Mathematics Stack Exchange
Mathematics Stack Exchange

Questions tagged [arithmetic]

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. Questions about number theory (sometimes called "arithmetic") should not use this tag and should instead use (number-theory) or (elementary-number-theory).

Arithmetic is defined as operations upon numbers using $4$ main operations along with many others:

addition - the sum of two numbers

subtraction - the difference of two numbers also defined as the addition of negative numbers

multiplication - the area of a rectangle with sides of lengths equal to the two operands

division - the number of times one number can be subtracted from another before equaling zero. Sometimes it will allow decimals and in other cases there will be a remainder left over when a number doesn't go into another evenly

See Arithmetic.

6283 questions
2
votes
1 answer

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 get help please. Thanks in advance !
user307640
  • 2,632
  • 2
  • 17
  • 27
2
votes
1 answer

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 as the product of three prime factors ? Thanks in…
user307640
  • 2,632
  • 2
  • 17
  • 27
2
votes
3 answers

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 different aircrafts such as: Aircrafts: …
Black_Zero
  • 121
2
votes
1 answer

Summations manipulation: is this one right?

I've got a summation like this: $\sum_{l=1}^L \sum_{i=1}^I p_l c_l^i = \sum_{l=1}^L \sum_{i=1}^I p_l w_l^i$ Is it right to bring $ p_l $ out of the symbol $ \sum_{i=1}^I $ such that: $\sum_{l=1}^L p_l \sum_{i=1}^I c_l^i = \sum_{l=1}^L p_l…
Luigi
  • 305
  • 1
  • 3
  • 14
2
votes
2 answers

Very simple rate combination

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 and I wanted to confirm. Thanks and apologies for…
tom redfern
  • 207
2
votes
2 answers

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 inequality and solve for $x$. I'm not sure how to…
user307640
  • 2,632
  • 2
  • 17
  • 27
2
votes
2 answers

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 Painters worked at the same initial rate ,…
user307640
  • 2,632
  • 2
  • 17
  • 27
2
votes
4 answers

$10+10\times 0$ equals $0$ or $10$

I thought $10+10\times 0$ equals $0$ because: $$10+10 = 20$$ And $$20\times 0 = 0$$ I know about BEDMAS and came up with conclusion it should be $$0$$ not $$10$$ But as per this, answer is $10$, are they right?
Blaster
  • 162
2
votes
2 answers

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 $x$ There are plenty of ways to do this, but the…
Nico A
  • 4,934
  • 4
  • 23
  • 49
2
votes
2 answers

Time Difference and Arithmetic - Suggestions..

I am currently dealing with problems in which I need to find the difference between different times. One trick that worked for me until now was from here a short summary of which is For Adding Times Add the hours Add the minutes If the minutes are…
Rajeshwar
  • 1,629
2
votes
3 answers

Simplifying a fraction

I'm in doubt on how to simplify $ \left (-\dfrac{1}{243} \right )^{-\frac{2}{3}}$. I've started with $\left (-\dfrac{1}{9\sqrt{3}} \right )^{-\frac{2}{3}}$ but now I'm stuck because of this minus signal in the main fraction ? Thanks in advance.
aajjbb
  • 1,065
2
votes
1 answer

Dividing by 1000 twice?

If I take any whole number and divide by 1000 twice then is it only mathematically possible to have a maximum of 6 numbers right of the decimal point. Example 999 / 1000 / 1000 = 0.000999 58679 / 1000 / 1000 = 0.058679 My maths teacher has set all…
cgwebprojects
  • 121
2
votes
3 answers

Prove that no integer of the form $7k+3 (k \in \mathbb Z) $ is a perfect square.

What I have is this, and I would like to make sure that I did it correctly. Suppose an integer of form $7k + r$, where $k \in \mathbb Z$ and $0 < r < 7$ is a perfect square. Then $7q+r =0$ ore $7q+r =1$. Therefore $r = 0$, and $r = 1$.
Dory
2
votes
1 answer

Division with decimal in the divisor

I understand HOW to do division with a decimal in the divisor, but my question is MUST we remove the decimal in the divisor and if so, why? Thanks.
Adam
  • 21
2
votes
4 answers

How to multiply Roman numerals?

How to multiply Roman numerals? I need an algorithm of multiplication of numbers written in Roman numbers. Help me please.
Maria
  • 271
1 2 3
…
99 100