Understand the Standard Algorithm for Division -9 (a) Hse the standard algorithm to find \( 546 \div 13 \). (b) Divide ? by 13 . The first digit goes in the ?

To solve the problems using the standard algorithm for division, let's break them down step by step. ### (a) Use the standard algorithm to find \( 546 \div 13 \). 1. **Set up the division**: Write 546 under the long division symbol and 13 outside. ``` ______ 13 | 546 ``` 2. **Determine how many times 13 goes into the first part of 546**: Look at the first digit (5). Since 13 is greater than 5, we look at the first two digits (54). 3. **Estimate how many times 13 fits into 54**: - 13 × 4 = 52 (this works) - 13 × 5 = 65 (this is too much) - So, we can use 4. 4. **Write 4 above the division line**: ``` 4 ______ 13 | 546 - 52 ------ 2 ``` 5. **Subtract 52 from 54**: This gives us 2. Bring down the next digit (6) from 546, making it 26. ``` 4 ______ 13 | 546 - 52 ------ 26 ``` 6. **Determine how many times 13 goes into 26**: - 13 × 2 = 26 (this works) - 13 × 3 = 39 (this is too much) - So, we can use 2. 7. **Write 2 above the division line**: ``` 42 ______ 13 | 546 - 52 ------ 26 - 26 ------ 0 ``` 8. **Subtract 26 from 26**: This gives us 0, which means there is no remainder. So, \( 546 \div 13 = 42 \). ### (b) Divide ? by 13. The first digit goes in the ?. To determine what the first digit could be, we need to find a digit that, when divided by 13, gives a whole number. The first digit must be less than 13, so it can be any digit from 0 to 9. However, if we want to find the first digit that can be used in a division problem with 13, we can consider the smallest number that is greater than or equal to 13. The first digit that can be used in the division by 13 is 1, as it is the first digit of the smallest two-digit number (13). So, the answer to the second part is that the first digit that can go in the ? is **1**.