Question

-4/3 and 6/3 between How many numbers​

Answer 1

Answer:

-3/3,-2/3,-1/3,0/3,1/3,2/3,4/3,5/3

There are totally 8 no.s

Answer 2

Step-by-step explanation:

Ans. 71

Explanation:

Step 1. We need to find total numbers which are divisible by 3 = 500 /3 = 166

Step 2. Now, we don’t want the numbers which are divisible by 2 or 7.

Let us consider the numbers which are divisible by 2 in 166 numbers.

Step 3. Now, 166 numbers are completely divisible by 3 and we want to remove the numbers which are divisible by 2 from them. So, we have to find LCM of (2, 3) = 6.

Step4. Now, divide 500 by 6 = 83

So, we need to subtract these 83 numbers from 166, as they are divisible by 2 as well.

Therefore, 166 - 83 = 83.

Step 5. Now, we have to remove the numbers which are divisible by 7 from these 83 numbers. So, take LCM of 3 and 7 = 21, divide 500 by 21 = 23.

Therefore, 83 - 23 = 60

Step 6. While subtracting the numbers which are divisible by 7 we have considered some numbers which we have already removed in Step 4.

(Ex. 42 is divisible by 2 as well as 7, so, already we have deleted 1 occurrence of 42 in step 4 and in step 5 also we have deleted it again which we were not supposed to do but we did it for our convenience. Now, let’s find out such numbers and add them to get correct answer.)

Step 7. How to find them? Take LCM of 3, 2 and 7 = 42. Divide 500 by 42 = 11.

Now, add 11 in our answer.

i.e., 60 + 11 = 71

Note: Here we have given all the three prime numbers(2, 3 and 7). That’s why we have applied above logic if it would have been different then don’t apply above logic directly! Understand the question, think and then only proceed towards answer.

Sorry for grammatical mistakes if any! :)