Which answer is correct for the equation 3-3*6+2=? -13 or -17?
-13This BODMAS always lead to the confusion but only when if you are not aware of its rule.BODMAS means Bracket Open Divide Multiply Add Subtraction. In BODMAS questions BRACKETS () helps alot and elminate many confusions.In our question 3–3*6+2 we dont have divide so we will go for next i.e MULTIPLY. Put the bracket. And solve it first. 3-(3*6)+2(3*6)=18this will make our equation: 3–18+2Again put the bracket. 3(-18+2).Here you may ask one doubt WHY DID I INCLUDED MINUS SIGN OF 18 IN THE BRACKET.When we do Addition or Subtraction we always consider the sign of every number.Examples- (-10+2) = -8. SINCE “+”and “-” together results “-” hence we subtracted 2 from 10 and got 8. Now we will see which one is greater 10 or 2. Ofcourse, it is 10 and it is with the MINUS (-) sign hence ans. i.e 8 will take its sign and our ans for this example will be -8.Another example I’d like to discuss so that in future it will be helpful for you.Let's consider (-2–3). Ans will be “-5”. As per the above explanation we will see the sign of the both the numbers. Both have MINUS sign and “-” and “-” together results addition. hence we will add 3 and 2. Now again we will check which one is greater 2 or 3. It is 3 and it is with the minus sign. That's why ans is. “-5”.From the above examples what we concluded are:-Always put the bracket and in bracket dont forget to include their respective signs. i.e “+” or “-”.After performing operation dont forget to check which one is greater and give its sign to the ans.And remember for operation, for same signs do addtion and for opposite signs do subtraction.Now we can proceed with our actual questionwhere we left it.3(-18+2).=> 3–16 {.: we subtracted because we have opposite signs and -16 because 18 is greater and it has minus sign }=> (3–16) = -13 {.: minus sign because 16 is greater }.I hope all above explanations will be helpful to solve other questions.Goodluck!
How do I interchange the digits of 63 to make a new number? Is the result an odd number? Why?
Here is a method to interchange a 2-digit number:Multiply the units digit by 10.Divide the tens digit by 10. Discard the quotient. Keep the remainder.Add the results of steps 1 & 2.Therefore, to interchange 63:Multiply 3 by 10 = 30Divide 6 by 10 = 0 remainder 6Add 30 and 6 = 36Since the new number (36) has no remainder when divided by 2, it is even.Good luck!
In the multiplication of the two-digit number AB...?
(10A + B)C = 100A + 10A + A (10A + B)C = 111A C = 111A / (10A + B) Back in digit form: C = AAA / AB That isn't too tricky so maybe you wanted real numbers that work. Conditions: A, B, C are all some integer value, 0 through 9. And A != B, B != C, C != A. Solving: C can't be 0 because then A would have to be 0 and they can't be the same. To solve this I'm using a calculator to find the divisors of AAA. Then in the list of divisors I look for one that could work for AB. Then if dividing the guessed AAA by AB gives a one digit number, that number is C and the problem is done. The only thing that works is: A = 3, B = 7, C = 9 Because 333 / 37 = 9
Permutation, combinations and the multiplication.?
Serial numbers for a product are to be made using 3 letters followed by 2 numbers. If the letters are to be taken from the first letters of the alphabet with no repeats and the numbers are taken from the digits 0 through 9 with no repeats, how many serial numbers can be generated? how do i solve this? Sorry i left out the numbers by accident
A 4-digit number multiplied by 4 gives same number in reverse order. What is the four digit number and how do I prove it?
Lets say the number is written as ABCD (1000a+100b+10c+d).Multiplying it by 4, gives you DCBA (1000d+100c+10b+a)By divisibility of 4, BA is a two-digit number divisible by 4.Now, the largest possible value of ABCD is 2499, because anything more will result in a five digit number when multiplied by 4.Out of the two possibilites 1 and 2 for A, [3] follows that A is even, so 2.From [5], D is either 8 or 9. However, since D times 4 would end in 2, D is 8.Using [2], 4000a+400b+40c+4d = 1000d+100c+10b+a, which would simplify to 2c-13b = 1 after substituting A = 2 and D = 8.The only possible value of (b,c) where they would both be single digit integers is (1,7). Also to note from [3], B is odd. And from [4], B is either 1 or 3.The answer you're looking for is 2178, multiplied by 4 gives 8712.
Do you dare to awnser the most ultimate unknown question?
i think il give that 1 a BREAST`??
I have in mind a number which, when you remove the units digit and place it at the front, gives the same?
What you need is a number with n+1 digits, call it 10x+u where u denotes the unit digit and x denotes the other digits. And you tell us that u*10^n+x = 2*(10x+u). Hence we have u*(10^n-2) = 19x or x = u*(10^n-2)/19. Note that x must have n digits for 10x+u to have n+1 digits. And since 10^n-2 has n digits u/19 has to be greater than 1/10. Thus u = 0 and u = 1 are excluded. Since 19 is a prime number and u is a digit, ie. 2≤u≤9 u and 19 are relatively prime so for x = u*(10^n-2)/19 to be an integer 19 has to divide 10^n-2. This lay down restrictions on the integer n. Since 10^17 ≡ 2 mod 19 and because Fermats little theorem states that 10^18 ≡ 1 mod 19 we see that for n = 17+18k where k is an integer it holds that 10^n ≡ 2 mod 19 or put otherwise 10^n-2 is divisible by 19. It seems that this will work. Let's test it: k = 0 n = 17+18k = 17 (10^n-2)/19 = 5263157894736842 u = 2 x = 10526315789473684 The number will be 105263157894736842 and when you move the unit digit in front it becomes 210526315789473684 which is actually twice the original number. With the same setup but u changed from 2 to 3 we get the number 157894736842105263 which doubled becomes 315789473684210526. As a last test: k = 3 n = 17+18k = 71 u = 7 x = u*(10^n-2)/19 = 368421052631578947\ 368421052631578947\ 368421052631578947\ 36842105263157894 The number will be 368421052631578947\ 368421052631578947\ 368421052631578947\ 368421052631578947 which doubled becomes 736842105263157894\ 736842105263157894\ 736842105263157894\ 736842105263157894
On which integer can you move the last digit to the beginning of the number, resulting in twice the original number?
Good question: (If you aren't writing this out by hand, make sure your calculator can process long digits). Other wise you're going to get hung up in the calculators limitations and miss the point of this question. (I'm imagining an INTP Math whiz who has a life path or inner dream num7, trying these calculations over and over again to no avail. haha)The answer is : 26315789473684210(5)Move the (5) to the front and it's evenly divisible by two=(5)2631578947368421026315789473684210(5) X 2=(5)26315789473684210You should know the number 526315789473684210 is also a magical number. For one: If you add all the digits up, they are 81=8+1=(9) 9 being the magical number that when multiplied by anything except 0, adding the remaining digits becomes 9 again (once reduced in finality). For example9X4=45=4+5=(9)9X11=99=9+9=18=8+1=(9)48392087X9=435528783=4+3+5+5+2+8+7+8+3=45=4+5=(9)(You try)Secondly, and I'd say more interestingly the number 526315789473684210when multiplied by any number less than 19 is fairly simple to calculate using memory tricks.(This part is even more interesting considering the aforementioned relation ship to the number 9)Example:(5)26315789473684210 X (12)=6315789473684210520Mental shortcut: (The key is in memorizing the number 526315789473684210, the more your remember this number the easier the math gets)To start, always take 5(the first number of our magic number)X the number you are multiplying (12 in this example)=60Now, find the first number that follows (60) in the magic number 52(63)15789473684210; that number is 63 in this example (this number will always be listed first followed the sequential digits (6315789473684210)Finally simply add the former portion of the magic number that hasn't been used and add a zero: 6315789473684210(52)+0=6315789473684210Too good to be true? Let's try another example:526315789473684210 X 18=94736842105263157805X18=90; closest number is 94list the first sequence 9473684210; add the former sequence 52631578=947368421052631578; add zero and the answer is :9473684210526315780Remember, this trick only works when multiplying any number 1-18, after this the rule changes...a part of the reason why this works is our magical number 9.(you try)Oh right, now, what happens when 526315789473684210 is multiplied by 19 (1+9=10=1+0=1; the first of "the second cycle" numbers exceeding the magical number 9)526315789473684210 X 19=9999999999999999990 (beautiful)Hope I didn't get carried away and that this helps.