Finding Missing Blocks: Making 48 Blocks Divisible by 10

Divisibility Rules with Modular Arithmetic

In total we have 48 blocks. How many ones do we need to add in order for the number of blocks to be divisible by 10?

❤️ Continue Your Math Journey!

We have hundreds of course questions with personalized recommendations + Account 100% premium

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

In total we have 48 blocks. How many ones do we need to add in order for the number of blocks to be divisible by 10?

2

Step-by-step solution

To solve this problem, follow these steps:

  • Step 1: Identify the remainder of 48 when divided by 10.
  • Step 2: Calculate how many blocks need to be added to remove the remainder and reach the next multiple of 10.

Let's work through these steps:

Step 1: Calculate 48mod10 48 \mod 10 .
When 48 is divided by 10, the quotient is 4 with a remainder of 8. Thus, 48mod10=8 48 \mod 10 = 8 .

Step 2: Since we want the total number of blocks to be divisible by 10, we need to reach the next multiple of 10, which is 50.
To find out how many blocks need to be added, subtract the remainder from 10:
108=2 10 - 8 = 2 .

Therefore, we need to add 2 blocks to the original 48 blocks to make the total divisible by 10. Hence, the correct choice is 2.

3

Final Answer

2 2

Key Points to Remember

Essential concepts to master this topic
  • Remainder: Find remainder when dividing by the target number
  • Technique: Calculate 48 ÷ 10 = 4 remainder 8
  • Check: Verify 48 + 2 = 50, and 50 ÷ 10 = 5 exactly ✓

Common Mistakes

Avoid these frequent errors
  • Adding the remainder instead of subtracting from 10
    Don't add the remainder 8 to get 48 + 8 = 56! This moves further from divisibility by 10. Always subtract the remainder from 10: we need 10 - 8 = 2 more blocks to reach the next multiple of 10.

Practice Quiz

Test your knowledge with interactive questions

If we have 67 blocks in total, how many blocks will remain if we remove 5 tens and 4 ones?

FAQ

Everything you need to know about this question

What does 'divisible by 10' actually mean?

+

A number is divisible by 10 when it can be divided by 10 with no remainder. Examples: 20, 30, 50, 100 are all divisible by 10.

Why do I subtract the remainder from 10?

+

The remainder tells us how far we are from the next multiple of 10. Since 48 has remainder 8, we need 108=2 10 - 8 = 2 more to reach 50.

What if the number was already divisible by 10?

+

If a number like 40 is already divisible by 10, the remainder is 0, so you don't need to add anything! 100=0 10 - 0 = 0 blocks needed.

Can I use this method for other numbers like 5 or 3?

+

Absolutely! To make any number divisible by 5, find the remainder when dividing by 5, then subtract from 5. Same logic works for any divisor.

How do I find the remainder quickly?

+

Look at the last digit for divisibility by 10! Since 48 ends in 8, the remainder when dividing by 10 is simply 8.

🌟 Unlock Your Math Potential

Get unlimited access to all 18 Natural Numbers around 100 questions, detailed video solutions, and personalized progress tracking.

📹

Unlimited Video Solutions

Step-by-step explanations for every problem

📊

Progress Analytics

Track your mastery across all topics

🚫

Ad-Free Learning

Focus on math without distractions

No credit card required • Cancel anytime

More Questions

Click on any question to see the complete solution with step-by-step explanations