1. Write the following numbers in descending order: a) $$ 18764321 ; 18674321 ; 18674231 ; 18764123 ; 18467321 ; 18467123 $$ b) $$ 124689135 ; 124869135 ; 124968153 ; 124896135 ; 124189635 ; 124168539 $$ c) $$ 278356281 ; 278536281 ; 278235681 ; 278512638 ; 278635182 ; 278135628 $$

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UpStudy AI · Accepted Answer

Sure, let's arrange each set of numbers in **descending order**. We'll compare each digit from left to right to determine the order.

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### **1.a)**
**Numbers:** 
$$ 18,\!764,\!321 ; 18,\!674,\!321 ; 18,\!674,\!231 ; 18,\!764,\!123 ; 18,\!467,\!321 ; 18,\!467,\!123 $$

**Step-by-Step Ordering:**

1. **Compare the first two digits (18)** for all numbers—they are the same.
2. **Third digit:**
   - **7** in $$ 18,\!764,\!321 $$ and $$ 18,\!764,\!123 $$ → higher than **6** in the other numbers.
3. **Between $$ 18,\!764,\!321 $$ and $$ 18,\!764,\!123 $$:**
   - **4th digit:** Both have **6**.
   - **5th digit:** Both have **4**.
   - **6th digit:** **3** in $$ 18,\!764,\!321 $$ vs. **1** in $$ 18,\!764,\!123 $$ → $$ 18,\!764,\!321 > 18,\!764,\!123 $$.
4. **Next, compare numbers starting with $$ 18,\!674,\! $$:**
   - Between $$ 18,\!674,\!321 $$ and $$ 18,\!674,\!231 $$:
     - **6th digit:** **3** vs. **2** → $$ 18,\!674,\!321 > 18,\!674,\!231 $$.
5. **Lastly, arrange the remaining numbers starting with $$ 18,\!467,\! $$:**
   - Between $$ 18,\!467,\!321 $$ and $$ 18,\!467,\!123 $$:
     - **6th digit:** **3** vs. **1** → $$ 18,\!467,\!321 > 18,\!467,\!123 $$.

**Final Descending Order:**
$$
18,\!764,\!321 > 18,\!764,\!123 > 18,\!674,\!321 > 18,\!674,\!231 > 18,\!467,\!321 > 18,\!467,\!123
$$

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### **1.b)**
**Numbers:** 
$$ 124,\!689,\!135 ; 124,\!869,\!135 ; 124,\!968,\!153 ; 124,\!896,\!135 ; 124,\!189,\!635 ; 124,\!168,\!539 $$

**Step-by-Step Ordering:**

1. All numbers start with $$ 124 $$, so we move to the next digits.
2. **4th to 6th digits:**
   - $$ 689 $$, $$ 869 $$, $$ 968 $$, $$ 896 $$, $$ 189 $$, $$ 168 $$.
3. **Descending order of the middle three digits:**
   - $$ 968 > 896 > 869 > 689 > 189 > 168 $$.
4. **Arrange accordingly:**
   - $$ 124,\!968,\!153 > 124,\!896,\!135 > 124,\!869,\!135 > 124,\!689,\!135 > 124,\!189,\!635 > 124,\!168,\!539 $$.

**Final Descending Order:**
$$
124,\!968,\!153 > 124,\!896,\!135 > 124,\!869,\!135 > 124,\!689,\!135 > 124,\!189,\!635 > 124,\!168,\!539
$$

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### **1.c)**
**Numbers:** 
$$ 278,\!356,\!281 ; 278,\!536,\!281 ; 278,\!235,\!681 ; 278,\!512,\!638 ; 278,\!635,\!182 ; 278,\!135,\!628 $$

**Step-by-Step Ordering:**

1. All numbers start with $$ 278 $$, so we inspect the next set of digits.
2. **4th to 6th digits:**
   - $$ 356 $$, $$ 536 $$, $$ 235 $$, $$ 512 $$, $$ 635 $$, $$ 135 $$.
3. **Descending order of the middle three digits:**
   - $$ 635 > 536 > 512 > 356 > 235 > 135 $$.
4. **Arrange accordingly:**
   - $$ 278,\!635,\!182 > 278,\!536,\!281 > 278,\!512,\!638 > 278,\!356,\!281 > 278,\!235,\!681 > 278,\!135,\!628 $$.

**Final Descending Order:**
$$
278,\!635,\!182 > 278,\!536,\!281 > 278,\!512,\!638 > 278,\!356,\!281 > 278,\!235,\!681 > 278,\!135,\!628
$$

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If you have any further questions or need additional assistance, feel free to ask!
**Descending Order:** 1. **a)** - $$ 18,\!764,\!321 $$ - $$ 18,\!764,\!123 $$ - $$ 18,\!674,\!321 $$ - $$ 18,\!674,\!231 $$ - $$ 18,\!467,\!321 $$ - $$ 18,\!467,\!123 $$ 2. **b)** - $$ 124,\!968,\!153 $$ - $$ 124,\!896,\!135 $$ - $$ 124,\!869,\!135 $$ - $$ 124,\!689,\!135 $$ - $$ 124,\!189,\!635 $$ - $$ 124,\!168,\!539 $$ 3. **c)** - $$ 278,\!635,\!182 $$ - $$ 278,\!536,\!281 $$ - $$ 278,\!512,\!638 $$ - $$ 278,\!356,\!281 $$ - $$ 278,\!235,\!681 $$ - $$ 278,\!135,\!628 $$

1. Write the following numbers in descending order: a) \( 18764321 ; 18674321 ; 18674231 ; 18764123 ; 18467321 ; 18467123 \) b) \( 124689135 ; 124869135 ; 124968153 ; 124896135 ; 124189635 ; 124168539 \) c) \( 278356281 ; 278536281 ; 278235681 ; 278512638 ; 278635182 ; 278135628 \)

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