Fill in the missing numbers. X X 15 25 996 3 2 69 4 4 7 1 25 996 3269 8 64 12 8 8 764 12 8 2 2

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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**Fill in the Missing Numbers Exercise**

In this exercise, you will practice multiplication by filling in the missing numbers in the long multiplication problem. This helps build your understanding of the multiplication process and enhances your problem-solving skills.

First, let's look at the partially completed problem:

       4  _  8
   ×    7  6  4
  ______________
         1  _  2
+     2  5  _  8
+ _  9  9  6  _
_________________
     3  2  6  9  _  2

Your task is to find and fill in all the missing numbers (represented by underscores).

**Detailed Explanation:**

Multiplication in columns involves multiplying each digit of the second number (764) by each digit of the first number (4_8) and then summing up the results, taking care of placing each intermediate result in the correct column. 

1. **Illustration of Partial Multiplication:**
   In the first part, we can see that 764 is multiplied by a number starting with 8, resulting in:
         1  _  2
     The next step, 764 is multiplied by another number resulting in:
       2  5  _  8
     Finally, 764 is multiplied by the third number resulting in:
     _  9  9  6  _

2. **Summation of Results:**
   After calculating the above intermediate products, they are added together sequentially as shown:
       3  2  6  9  _  2

**Interactive Activity:**

Using the diagram below, fill in the missing numbers by following the steps of long multiplication.

       4    [ ]   8
   ×    7   6   4
  _______________
         1    [ ]    2
+     2   5   [ ]   8
+ [ ]   9   9   6
_________________
     3   2   6   9   [ ]   2

In the provided diagram, placeholders represent the missing digits. Calculate systematically to find the correct values and complete the multiplication process. 

**Exercises like these are essential for developing mathematical precision and confidence in dealing with multiplication problems. Happy solving
Transcribed Image Text:**Fill in the Missing Numbers Exercise** In this exercise, you will practice multiplication by filling in the missing numbers in the long multiplication problem. This helps build your understanding of the multiplication process and enhances your problem-solving skills. First, let's look at the partially completed problem: 4 _ 8 × 7 6 4 ______________ 1 _ 2 + 2 5 _ 8 + _ 9 9 6 _ _________________ 3 2 6 9 _ 2 Your task is to find and fill in all the missing numbers (represented by underscores). **Detailed Explanation:** Multiplication in columns involves multiplying each digit of the second number (764) by each digit of the first number (4_8) and then summing up the results, taking care of placing each intermediate result in the correct column. 1. **Illustration of Partial Multiplication:** In the first part, we can see that 764 is multiplied by a number starting with 8, resulting in: 1 _ 2 The next step, 764 is multiplied by another number resulting in: 2 5 _ 8 Finally, 764 is multiplied by the third number resulting in: _ 9 9 6 _ 2. **Summation of Results:** After calculating the above intermediate products, they are added together sequentially as shown: 3 2 6 9 _ 2 **Interactive Activity:** Using the diagram below, fill in the missing numbers by following the steps of long multiplication. 4 [ ] 8 × 7 6 4 _______________ 1 [ ] 2 + 2 5 [ ] 8 + [ ] 9 9 6 _________________ 3 2 6 9 [ ] 2 In the provided diagram, placeholders represent the missing digits. Calculate systematically to find the correct values and complete the multiplication process. **Exercises like these are essential for developing mathematical precision and confidence in dealing with multiplication problems. Happy solving
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