frac{2}{99},\frac{3}{98},...,\frac{97}{4},\frac{98}{3},\frac{99}{2}% $$ are irreducible. My attempt is: if $a/b$ is irreducible, than $\left( a,b\right) =1$. Now, I choose $a=k,k=2,3,...
2
votes
1answer
37 views

Bound for Chebyshev function

Consider the Chebyshev function defined as: $\psi(x)=\sum\limits_{n\leq x} \Lambda(n)$, where $\Lambda(n)=\log p$ if $n$ is a power of some prime $p$ and is equal to $0$ otherwise. Could someone ...
2
votes
1answer
23 views

Factorisation and hence …

Factorise $2x^2 + 8x + 6$ completely . Hence express 286 as the product of three prime factors . Workings - $2x^2 + 8x + 6 = 2(x^2 + 4x + 3) =2(x+3)(x+1)$ How do I use my answer above to express 286 ...
-1
votes
2answers
65 views

What is 2-2+2 ? a-b+c = (a - (b+c)) or (a+(-b+c))?

I am little bit confused for manipulating bigger maths, So i am asking a simpler version. According to BODMAS we do first addition then Subtraction. a-b+c = (a - (b+c)) or (a+(-b+c)) ?
0
votes
0answers
28 views

Division by power of 3.

Is there any fast division algorithm to divide a binary number by power of $3$. I want to find the $q,r$ for $a=q*3^b+r$, $b$ is constant.
6
votes
4answers
121 views

Could we “invent” a number $h$ such that $h = {{1}\over{0}}$, similarly to the way we “invented” $i=\sqrt{-1}$? [duplicate]

$\sqrt{-1}$ was completely undefined in the world before complex numbers. So we came up with $i$. $1\over0$ is completely undefined in today's world; is there a reason we haven't come up with a new ...
-2
votes
2answers
44 views

How long until the earth is covered in pumpkin vines? [closed]

There are 500 seeds in an average pumpkin. It takes 20 weeks to produce a vine with 1 pumpkin from a seed and then the vine withers. A live vine covers 2 square meters of land. The earths diameter is ...
0
votes
1answer
89 views

Quintillion bytes to terabytes

I am trying to convert 2.5 quintillion bytes to terabytes (IBM's estimate on the amount of data produced daily), could someone check if my calculations are correct? ...
1
vote
1answer
36 views

How casting out $11$s works?

Following line are quoted from the book Secrets of Mental Math by Arthur Benjamin and Michael Shermer. To double-check your answer another way, you can use the method known as casting out ...
0
votes
1answer
41 views

Probability questions involving chance of drawing particular poker hands.

I am trying to design a program to calculate the probability of getting a set of poker hands, but I've been having trouble finding where to start. It would really help me out if someone could assist ...
0
votes
2answers
44 views

Irrationality of $ 1/a + 1/b$

I have thought about this and was wondering if anyone could provide an example of real numbers $a$ and $b$ such that $a + b$ is rational but $1/a + 1/b$ is irrational or prove the statement false.
1
vote
2answers
17 views

Rounding currency values [closed]

If I have a receipt with the following: 4.37 4.37 Each item discounted at 10% 4.37 * 10% = .44. rounded from .437 4.37 * 10% = .44 rounded from .437 total discount .88 subtotal is 7.87 ...
3
votes
1answer
71 views

Can anybody help me with math expressions?

So , I am in $7^{th}$ grade and my teacher gave me some really hard homework. What I have to do is use math expressions that equals each number between $1$ and $100$ , only using the numbers $1,2,3,4$....
7
votes
1answer
96 views

A number 47_ _74 is a multiple of consecutive numbers. Find the numbers.

I had recently solved a problem. A number 47_ _74 is multiple of at least two consecutive numbers. Find the numbers. The list of numbers may be of any length $\ge 2$. I first saw that if they ...
2
votes
0answers
23 views

Partition of an integer of a particular type

I'm working on a project, but i'm stuck because i would need to count the different partitions of an integer which verify a certain property. I've never seen anyone looking at such a kind of ...
1
vote
1answer
43 views

Number of ways to write a number as a sum of powers

Lets denote $\mathcal N_{k,n}$ the function that return the number of ways to write a given number as sum of $k$ numbers to the $n$-th power. For example : $\mathcal N_{3,2}(1)=3$ because \begin{...
1
vote
2answers
35 views

Computing midpoint of an interval overflow

For computing the midpoint m of an interval $[a, b]$, which of the following two formulas is preferable in floating-point arithmetic? Why? When? (Hint: Devise examples for which the "midpoint" given ...
0
votes
3answers
36 views

Comparing two fractions

I saw this problem from an elementary textbook: Let $$ A = \frac{2014}{2015} + \frac{2015}{2016} $$ and $$ B = \frac{2014 + 2015}{2015 + 2016} $$ Compare $A$ and $B$. I know the answer is $A \...
3
votes
3answers
130 views

Wolfram Alpha wrong answers on $(-8)^{1/3}$ and more? [duplicate]

Wolfram Alpha doesn't give $-2$ for $(-8)^{1/3}$, and it absolutely fails to draw $f(x)=x^{1/3}$ - does anyone know why? Am I missing something very 'deep' Wolfram Alpha is trying to teach me? Here'...
0
votes
2answers
49 views

Geometry Math 8th (Area of a Trapezoid) [closed]

The windshield in a truck is in the shape of a trapezoid. The lengths of the bases of the trapezoid are 70 inches and 79 inches. The height is 35 inches. Find the area of the glass in the windshield.
-4
votes
1answer
46 views

Mathematical Limerick [closed]

A dozen, a gross and a score, Plus three times the square root of four, Divided by seven, Plus five times eleven, Is nine squared and not a bit more. Question $1$: Does this limerick actually ...
19
votes
5answers
520 views

How to arrange these 10 digits to make a correct equation?

My daughter brought home the "problem of the week" last night and it was explained to me as this: Given the following digits: $$1\ \ 1\ \ 2\ \ 3\ \ 3\ \ 4\ \ 5\ \ 6\ \ 6\ \ 7$$ Arrange them ...
0
votes
1answer
18 views

Problems involving time and speed ,

I have a test coming up and there will be a similar question like this . But I don't understand it but I got lucky during a practice . The question is - A cargo train enters a 1.8km tunnel and takes ...
0
votes
1answer
29 views

Could you explain to me this equation?

Could someone explain to me this equation ? $W = 5\sqrt 2 + \sqrt3 $ $\frac{1}{w} = \frac {5\sqrt2 - \sqrt3}{47}$ Why does W+$\frac{1}{w}$ = $5\sqrt 2 + \sqrt3 +\frac {5\sqrt2 - \sqrt3}{47}$ = $...
0
votes
0answers
11 views

Profit and loss understanding problem

The cost of producing a math book is made up of 3 main components , overheads , type setting and printing . In 2010, the cost of overheads for a book is \$1400 , the cost of type setting a page is \$...
1
vote
2answers
26 views

Definition of Division with Remainder

I have a trivial question. When we divide say 5 by 2, quotient is 2 and remainder is 1. However say we divide -5 by 2, then should we have a quotient -2 and remainder -1 or quotient -3 and remainder 1?...
1
vote
2answers
100 views

How can I add such two series?

I know that for two series $\space \sum^{L}_{n=0} a_n \space$ and $\space \sum^{L}_{k=0} b_k$ we can say $$\sum^{L}_{n=0} a_n \space + \sum^{L}_{k=0} b_k= \sum^{L}_{j=0} {a_j} + {b_j}\\$$ But what ...
1
vote
1answer
36 views

Find no of nuts and raisins.

Grandmother made 20 gingerbread biscuits for her grandchildren. She decorated them with raisins and nuts. First she decorated 15 cakes with raisins and then 15 cakes with nuts. At least how many cakes ...
-2
votes
1answer
31 views

Find the length of the smallest square?

A rectangular paper sheet measures 192 * 84 mm. You cut the sheet along just one straight line to get two parts, one of which is a square. Then you do the same with the non-square part of the sheet, ...
-1
votes
2answers
42 views

$V= 3b + 2b^2$ - what's the value of $V$ when $b=4$? [closed]

Do I multiply $4$ to the power of $2$ or do I multiply $8$ to the power of $2$? What is the answer? I'm thinking it's $76$.
1
vote
3answers
76 views

Three-digit numbers whose digits and digit sum are all prime

How many 3$$-digit numbers are there such that each of the digits is prime, and the sum of the digits is prime? Shouldn't it be $0$, because the only one digit primes are $2,3,5,7$, and so the ...
22
votes
8answers
4k views

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 ...
0
votes
2answers
31 views

Is there a physical analog for division by a fraction?

Dividing by a fraction seems anomalous in the set of arithmetic operations inasmuch at it appears to have no analog in the physical world. Is this the case? Or is there some physical analog to the ...
4
votes
6answers
142 views

Why does $\binom{n}{2} =[ (n-1) + (n-2) + (n-3)+\cdots +1]$?

I was recently doing a homework problem that involved finding the number of lines used to connect a given number of points on a circle. Looking at it logically, I saw that that for the first point, ...
0
votes
1answer
50 views

What would be a formula for this?

I'm trying to find a formula for this scenario: I need \$$302$. I gain \$$2$ every second. I gain \$$5$ every $5$ seconds. When will I reach \$$302$? Both of these rates are working together. ...
1
vote
1answer
9 views

Profit and loss qn

The cake shop made a profit of $100/3 \, \%$on every cake sold . Calculate the selling price of a $1.5$kg strawberry cake if the profit made was $\$5.40$ My workings and thoughts - I find cost ...
0
votes
0answers
30 views

Defining addition operation in symmetric group.

We know that every integer $n\in\Bbb Z$ has an unique prime decomposition $$n=p_1\cdot\dots\cdot p_r$$ where $r$ is number of prime factors $p_i$ of $n$. We know that every member $\sigma\in S_n$ has ...
1
vote
2answers
20 views

Unit conversion multiplication

This is going to sound like a really dumb question. At first I thought it was just my brain failing to function, but I can't work my mind around it. I'm using a problem to demonstrate the conceptual ...
10
votes
8answers
211 views

Show $\frac{3997}{4001}>\frac{4996}{5001}$

I wish to show that $$\frac{3997}{4001}>\frac{4996}{5001}.$$ Of course, with a calculator, this is incredibly simple. But is there anyway of showing this through pure analysis? So far, I just ...
1
vote
5answers
66 views

Four statements, One statement is false math problem

When trying to recall some facts about the ages of his three aunts, Josh made the following claims: Alice is fifteen years younger than twice Catherine’s age. Beatrice is twelve years older than ...
0
votes
1answer
22 views

Using indices to find an unknown

$1458^n = 2^n / 9$ I'm told to find the value of $n$. How to do that? It is my first time encountering this type of problem when I can't find make every number a constant . What do I do here . Can ...
0
votes
0answers
44 views

Find the Maximum value of the product

Given $X$ and $Y$ as two Number.I have to find the maximum value of $X\times Y$.I can perform total of $K$ operation on $X$ and $Y$. In one operation I can increase or decrease the value of $X$ or $Y$....
2
votes
2answers
39 views

Why to use ratios to compare two quantities and not difference?

I was listening a lecture on computer performance measurement and the professor was giving an analogy of aircrafts performance measurement. He showed a table which contained different parameters of ...
1
vote
0answers
8 views

How to prove mathematically these two different definitions of background-position property as equivalent?

I've been reading about how percentage values work for background-position position property. The official definition is that ...
1
vote
2answers
129 views

Is there a difference between$ -(1000)$ and $(-1000)$? [closed]

Or are they equal? If they aren't, when one you use one and not the other?
13
votes
5answers
176 views

Significance of multiplying $-1$ by $-1$

Maybe this is a weird question but it's been bugging me. In the childhood we were taught that $4 \times 3$ means $4+4+4$ i.e. adding 4, 3 times. My question is then how would you explain $-1 \times ...
2
votes
1answer
40 views

Cricket player ranking equation

I need to figure out how to create an equation that gives a cricket player a ranking score based on their batting and bowling averages. For those who don't know cricket, basically, the higher your ...
0
votes
1answer
21 views

Ordinary Annuity future value

I have a problem to calculate future value of this problem: "The parents of a newborn baby set up an account to cover the cost of college they deposited 1,500 every birthday in an account that pays 8%...
0
votes
1answer
42 views

Factorisation and factors

Factorise $3x^2 + 26x + 51$. Hence , find the two factors of $32651$ Workings $$3x^2 + 26x + 51= (x+3)(3x+17) $$ I don't understand how can I use the answer above to help me find factors of $32651$...
1
vote
2answers
40 views

How can find the numbers of digits of power numbers

let $a$ and $n$ are natural numbers and $A=a^n$. Then how we can find the numbers of digits of $a^n$. For example $A= 2^{101}$. Then we $2^{10}=1024\cong=1000=10^3$. So $2^{101}=2\times (2^{10})^{10}...