Part a: select the correct solution to the following division problems. 77,672 ÷ 5,548 = 14 288,184 ÷ 34 = 8,465 part b: explain how you solved the problem using first, next, and last. show your work.

We have two division problems:

Now, let's solve these problems step-by-step

A)

We will solve this question by long division method

First, let's identify the divisor and dividend. The number to be divided is 77,672 hence this is the dividend, and it needs to be divided by 5,548 which is the divisor

Next, since the divisor (5548) is a 4-digit number, we will look at the first 4 digits of the dividend (7767) and see what multiple of 5548 is less than or equal to 7767. That multiple is 1. So we write 1 in the quotient and multiply 5548 with 1 and subtract the product (5548*1 = 5548) from 7767. The remainder that we get is 2219.

Next, we bring down the 5th digit of the dividend (i.e. 2) next to the remainder, to create the number 22192. Now, we see what multiple of 5548 is less than or equal to 22192. That multiple is 4. So we write 4 next to the quotient and multiply 5548 with 4 and subtract the product (22192) from 22192. Now, the remainder is zero. Hence, we have solved the entire problem

Last, we look at the quotient i.e. 14, which is the solution to the problem.

Please refer to the attached image for visualization

B)

We will solve this question by long division method

First, let's identify the divisor and dividend. The number to be divided is 288,184 hence this is the dividend, and it needs to be divided by 34 which is the divisor

Next, since the divisor (34) is a 2-digit number, we will look at the first 2 digits of the dividend (28) and see what multiple of 34 is less than or equal to 28. We see that the divisor is greater than the first 2 digits of the dividend, hence we look at another digit. Now, we check what multiple of 34 is less than or equal to 288. That multiple is 8. So we write 8 next to the quotient and multiply 34 with 8 and subtract the product (34*8 = 272) from 288. The remainder that we get is 16.

Next, we bring down the 4th digit of the dividend (i.e. 1) next to the remainder, to create the number 161. Now, we see what multiple of 34 is less than or equal to 161. That multiple is 4. So we write 4 next to the quotient and multiply 34 with 4 and subtract the product (136) from 161. Now, the remainder is 25.

Next, we bring down the 5th digit of the dividend (i.e. 8) next to the remainder, to create the number 258. Now, we see what multiple of 34 is less than or equal to 258. That multiple is 7. So we write 7 next to the quotient and multiply 34 with 7 and subtract the product (238) from 258. Now, the remainder is 20.

Next, we bring down the 6th digit of the dividend (i.e. 4) next to the remainder, to create the number 204. Now, we see what multiple of 34 is less than or equal to 204. That multiple is 6. So we write 6 next to the quotient and multiply 34 with 6 and subtract the product (204) from 204. Now, the remainder is 0.

Hence, we have solved the entire problem

Last, we look at the quotient i.e. 8476, which is the solution to the problem.

Please refer to the attached image for visualization.