Examples with solutions for Addition: Addition of 2-digit-and 1-digit numbers with the regrouping of both tens and ones

Exercise #1

In the picture we have a total of 35 blocks. Comprised of 3 tens and 5 ones. If we add a further 5 ones how many blocks will we have in total?

Step-by-Step Solution

Given the problem, we begin by identifying that the original number of blocks is 35, composed of 3 tens and 5 ones.

Step 1: Identify the current number of tens and ones: - 35 35 blocks means 3 3 tens and 5 5 ones.

Step 2: Add the additional ones: - We add 5 5 more ones to the current 5 5 ones: 5+5=10 5 + 5 = 10 .

Step 3: Regroup the ones into tens and ones: - Since 10 10 is equal to one ten, the ones become 0 0 , and the tens increase by 1 1 .

Step 4: Calculate the new total number of blocks: - The original 3 3 tens plus the additional 1 1 ten from regrouping gives us 4 4 tens. - Therefore, we now have 4×10=40 4 \times 10 = 40 blocks in total.

Thus, the new total number of blocks is 40 40 .

Answer

40 40

Exercise #2

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?

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.

Answer

2 2

Exercise #3

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

Exercise #4

What is the least amount of units we can add to the number 34 in order to get a number consisting only of whole tens?

Step-by-Step Solution

To solve this problem, we'll follow these steps:

  • Calculate the next multiple of ten greater than 34.
  • Determine the difference between this next multiple of ten and 34.

Now, let's calculate:

The smallest multiple of ten greater than 34 is 40. Therefore, we need to calculate 4034 40 - 34 .

The difference is 4034=6 40 - 34 = 6 .

Therefore, the solution to the problem is 6 6 .

Answer

6 6

Exercise #5

If we have 88 blocks and we add a further 6 blocks, how many blocks will we have in total?

Step-by-Step Solution

To determine the total number of blocks, we need to add the initial quantity of blocks to the additional blocks. Here's how you can calculate it step by step:

  • Step 1: Identify the initial number of blocks, which is 88.
  • Step 2: Identify the number of additional blocks being added, which is 6.
  • Step 3: Perform the addition: 88+6 88 + 6 .

Now, let's perform the addition:

88+6=94 88 + 6 = 94

Therefore, the total number of blocks after adding 88 and 6 is 94 94 .

Answer

94 94

Exercise #6

If we have 63 blocks in total and we add a further 9 ones, how many blocks will we have in total?

Step-by-Step Solution

To solve this problem, we need to add the additional blocks to the existing blocks:

  • Step 1: Start with the initial number of blocks, which is 63.
  • Step 2: Add the additional blocks, which are 9, using the addition operation.
  • Step 3: Perform the addition: 63+9 63 + 9 .

Now, let's calculate:

Performing the addition, we have:

63+9=72 63 + 9 = 72

This calculation gives us the total number of blocks. Therefore, the solution to the problem is that there are 72 blocks in total.

Answer

72 72

Exercise #7

If we have 57 blocks and we add a further 8 blocks, how many blocks will we have in total?

Step-by-Step Solution

To solve this problem, follow these steps:

  • Step 1: Identify Given Information: We have 57 blocks initially.
  • Step 2: Apply Addition: We will add 8 blocks to the initial 57 blocks.
  • Step 3: Perform Calculation: Calculate the sum using addition.

Now, carrying out the calculation:
We start with 57 57 blocks. When we add another 8 8 blocks, the operation is:
57+8=65 57 + 8 = 65

Therefore, after adding the additional blocks, we have a total of 65 65 blocks.

Answer

65 65

Exercise #8

If we have 48 blocks and we add a further 4 blocks, how many blocks will we have in total?

Step-by-Step Solution

To solve this problem, we will perform a simple addition. We begin with 48 blocks and add 4 more blocks. Our task is to find out the total number of blocks.

Let's calculate step by step:

  • Step 1: Identify the initial number of blocks. This is given as 48 48 .
  • Step 2: Identify how many blocks are added. This is given as 4 4 .
  • Step 3: Perform the addition of these two numbers: 48+4 48 + 4 .

By performing the addition,

48+4=52 48 + 4 = 52 .

Therefore, after adding the 4 blocks, the total number of blocks we have is 52 52 .

Answer

52 52