Use long division to divide the following calculator: *a ) \( 8700 \div 60 \) *b) \( 34719 \div 71 \) (c) \( 208640 \div 160 \) d) \( 102024 \div 156 \)

Sure! Let's perform each division using the long division method step-by-step. --- ### **a) \( 8700 \div 60 \)** **Step 1:** Set up the long division. ``` ____ 60 ) 8700 ``` **Step 2:** Determine how many times 60 fits into the first part of 8700. - 60 fits into 87 once (since \(60 \times 1 = 60\)). ``` 1 ____ 60 ) 8700 60 --- 270 ``` **Step 3:** Bring down the next digit (0) to make it 270. - 60 fits into 270 four times (since \(60 \times 4 = 240\)). ``` 14 ____ 60 ) 8700 60 --- 270 240 --- 30 ``` **Step 4:** Bring down the final digit (0) to make it 300. - 60 fits into 300 five times (since \(60 \times 5 = 300\)). ``` 145 ____ 60 ) 8700 60 --- 270 240 --- 300 300 --- 0 ``` **Final Answer:** \( 8700 \div 60 = 145 \) --- ### **b) \( 34,\!719 \div 71 \)** **Step 1:** Set up the long division. ``` ______ 71 ) 34719 ``` **Step 2:** Determine how many times 71 fits into 347. - \(71 \times 4 = 284\) - \(71 \times 5 = 355\) (too big) So, 4 times. ``` 4 ______ 71 ) 34719 284 ---- 630 ``` **Step 3:** Bring down the next digit (1) to make it 631. - \(71 \times 8 = 568\) - \(71 \times 9 = 639\) (too big) So, 8 times. ``` 48 ______ 71 ) 34719 284 ---- 630 568 ---- 62 ``` **Step 4:** Bring down the next digit (9) to make it 629. - \(71 \times 8 = 568\) - \(71 \times 9 = 639\) (too big) So, 8 times. ``` 488 ______ 71 ) 34719 284 ---- 630 568 ---- 629 568 ---- 61 ``` **Final Answer:** \( 34,\!719 \div 71 = 488 \) with a remainder of 61. Alternatively, as a mixed number: \( 34,\!719 \div 71 = 488 \frac{61}{71} \) --- ### **c) \( 208,\!640 \div 160 \)** **Step 1:** Set up the long division. ``` _________ 160 ) 208640 ``` **Step 2:** Determine how many times 160 fits into 2086. - \(160 \times 13 = 2080\) So, 13 times. ``` 130 _________ 160 ) 208640 2080 ------- 64 ``` **Step 3:** Bring down the next digit (4) to make it 64. Since 64 is less than 160, append a 0 to the quotient and bring down the next digit. ``` 1304 _________ 160 ) 208640 2080 ------- 64 4 ``` **Step 4:** 160 fits into 640 exactly 4 times (since \(160 \times 4 = 640\)). ``` 1304 _________ 160 ) 208640 2080 ------- 640 640 ---- 0 ``` **Final Answer:** \( 208,\!640 \div 160 = 1,\!304 \) --- ### **d) \( 102,\!024 \div 156 \)** **Step 1:** Set up the long division. ``` ________ 156 ) 102024 ``` **Step 2:** Determine how many times 156 fits into 1020. - \(156 \times 6 = 936\) - \(156 \times 7 = 1092\) (too big) So, 6 times. ``` 6 ________ 156 ) 102024 936 ---- 660 ``` **Step 3:** Bring down the next digit (2) to make it 6602. - **Wait:** Actually, after subtracting 936 from 1020, we have 84, then bring down the next digit (0), making it 840. **Correcting Step 2:** After subtracting 936 from 1020: ``` 6 ________ 156 ) 102024 936 ---- 840 ``` **Step 3:** Determine how many times 156 fits into 840. - \(156 \times 5 = 780\) - \(156 \times 6 = 936\) (too big) So, 5 times. ``` 65 ________ 156 ) 102024 936 ---- 840 780 ---- 60 ``` **Step 4:** Bring down the next digit (2) to make it 602. - \(156 \times 3 = 468\) - \(156 \times 4 = 624\) (too big) So, 3 times. ``` 653 ________ 156 ) 102024 936 ---- 840 780 ---- 602 468 ---- 134 ``` **Step 5:** Bring down the next digit (4) to make it 1344. - \(156 \times 8 = 1248\) - \(156 \times 9 = 1404\) (too big) So, 8 times. ``` 6538 ________ 156 ) 102024 936 ---- 840 780 ---- 602 468 ---- 1344 1248 ---- 96 ``` **Final Answer:** \( 102,\!024 \div 156 = 6538 \) with a remainder of 96. Alternatively, as a mixed number: \( 102,\!024 \div 156 = 6538 \frac{96}{156} \) --- **Summary of Results:** a) \(8700 \div 60 = 145\) b) \(34,\!719 \div 71 = 488\) with a remainder of 61 c) \(208,\!640 \div 160 = 1,\!304\) d) \(102,\!024 \div 156 = 6538\) with a remainder of 96