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.

learn more… | top users | synonyms (1)

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}...
8
votes
1answer
139 views

Prove that $| S |\leq5$

For any $a,b \in S$ there exists $c \in S$ such that $a,b,c$ form an arithmetic progression in some order. Prove that $| S |\leq5$. I am struggling to find examples where it works. I found a ...
0
votes
4answers
33 views

Identifying numbers that have the same given HCF and LCM

Two numbers have a highest common factor of $12$ and a lowest common multiple of $600$. Besides $12$ and $600$ themselves , find another pair of numbers that fulfill the above condition . I'm not ...
1
vote
2answers
60 views

Lowest common multiple

A number has exactly 8 factors . Two of the factors are 27 and 75. List all the factors of the given Number . I find LCM of 27 and 75 and the LCM value is the Number. I did this luckily and I got ...
0
votes
0answers
5 views

Rounding off figures

A solid block has a mass of 23 grams when corrected to the nearest gram. Find the greatest possible mass of the block . My answer is 23.4kg and I got wrong and the answer is 23.5kg . I was wondering ...
1
vote
1answer
23 views

Sum of the number sequence that consists of multiplications of neighbor numbers

Say there is sequnce of number $A(i) = i * (i+1)$, i.e. like 1*2, 2*3, 3*4 and so on. Is there any formula that allows to compute sum of the first N such numbers?
17
votes
2answers
1k views

Can every integer greater than 5 be written as the sum of exactly one prime and one composite?

I worked it out up to 15. 6 = 4 + 2 7 = 4 + 3 8 = 6 + 2 9 = 4 + 5 10 = 8 + 2 11 = 9 + 2 12 = 10 + 2 13 = 10 + 3 14 = 9 + 5 15 = 12 + 3 Does this trend continue forever? I ...
2
votes
2answers
28 views

Very simple rate combination [closed]

If I borrow £150 in total - £100 at 5% and £50 at 10%, what is the combined rate of my loan? If my instincts are correct, the combined rate should be 6.25%? I'm just trying to model this in software ...
0
votes
3answers
52 views

Question about numbers

I have a few questions here that is bothering me a little .. Is '$0$' an even and odd number ? Because $0$ divided by $2$ and $3$ will give you $0$ which is still a whole number Are numbers like $-...
0
votes
1answer
56 views

Proving $(a + b) \cdot (e+ c) = ae+ac+be+bc$. [closed]

The multiplication of two terms say $(a + b) \cdot (e+ c)$ involves multiplying corresponding elements i.e. $ae+ac+be+bc$. How was this proved?
2
votes
1answer
50 views

Converting Integers from One Base to Another Digit by Digit

So I’ve done some hands-on work with converting integers from one base to another using the well-known method of division and taking the remainder. The most generic algorithm involves dividing the ...
3
votes
3answers
62 views

multiplication and addition fractions

Try to visualize process of multiplication fraction addition is obvious, need to split each part to the same size - "reduce to a common denominator" for example $$\frac23 +\frac24 = \frac{8}{12}...
2
votes
2answers
31 views

What inequality does the units digit of a two digit number less than $40$ satisfy if the sum of the units digit and tens digit equals $8$?

For a two digit number , the sum of the "units digit" and "tens digit" is $8$ and the two-digit number is less than $40$. Denoting that the "units digit" of the two-digit number to be $x$, form an ...
1
vote
1answer
44 views

Existence of subsequences in square roots

For any sequence of decimal digits $x_1x_2 \ldots x_m$ there exists $n \in \mathbb{N} $ such that this seqence occurs (as a substring) in the decimal expansion of the fractional part of $ \sqrt{n} $ ....
1
vote
0answers
59 views

Theorem of two squares. Proving $p$ can be written as a sum of two squares.

Hi I'm having trouble with this problem. Let $p$ be a prime number such that $p\equiv 1\pmod4$. We want to prove that we can write it as a sum of two squares. Let $S:=\{(a,b,c)\in\mathbb N^2 \times \...
0
votes
0answers
30 views

Cases of the Erdos-Selfridge Theorem

I'm having a difficult time trying to understand/proceed with this problem. Problem: The goal of this problem is to study particular cases of the Erdos-Selfridge theorem which says that: . We call ...
0
votes
3answers
109 views

Is it possible to build a formula that prevents negative numbers? [closed]

I have a calculation that goes like this: $$\text{<any positive number>} - 100$$ As long as the result is a positive number it is acceptable. However, if the result is a negative number, I ...
2
votes
2answers
72 views

Deducing an integer from $0$-$15$ and lying

I'm interested in reducing the upperbound of the number of questions needed and in finding alternate solutions to solve the following question: Suppose I have thought up an integer between $0$ and ...
3
votes
1answer
62 views

Determining which number pair has greater product - without multiplying.

This is a 5x5 multiplication table. ...
-2
votes
4answers
100 views

If the sum of $m$ and $n$ is odd then exactly one of them is odd. [closed]

Let $m,n$ be integers. Prove that if $m + n$ is odd, then exactly one of $m$ or $n$ is odd. What is the approach to prove this?
-2
votes
1answer
59 views

Which branch of mathematics deals with errors? [closed]

Maths is a concrete language which is definite in terms of it's accuracy. But, it seems mathematics also has it's flaws. Consider an example such as: seeing this we can only say that the whole ...
3
votes
2answers
63 views

Does the term “selling price” mean the “cost price” or the “sale price” of a product/commodity?

I have been told that the idiom "selling price" is the same as the cost price of an item, that is the amount which a seller pays to, e.g. a wholesale merchant. The seller later sells the commodity at ...
1
vote
5answers
39 views

How to calculate the price of a product without the sales tax, if we know the price including the tax and the rate of the tax?

The question is The price of a mobile phone is $8800 inclusive of a 10% GST (General Sales Tax). What is the original price of the mobile phone? This is how I approached it: The Sale Price <...
0
votes
3answers
28 views

Factorising large numbers

Can I get some hint for this question, please? I'm told to find the value of $p$ in the following equation $$\dfrac{1}{(2p-1)^4} = \dfrac{1-2p}{32}$$ Here's my thought process ... I can't ...
0
votes
1answer
18 views

Inverse proportion

I am not sure how to approach this question, can I get some help? This is an inverse proportion question. $y$ is inversely proportional to the square of $x$. Find the percentage change of $x$ when $...
3
votes
3answers
50 views

From a set of positive consecutive integers starting with $1$, one number is erased and the AM of the remaining numbers is $\frac{602}{17}$

A set of positive consecutive integers starting with one is written on a blackboard. One number is erased and the AM of the remaining numbers is $\frac{602}{17}$. The erased number is 6 7 8 9 ...
2
votes
2answers
18 views

Proportion understanding

49 Painters are required to complete a painting job in 12 days . However, due to unforeseen circumstances , there was a delay and only one third of the job was completed in 5 days . Assuming that all ...
2
votes
4answers
123 views

Prove or disprove: If $n^3$ is odd then $n$ is odd.

If $n^3$ is odd, then $n$ is odd. I need to prove or disprove by means of counterexample why this is true or false. $\forall x P(x) = x^3$, $x = 1,3,5,7,9$ I am having a very difficult time ...
0
votes
1answer
28 views

Proportions question

I do not know how to approach this qn properly .. Qn - 6 workers working 8 Hours per day were tasked to complete a building project in 5 days . After working for 3 days , 2 of the workers were sick ...
3
votes
7answers
123 views

What do the square brackets mean in $[5-(6-7(2-6)+2)]+4$?

While watching a youtube video about a Simpsons math episode at 1:27 there's a puzzle that includes square brackets. $$[5-(6-7(2-6)+2)]+4$$ Apparently the answer is $-27$ which I can't figure out ...
0
votes
0answers
29 views

Percents question [duplicate]

A vacuum is priced at \$$340$ with an allowed trade-in of \$$135$ on an old unit. If the sales tax of $4$ $3/4$% is charged on the price of the new vacuum unit before the trade-in, find the total cost ...
-1
votes
1answer
32 views

Percent story problem [closed]

A vacuum is priced at \$$340$ with an allowed trade-in of \$$135$ on an old unit. If the sales tax of $4$ $3/4$% is charged on the price of the new vacuum unit before the trade-in, find the total cost ...
1
vote
1answer
50 views

simple arithmatic

in sexagesimal method 1 rtangle =90 degrees then 0.942387rtangle =? actually in unitary method 1 is the least count but if we get something like .95,.88.How to calculate this?
0
votes
1answer
33 views

Indices solving for $x$

Sorry this is a simple question but I'm having difficulty with it . $$2(16^{3x+2}) = 1 / 8^{5x-4}$$ I'm told to solve for $x$. My working - $$2(16^{3x+2}) = 1 / 8^{5x-4}$$ $$32^{3x+2} = 8^{-5x+4}...
1
vote
1answer
25 views

Proportion problems

Tension T, newtons , of a string is inversely proportional to the square of the frequency, f Hz , of the note produced . When the tension is 80N , the string produces a note with frequency of 400 Hz . ...
4
votes
5answers
114 views

What is the value of $3-3\times 6+2$?

Please could someone help me and my brother settle our dispute? We have been looking at the following equation: $$3-3\times 6+2=$$ This may look familiar but I have yet to find a fully conclusive ...
2
votes
4answers
71 views

Proving $a \leq \frac{a+b}{2} \leq b$

I want to prove the following $a \leq \frac{a+b}{2} \leq b$, where we know that $0 \leq a \leq b$. My proof goes as follows. Suppose $a \leq \frac{a+b}{2} \leq b$, then we know $a \leq \frac{a+b}{2}$ ...
2
votes
1answer
37 views

Division by rational (decimal) number meaning

When I say, that I exchanged 42 CZK into 1,5 euro. Why do I get the rate for one euro by dividing? 1) How do you explain this division in words. Like when you say when doing integer division, that ...
2
votes
1answer
61 views

What word to use to describe the mathematical objects and axioms of a branch of math

I'm trying to write a paragraph which describes the objects and rules of a branch of mathematics. But I'm stuck as to what word I should use here. Example: (fill the blank) Arithmetic is an ...
0
votes
3answers
56 views

How to solve 'a÷b(c+d)'? [duplicate]

How to solve $a÷b(c+d)$? For example, $2÷4(8+16)$. Is it $($$\frac{2}{4}$$)(8+16)$ = $\frac{1}{2}$(8+16) = $\frac{1}{2}$(24) = 12? or $\frac{2}{4(8+16)}$ = $\frac{2}{4*24}$ = $\frac{2}{96}$ = $\...
1
vote
4answers
152 views

Finding remainder of the big integer?

The value of the expression $\mathrm{13^{99}(mod 17)}$, in the range $0$ to $16$, is_______? My attempt : Somewhere it explain as: Note: for remainder cycle $\mathrm{13^1mod17=13, 13^2mod17=16,...
7
votes
0answers
60 views

To what extent can the fondamental theorem of arithmetic be used to give a canonical form to non-integer numbers?

The fundamental theorem of arithmetic gives us a unique way of writing any non-zero integer. For any $n \in \mathbb{Z}^*$, we have a unique decomposition : $$n = (-1)^\epsilon \prod\limits_{i \in \...
1
vote
1answer
38 views

Encoding 2 numbers into 1

Say we have two integers, $a$ and $b$. I need a way to combine these numbers into one unique number $x$, such that they can both be recovered from $x$ and no other numbers can be recovered from $x$ ...
2
votes
3answers
75 views

Prove that if $ 2^n $ divides $ 3^m-1 $ then $ 2^{n-2} $ divides $ m $ [closed]

I got a difficult problem. It's kind of difficult to prove. Can you do it? Let $ m,n\geq 3 $ be two positive integers. Prove that if $ 2^n $ divides $ 3^m -1$ then $ 2^{n-2} $ divides $ m $ Thanks ...