Divisibility by 10: Finding Extra Blocks to Add to 27

Divisibility Rules with Remainder Calculations

If we have 27 blocks in total and we want to add enough blocks in order that the total number of blocks will be divisible by 10, how many extra blocks must we add?

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Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

If we have 27 blocks in total and we want to add enough blocks in order that the total number of blocks will be divisible by 10, how many extra blocks must we add?

2

Step-by-step solution

To solve this problem of determining how many blocks need to be added to 27 in order to make it divisible by 10, we will follow these steps:

  • Step 1: Calculate the remainder when 27 is divided by 10.
  • Step 2: Determine how many blocks are needed to reach the next multiple of 10.

Let's work through each step:

Step 1: Calculate the remainder:

When we divide 27 by 10, we perform the calculation 27÷10=2 27 \div 10 = 2 remainder 7 7 . This means, 277(mod10) 27 \equiv 7 \pmod{10} .

Step 2: Find how many more blocks are needed:

We want the total to be a multiple of 10. The next multiple of 10 after 27 is 30.

To find how many more blocks we need, we subtract the remainder from 10:

107=3 10 - 7 = 3

Therefore, we need to add 3 blocks to the current 27 blocks to make the total divisible by 10.

Thus, the number of additional blocks needed is 3\boxed{3}.

3

Final Answer

3 3

Key Points to Remember

Essential concepts to master this topic
  • Rule: To find blocks needed, subtract remainder from 10
  • Technique: 27 ÷ 10 = 2 remainder 7, so need 10 - 7 = 3
  • Check: 27 + 3 = 30, and 30 ÷ 10 = 3 with no remainder ✓

Common Mistakes

Avoid these frequent errors
  • Adding the remainder instead of subtracting it from 10
    Don't add the remainder 7 to get 27 + 7 = 34! This gives you a number that's even further from being divisible by 10. Always subtract the remainder from 10 to find how many more you need to reach the next multiple.

Practice Quiz

Test your knowledge with interactive questions

If we have 85 blocks in total, how many blocks will remain if we remove 4 tens and 1 one?

FAQ

Everything you need to know about this question

Why can't I just keep adding 1 until I get to a multiple of 10?

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You could, but it's much slower! Using the remainder method gives you the answer instantly. Find the remainder when dividing by 10, then subtract from 10.

What if the number is already divisible by 10?

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Great question! If there's no remainder (like 30 ÷ 10 = 3 remainder 0), then you don't need to add any blocks. The answer would be 0.

How do I find the remainder without a calculator?

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Look at the ones digit! For 27, the ones digit is 7. That's your remainder when dividing by 10. So you need 107=3 10 - 7 = 3 more blocks.

Does this method work for divisibility by other numbers?

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Yes! The same principle works for any number. Find the remainder when dividing, then subtract from the divisor. For example, to make 27 divisible by 5: 27÷5=5 27 ÷ 5 = 5 remainder 2 2 , so add 52=3 5 - 2 = 3 .

What's the next multiple of 10 after 27?

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The next multiple of 10 after 27 is 30. You can find this by adding the remainder to the original number: 27+3=30 27 + 3 = 30 .

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