Math, asked by Bindi2251, 1 year ago

How many numbers between 400 to 700 both exclusive are divisible by 9 or 11?

Answers

Answered by TooFree
9

Find the number of terms that are divisible by 9:


Find the smallest dividend:

Smallest number = dividend ÷ divisor (round up)

Smallest number = 400 ÷ 9 = 44.44 ≈ 45 (round up)

Smallest dividend = 45 x 9 = 405


Find the largest dividend:

Smallest number = dividend ÷ divisor (round down)

Smallest number = 700 ÷ 9 = 77.77 ≈ 77 (round down)

Smallest dividend = 77 x 9  = 693


Find the number of terms:

an = a1 + (n - 1)d

693 = 405 + (n - 1)9

693 = 405 + 9n - 9

693 = 9n + 396

9n = 297

n = 33


--------------------------------------------------------------------------------------------------


Find the number of terms that are divisible by 11:


Find the smallest dividend:

Smallest number = dividend ÷ divisor (round up)

Smallest number = 400 ÷ 11 = 36.36 ≈ 37 (round up)

Smallest dividend = 37 x 11 = 407


Find the largest dividend:

Smallest number = dividend ÷ divisor (round down)

Smallest number = 700 ÷ 11 = 63.63 ≈ 63 (round down)

Smallest dividend = 63 x 11  = 693


Find the number of terms:

an = a1 + (n - 1)d

693 = 407 + (n - 1)11

693 = 407 + 11n - 11

693 = 11n + 396

11n = 297

n = 27


--------------------------------------------------------------------------------------------------


Find the duplicates :

(Some numbers that are divisible by 9 are also divisible by 11)

Divisor = 9 x 11 = 99


Find the smallest dividend:

Smallest number = dividend ÷ divisor (round up)

Smallest number = 400 ÷ 99 = 4.04  ≈ 5 (round up)

Smallest dividend = 99 x 5 = 495


Find the largest dividend:

Smallest number = dividend ÷ divisor (round down)

Smallest number = 700 ÷ 99 = 7.07 ≈ 7 (round down)

Smallest dividend = 7 x 99  = 693


Find the number of terms:

an = a1 + (n - 1)d

693 = 495 + (n - 1)99

693 = 495 + 99n - 99

693 = 396 + 99n

99n = 297

n = 3


--------------------------------------------------------------------------------------------------


Find the total number of numbers that can be divisible by 9 and 11 between 400 and 700:

33 + 27 - 3 = 57


--------------------------------------------------------------------------------------------------

Answer: There are 57 numbers

--------------------------------------------------------------------------------------------------

Answered by Shaizakincsem
2

Thank you for asking this question:

We will assume as the least no divisible by 9 is 405

And the most is 693

So AP will be formed

405,414,423..........................693

The formula for nth term is given by:

an=a+(n-1)d

So, 693=405+(n-1)9

288=(n-1)9

32=n-1

So, n=33

If there is any confusion please leave a comment below.

Similar questions