Problem 66 Multiply. $$ \begin{array}{r... [FREE SOLUTION]

91影视

Basic College Mathematics

Marvin L. Bittinger, Judith A. Beecher, Barbara L. Johnson

$Math Studyset 91影视 Explanations$ Math

13 Edition

Chapter 1: Problem 66

Multiply. $$ \begin{array}{r} 268 \\ \times \quad 35 \\ \hline \end{array} $$

Short Answer

Expert verified

9380

Step by step solution

Multiply the Units Place

Multiply the digit in the units place of the bottom number (5) by each digit in the top number (268) from right to left. 5 脳 8 = 40, write 0 and carry over the 4. 5 脳 6 = 30, add the carry-over (4), resulting in 34; write 4 and carry over the 3. 5 脳 2 = 10, add the carry-over (3), resulting in 13; write 13. The first intermediate product is 1340.

Multiply the Tens Place

Add a 0 at the end of the result because this multiplication is taking place in the tens place. Multiply the digit in the tens place of the bottom number (3) by each digit in the top number (268) from right to left. 3 脳 8 = 24, write 4 and carry over the 2. 3 脳 6 = 18, add the carry-over (2), resulting in 20; write 0 and carry over the 2. 3 脳 2 = 6, add the carry-over (2), resulting in 8; write 8. The second intermediate product is 8040.

Add the Intermediate Products

Add the intermediate products to get the final product. Align the numbers by their place values: 1340 +8040 ------ Start adding from the rightmost digit: 0 + 0 = 0 4 + 4 = 8 3 + 0 = 3 1 + 8 = 9 The final result is 9380.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Basic Arithmetic

Basic arithmetic operations form the foundation of mathematics, covering addition, subtraction, multiplication, and division. In this exercise, we use multiplication. Multiplication can be viewed as repeated addition.
If you multiply 3 by 4, it is the same as adding 3 four times (3+3+3+3).
Each digit of the numbers being multiplied can be operated on separately before combining the results.
This method breaks a large problem into smaller, easy-to-manage steps.

Intermediate Products

When performing multiplication, intermediate products are the partial results you get before adding everything together.
Let's illustrate this using our exercise:

First, we multiplied 268 by 5 (units place of 35)

We started multiplying from the rightmost digit:

5 脳 8 = 40 (write 0, carry over 4)
5 脳 6 = 30, plus carry-over 4 = 34 (write 4, carry over 3)
5 脳 2 = 10, plus carry-over 3 = 13 (write 13)

The first intermediate product is 1340.

Second, we multiplied 268 by 3 (tens place of 35)

Always remember to add a zero since we are now dealing with the tens place:

3 脳 8 = 24 (write 4, carry over 2)
3 脳 6 = 18, plus carry-over 2 = 20 (write 0, carry over 2)
3 脳 2 = 6, plus carry-over 2 = 8 (write 8)

The second intermediate product is 8040.

Addition

After finding the intermediate products, the final step is to add them together.
Addition is one of the simplest arithmetic operations where numbers are combined to form a sum. Here, the intermediate products are:

1340
8040

We add these numbers by aligning their place values:

Start with the units: 0 + 0 = 0
Tens: 4 + 4 = 8
Hundreds: 3 + 0 = 3
Thousands: 1 + 8 = 9

So, the sum and final product of 268 multiplied by 35 is 9380.
This step-by-step method helps prevent mistakes and makes complex problems manageable.

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91影视

Multiply. $$ \begin{array}{r} 268 \\ \times \quad 35 \\ \hline \end{array} $$

Short Answer

Step by step solution

Multiply the Units Place

Multiply the Tens Place

Add the Intermediate Products

Key Concepts

Basic Arithmetic

Intermediate Products

Addition

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