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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10
votes
10answers
20k views

What is the fastest way to multiply two digit numbers?

I been playing different math games on my Android lately (for example: Math Cruncher). I've noticed that I'm unable to quickly (under 7-8 seconds) multiply two digit numbers (i.e $ 18 * 17$). So my ...
0
votes
1answer
12 views

Proportion questions relating with 3 subjects .

Eight men can build two houses in 20 days. How man men does it take to build 3 houses in 15 days My workings : $2 houses = 20 days$ $3 houses = 20.2.3= 120 days$ $1 men = 2 houses = 1/20 days$ ...
4
votes
2answers
55 views

Simplifying Fractions involving negative numbers

I want to simplify $$\frac{\frac{7}{-10} \times \frac{-15}{6}}{\frac{7}{-19} + \frac{-17}{-8}}$$ I really don't understand how to do this, or even how to start? Negative numbers make it even harder ...
0
votes
3answers
67 views

How many boys, girls, men and women are there?

In a village, there are exactly $10$% more boys than girls; $15$% more women than men; $20$% more children than adults. The population is less than $6000$. Solution: $b = g + 0.1g$--------(i), ...
1
vote
1answer
36 views

Three-Terms Ratios.

. How to write these ratios $X:Y:Z$ in terms of fraction i.e. either like $$\frac{\frac{X}{Y}}{Z}$$ or $$\frac{X}{\frac{Y}{Z}}$$?
0
votes
3answers
32 views

Find a fraction of a part that is shaded

In the figure , O is the centre of the two circles . The circles are divided into sectors of equal sizes. Given that the area of the shaded portion A is twice of the area of the shaded portion B ...
2
votes
4answers
44 views

Numerical property $P(n)$ such that $\forall n P(n)$ is false but a counterexample is difficult to find

I would like to find a nontrivial property $P(n)$ for $n \in \mathbb N$ such that $\forall n P(n)$ is false but the first counterexample can be found only for "very high" $n$ (so high that it wouldn't ...
2
votes
2answers
45 views

Is there a way to encode all decimal numbers between 0 and 1 into whole numbers?

Is there a way to encode ALL decimal numbers between 0 and 1 into whole numbers with a rationale that supports sum operations between the encoded numbers? so 1=0.1 2=0.2 3=0.3... 1+2 = 3 .. 0.2+0.1 ...
0
votes
2answers
41 views

Work and time problem

I came up with this problem: $150$ workers were employed to do a particular work. On first day, $150$ workers worked. On second day, $146$.. and each subsequent day, workers kept on decreasing by 4. ...
5
votes
4answers
29k views

Calculate Gross amount when only percent is known

Consider Rs.1000 as my Gross salary and suppose 20% is PF. so the simple thing is my NET amount is Rs.800. But when I know only my NET amount i.e. Rs.800 and I know that my 20% PF is already ...
1
vote
0answers
23 views

How can we prove that a number is a prime with some limits? [duplicate]

A simple python program implemented a simple fact that the number is prime if no numbers within it's square root including the square root and excluding 1 divide it. Empirically analyzing it for some ...
2
votes
1answer
35 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 ...
0
votes
1answer
27 views

multiplying parentheses with more variables than (a b) * (c d)

I want to solve $$ (1 - 2\lambda + \lambda^2)(1 - \lambda) + 2 - 3(1 - \lambda) = 0 $$ Eventually I would probably want to factor the polynomial, but I don't know how to multiply the parentheses of ...
2
votes
1answer
35 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 ...
1
vote
2answers
29 views

Expansion and factorisation

I have a little problems with a few questions here and I need help.. Thanks ... Factorise completely $$9x^4 - 4x^2 - 9x^2y^2 + 4y^2 $$ My workings .. $$ (3x^2+2x)(3x^2-2x) - y^2 (9x^2-4) = ...
0
votes
1answer
14 views

Evaluate by algebraic expansion of factorisation

Evaluate the following by algebraic expansion of factorisation . a) $2007^2$ b) $(503)(497)$ c) $20.5^2 - 19.5^2$ I'm not sure what does it mean by "algebraic expansion of factorisation ." Can I ...
0
votes
1answer
52 views

Carrying digit can only be 1. Why?

In the book "Algebra" by Gelfand, I have read a solution to a problem which assumes something that does not seem evident to me. Let's see: Problem 2. In the addition example: ...
-2
votes
3answers
34 views
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.
2
votes
1answer
21 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
58 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
2answers
32 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 ...
2
votes
1answer
60 views

Why does $ \frac {a}{b}$ of $c$ mean $ \frac {a}{b} \cdot c$ [closed]

When someone writes "$ \frac {a}{b}$ of $c$", why is the preposition "of" interpreted as multiplication of $c$ by $a/b$?
-2
votes
2answers
41 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
37 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
30 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 ...
7
votes
1answer
92 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 ...
0
votes
1answer
40 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
42 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.
12
votes
4answers
8k views

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 ...
19
votes
5answers
501 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
2answers
48 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.
1
vote
2answers
14 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 ...
1
vote
2answers
106 views

Time, Speed and Distance

A walks around a circular field at the rate of one round per hour while B runs around it at the rate of six rounds per hour. They start in the same direction from the same point at 7.30 a.m. They ...
2
votes
1answer
66 views

Can anybody help me with math expressions?

So , i am in 7th 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. I really ...
14
votes
1answer
418 views

Is the solution to this holiday puzzle unique?

I read the following question on internet. this site:(the link is broken now.) Start at 2011. By moving through the maze and doing any arithmetic operations you encounter, exit the maze with a ...
1
vote
1answer
41 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 ...
0
votes
3answers
82 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 ...
2
votes
0answers
21 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 ...
3
votes
5answers
6k views

negative number divided by positive number, what would be remainder?

my question is If $-27$ is divided by $5$, what would be the remainder?
0
votes
3answers
35 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 ...
1
vote
2answers
23 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 ...
5
votes
2answers
179 views

Can all math operations be reduced to a sufficiently complex algorithm?

Say I could only perform one operation (addition) from addition I could derive subtraction by adding a negative number. Also, from addition I could derive multiplication, like $ a n $, just add $ a $ ...
3
votes
3answers
122 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? ...
14
votes
6answers
29k views

cubic root of negative numbers

Excuse my lack of knowledge and expertise in math,but to me it would came naturally that the cubic root of $-8$ would be $-2$ since $(-2)^3 = -8$. But when I checked Wolfram Alpha for $\sqrt[3]{-8}$, ...
9
votes
3answers
726 views

Come up with some fun “equation Limericks”

We were discussing "Limericks" in my Calculus class. Specifically, "equation Limericks". A Limerick is a poem with five lines. The first, second, and fifth lines should have nine syllables each and ...
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 ...
3
votes
3answers
5k views

does negative zero exists? [closed]

does negative zero exists? In the set of integers and real numbers, there is no negative zero. I think zero is neutral and it is the only integer with having no positive or negative sign. However, can ...
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
28 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+$\frac{1}{w}$ = $5\sqrt 2 + \sqrt3 +\frac {5\sqrt2 - \sqrt3}{47}$ = ...