To solve the problem, we need to find the remainders of two divisions and then sum those remainders.
### Step 1: Divide 12112 by 11
To find the remainder when 12112 is divided by 11, we can perform the division:
1. **Divide 12112 by 11**:
- 11 goes into 121 (the first three digits of 12112) 11 times (11 x 11 = 121).
- Subtract 121 from 121 to get 0. Bring down the next digit, which is 1.
- Now we have 1. 11 goes into 1, 0 times. So, we write down 0 and bring down the next digit, which is 2.
- Now we have 12. 11 goes into 12, 1 time (11 x 1 = 11).
- Subtract 11 from 12 to get 1. Bring down the next digit, which is 2.
- Now we have 12 again. 11 goes into 12, 1 time (11 x 1 = 11).
- Subtract 11 from 12 to get 1. Bring down the last digit, which is 2.
- Now we have 12. 11 goes into 12, 1 time (11 x 1 = 11).
- Subtract 11 from 12 to get 1.
So, the remainder when 12112 is divided by 11 is **1**.
### Step 2: Divide 13223 by 13
Next, we find the remainder when 13223 is divided by 13:
1. **Divide 13223 by 13**:
- 13 goes into 132 (the first three digits of 13223) 10 times (13 x 10 = 130).
- Subtract 130 from 132 to get 2. Bring down the next digit, which is 2.
- Now we have 22. 13 goes into 22, 1 time (13 x 1 = 13).
- Subtract 13 from 22 to get 9. Bring down the last digit, which is 3.
- Now we have 93. 13 goes into 93, 7 times (13 x 7 = 91).
- Subtract 91 from 93 to get 2.
So, the remainder when 13223 is divided by 13 is **2**.
### Step 3: Sum the Remainders
Now, we sum the remainders obtained from both divisions:
- Remainder from 12112 ÷ 11 = 1
- Remainder from 13223 ÷ 13 = 2
Thus, the sum of the remainders is:
1 + 2 = **3**.
### Final Answer
The sum of the remainders obtained by dividing 12112 by 11 and 13223 by 13 is **3**.
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