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

learn more… | top users | synonyms (1)

0
votes
1answer
21 views

How to calculate a comparative percentage

We have 1002 seats in Head Start (all full) and 287 waiting for Head Start We have 48 seats in Early Head Start (all full) and 256 waiting for Early Head Start I'm trying to express to the directors ...
0
votes
1answer
39 views

Help with Geometric or Arithmetic progression

Evaluate $$2004\cdot\left(\frac{1}{1\cdot2} + \frac{1}{2\cdot3} + \frac{1}{3\cdot4}+\dots + \frac{1}{2003\cdot2004}\right)$$ I think that this is based on either geometric or arithmetic progressions ...
5
votes
4answers
234 views

Rational numbers - rationalization

Question: $$\frac{2\sqrt{6}}{\sqrt{2}+\sqrt{3}+\sqrt{5}}$$ equals: My approach: I tried to rationalize the denominator by multiplying it by ...
1
vote
4answers
47 views

Cancelling out square roots gives 2?

Question: If $$N = \frac{\sqrt{\sqrt{5}+2}+\sqrt{\sqrt{5}-2}}{\sqrt{\sqrt{5}+1}}$$Find N (This is a subset of a larger question) My approach: After rationalizing the denominator, by ...
6
votes
2answers
78 views

Is $\frac{0}{0}$ different from $\frac{1}{0}$?

In my mind, zero divided by zero answers the question of what $a$, when multiplied with zero, equals zero: $a * 0 = 0$ Obviously, any real number will satisfy this equation. However, one divided by ...
2
votes
1answer
102 views

Show that the last four digits of $2013^k$ are 0001

Show that a natural $k \ge 1$ exists s.t the last four digits of $2013^k$ (written as a decimal) are 0001. I understand that k must be of the form k=4m. The last digit of 2013 is 3 and only when ...
0
votes
0answers
23 views

Combination of numbers and operations to get a given result.

I have the five numbers $4$, $5$, $7$, $8$ and $11$ and the four rational operations $+$, $-$, $\times$ and $\div$. The problem is to get $20$. You can use each numbers once and each operation once. ...
2
votes
0answers
92 views

The set of all natural numbers is closed under addition

I'm trying to prove the theorem described in the title, but my proof is so obvious I doubt it is sufficient. Here's my way of proving it: Definition of addition: Let a, b, and c be natural numbers. ...
1
vote
0answers
29 views

Finding possible numbers to yield a certain arithmetic mean (average)

I'd like to know how I could find the possible numbers to yield a certain average number (arithmetic mean), given that: the arithmetic mean will be calculated from 20 integer numbers, each having a ...
0
votes
1answer
26 views

Given a natural number $a$ find its index in a set of structural descriptions

Looking at orbits of the collatz-like $(5x+1)/2^X$ - map I come to a useful structural description for all odd integers $a$. If I write $$ {5a+1 \over 2^A} \to b \qquad \qquad \text{for odd positive } ...
-2
votes
1answer
40 views

Basic Math Question equation to equal 21 [closed]

I feel really silly for even asking this but here it goes... I have numbers 1, 6, 7 and 5 (can be in any order in the equation- and may only be used once) By using only three of the operators /,*,-,+ ...
-1
votes
1answer
135 views

Conflict between $\pi$ and ($\sqrt2/81) \times 180$

Conflict between ${\pi}$and ($\frac{\sqrt2}{81})\times 180$. $\frac{\sqrt0.5}{40.5}$ = $\frac{\sqrt2}{81}$. If I have a number 486 per example and I divide 486 by 40.5 and then by $\sqrt2$ ,I would ...
6
votes
2answers
6k views

How to calculate the number of decimal digits for a binary number?

I was going to ask this on Stack Overflow, but finally decided this was more math than programming. I may still turn out to be wrong about that, but... Given a number represented in binary, it's ...
0
votes
2answers
45 views

for a friend's birthday, a special birthday card

My question is particulary, my friend will celebrate 27 years (March 19, 1987) and we will offer him the game Diablo 3 : The reaper of Souls . So, I would write on the card all the coincidences ...
6
votes
2answers
76 views

Mental Arithmetic

This is very possibly not the best place to ask this, however it's the best I could find but please suggest anywhere else that might be better suited. I'm building a sort of challenge revolving ...
3
votes
4answers
174 views

Why does $\sqrt{x^2}=|x|$? [duplicate]

By convention, we say that: $$\sqrt{x^2}=|x|$$ In fact, the above statement is how we define absolute value. We would not write $\sqrt{4}=-2$. Although logically it is correct, by convention it is ...
0
votes
2answers
48 views

Rationalising the Surds

Please help me rationalise and simplify: $$ \frac{1}{\sqrt[3]{2} - 1} \ - \ \frac{2}{\sqrt{3} - 2} \ . $$ I have tried using the cube of the denominator and the square of the denominator on the ...
5
votes
8answers
4k views

Meaning of $\dfrac{x-y}{y}$ versus $\dfrac{x}{y}-1$

I'm trying to understand what is probably a fairly simple math concept, but this is escaping me for some reason. Why are the results of these two expressions equal? Thanks for any responses. ...
0
votes
1answer
25 views

Using induction to prove $\sum\limits^n_{k=1} 9^k = 0.5 \cdot \sum\limits^{2n}_{k=1} (-1)^k \cdot 3^{k+1}$

$$\sum^n_{k=1} 9^k = 0.5 \cdot \left[\sum^{2n}_{k=1} (-1)^k \cdot 3^{k+1}\right]$$ I have tested both with a python script and it seems to be correct. For the life of me, I am unable to unwind the ...
1
vote
1answer
50 views

How to solve equations with modulus in them

For e.g. (100 * X) % 35 = 25 gives X = 2 and on similar note (100 * X) % 360 = 80 gives X = 8 and it can be possible that there is no X which satisfy this for e.g. (100 * X) % 360 = 70 there ...
40
votes
12answers
4k views

Is it wrong to tell children that 1/0 = NaN is incorrect, and should be ∞?

I was on the tube and overheard a dad questioning his kids about maths. The children were probably about 11 or 12 years old. After several more mundane questions he asked his daughter what 1/0 ...
1
vote
2answers
232 views

Reverse Engineer from digits sum

This question is about sums of digits of a number. Given that sum of digits of $19 = 1+9 = 10$. However, is there a way that, given $10$, we can come out with $19$? In this case, we assume that ...
13
votes
4answers
3k views

Aunt and Uncle's fuel oil tank dip stick problem

This problem first came to me in high school, and a couple times since, and I even assigned it for extra credit in one of my calculus classes after I became a teacher. So I know the solution. What I ...
3
votes
2answers
42 views

Arithmetic Problem Prime numbers

Let $p\equiv 2\mod 3$ an odd prime number. Prove that: $p \mid (x^3+y^3) \implies p \mid (x+y)$ , for any integers $x,y$ $p\mid (x+y)(x^2-xy+y^2) \implies p\mid (x+y)$ or $p\mid (x^2-xy+y^2) $ ...
1
vote
1answer
34 views

Reducing simultaneously a pair of fractions $\frac{a^2}{b},\frac{ a^3}{c}$ using only gcds

Given three positive integers $a,b,c$ and I want to find the smallest positive integers $a', b', c'$ such that $$ \frac{a^2}{b} = \frac{a'^2}{b'} \quad \text{and} \quad \frac{a^3}{c} = ...
9
votes
7answers
722 views

An equation, where the solution does not exist, but on solving the equation we got a solution. why this is happening?

The solution of the equation $\sqrt{(x+1)} -\sqrt{(x-1)}= \sqrt{(4x-1)}$ is $\frac{5}{4}$,but when we put $x=\frac{5}{4}$ in the given equation, then it does not satisfy the equation. Actually, if ...
2
votes
1answer
58 views

Finding when the distances to three cities again have different digits

Very confused on this question. How would you solve it, and what would be the answer(s). Recently I was driving down the freeway and spotted the following freeway sign with the distances to three ...
1
vote
0answers
19 views

Help with Calculating amount in pages by 2 working days

I need help with the following, I think I got this right, but wanted to pass it by the gurus/experts first: ...
0
votes
1answer
22 views

Column math please help

If I'm adding the sum of £100 +£320+£220+£20+£6+50p+20p+10p+5p+2p, how would I write that using column math. Thanks
0
votes
7answers
380 views

What is wrong in this proof?

\begin{align*} \frac{0}{0} &= \frac{100-100}{100-100} \\ &= \frac{10^2-10^2}{10(10-10)} \\ &= \frac{(10+10)(10-10)}{10(10-10)} \\ &= \frac{10+10}{10} \\ &= \frac{20}{10} \\ &= ...
0
votes
0answers
94 views

What book or (math)course do you recommend?

Can anyone recommend me a book or an online math course, that can help me to overcome my fear in math? I'm sick and tired of being afraid of numbers. Thanks in advance!
5
votes
1answer
301 views

Why does the method to find out log and cube roots work?

To find cube roots of any number with a simple calculator, the following method was given to us by our teacher, which is accurate to atleast one-tenths. 1)Take the number $X$, whose cube root needs ...
1
vote
2answers
73 views

Let $a,b,c \in \mathbb{R^+}$, does this inequality holds $\frac{a}{na + kb} + \frac{b}{nb+kc} + \frac{c}{nc + ka} \ge \frac{3}{k+n}$?

Does the following statement/inequality holds for $a,b,c \in \mathbb{R^+}$? $$\frac{a}{na + kb} + \frac{b}{nb+kc} + \frac{c}{nc + ka} \ge \frac{3}{k+n}$$ I've been thinking for hours and I ...
1
vote
2answers
29 views

Loan repayment calculations when interest compounding frequency does not match repayment frquency

Is there a formula for calculating loan repayments where interest is compounded daily, but repayments are made only monthly, for instance? I would like to be able to calculate the repayment amount ...
2
votes
1answer
53 views

Need help finding closed form of finite product

Is there a closed form for this product? $$\prod\limits_{k=1}^n (n+k)$$ I checked it on wolfram alpha but it uses something called the Pochhammer symbol. Does anyone else know of a nice explicit ...
-5
votes
1answer
52 views

“The Escalator” Question

The mathematician Henry wants to find the amount of steps visible at one time. For every step he takes, a volunteer takes one step. Henry reaches the top after 28 steps and the volunteer reaches the ...
3
votes
1answer
61 views

Can Pi prod be expressed using Sigma Notation?

My question is simple (but difficult for me): $\prod(x)$ be expressed interms of $\sum (x)$
1
vote
1answer
107 views

When can $a-(b-c) = (a-b)-c$?

What I'm asking is, when subtracting numbers is there any integers that make $a-(b-c) = (a-b)-c$? Besides $0$ of course. Thanks! Sorry for the stupid question.
18
votes
10answers
2k views

Does there exist a system such that the additive identity is non-zero?

I am trying to explain how although the additive identity is written as $0$, it is not the same as the number $0$. For example for a $2\times 2$ matrix the additive identity is $\begin{pmatrix} 0 ...
0
votes
1answer
23 views

Distribution of liquid among different capacity cans

There are three cans A,B,C. The capacities of A,B and C are 6 liters, 10 liters and 16 liters respectively. Can C contains 16 liters of milk. The milk has to be divided in them using these three cans ...
-1
votes
2answers
47 views

Fractions and division [closed]

well i am really stuck at division in school and i don't really under stand so how can you help me so i can learn better..so i really need help with rounding as well like if you round 69707 to the ...
0
votes
0answers
8 views

How to solve for maturity and interest when only given future borrowing & annual debt service

Consider this example: Debt Issued in 2015: 250,000 Projected Annual Debt Service due to Future Borrowings: 16,441 Debt Issued in 2016: 270,000 Projected Annual Debt Service due to Future ...
1
vote
4answers
92 views

what is the best and esiest way to find Square root?

Hi to all I'm new this forum . I want to know easiest way to find squre root of large number with in a seconds without using calculator. Suppose I have 2601 and ...
-3
votes
2answers
76 views

Can $7 + 4 \times 8$ have multiple answers?

My textbook says evaluate $7 + 4 \times 8$ in a revision course. Is it $7 + 4$, then multiply by 8 or $7 + (4 \times 8)$ ? The calculator automatically gives me the correct answer, so I am going to ...
0
votes
2answers
80 views

simplify $3x^2 \times x^2 + x^3 \times 2x$

Looking at an old assignment, and the function in the title is a derivative result of the product rule, but I've simplified it to $5x^4$, but I have forgotten how I got to that result. Anyone with a ...
2
votes
2answers
35 views

Arithmetic sets problem

I need help with a set problem Given: $$A=\{(\sqrt{n}+2) \in \Bbb Z \ /\ \ 16\le n^2 \le 1296 \}$$ $$B=\{({3m-2}) \in A \ /\ \ 4 \le 4m+3 \le 17 \}$$ Calculate the value of : $$n(A)\times n(B)$$ ...
1
vote
1answer
54 views

$pq\mid (a - pq) \implies pq\mid a$?

This may be a dumb question. I'm not a math major, but, since I'm studying logic, I decided to learn a bit of number theory. I've just begun my studies (I'm reading Davenport's The Higher Arithmetic) ...
0
votes
1answer
19 views

What percentage is the rest of the black cars in the parking lot

Ok so, Last Monday, a parking lot had 80 cars. Of those 80 cars, 25% were silver. 16 were red, and the rest were black. What percent of the cars were black
0
votes
1answer
111 views

What is zero times infinity? [duplicate]

If any number times zero is zero and any number time infinity is infinity, then what do you get when you multiply zero times infinity? Do they cancel one another out and equal any number since any ...
0
votes
3answers
50 views

negative exponent confusion

I am a bit confused with negative exponents so here is an example. Let $4$ to the $-3 = 1\div4\div4\div4 $ The thing which confuses me is the $1$, why we use $1$ before dividing. so if i do it ...