Divisibility by 10: Finding Extra Blocks to Add to 27

Question

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?

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}.

Answer

3 3