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Chapter 1: Problem 2

a. Multiply 8 and 47 by rewriting 47 as \(40+7\) and use the distributive property to obtain the result. b. Multiply 8 and 47 vertically.

Short Answer

Expert verified
Question: Multiply 8 and 47 using two different methods: (a) the distributive property, and (b) the vertical multiplication method. Answer: (a) Using the distributive property, we have 8 脳 (40+7) = 8 脳 40 + 8 脳 7 = 320 + 56 = 376. (b) Using the vertical multiplication method, we have: ``` 47 x 8 ------ 376 ``` So, 8 脳 47 = 376 in both methods.

Step by step solution

01

Rewrite 47 as \(40+7\) using the distributive property

We are given that 47 can be written as the sum of 40 and 7. So, the multiplication will become 8 times \((40+7)\).
02

Apply the distributive property

The distributive property states that \(a(b+c) = ab + ac\). We can apply this property to the multiplication 8 times \((40+7)\). So, \(8\times(40+7) = 8\times40 + 8\times7\).
03

Calculate the multiplication

Now, we can calculate the multiplication: \(8\times40 = 320\) and \(8\times7 = 56\). So, our expression becomes: \(8\times(40+7) = 320 + 56\).
04

Add the results

Finally, add the two numbers to get the final result: \(320 + 56 = 376\). So, \(8\times47 = 376\). Next, we will multiply 8 and 47 vertically.
05

Set up the vertical multiplication

To multiply 8 and 47 vertically, we write them down in a column format like this: ``` 47 x 8 ------ ```
06

Multiply the ones digit

Multiply the ones digit of 47 (which is 7) by 8. \(7\times8 = 56\). Write the 6 below the line and carry over the 5. ``` 47 x 8 ------ 6 +5 ```
07

Multiply the tens digit

Multiply the tens digit of 47 (which is 4) by 8. \(4\times8 = 32\). Now, add the carry-over 5: \(32+5=37\). Write 37 to the left of the 6. ``` 47 x 8 ------ 376 ```
08

Read the result

The result of the vertical multiplication is 376. So, \(8\times47 = 376\).

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