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Chapter 1: Problem 9

Write the repeated addition as multiplication and simplify. $$9+9+9$$

Short Answer

Expert verified
The multiplication form is $$9 \times 3$$, and it simplifies to 27.

Step by step solution

01

Identify the Repeated Number

Examine the addition problem: $$9+9+9$$. Notice that the number 9 is being added repeatedly.
02

Count the Number of Repetitions

Count how many times 9 appears in the addition problem. In this case, it appears 3 times.
03

Write as Multiplication

Convert the repeated addition into a multiplication problem. Since 9 is repeated 3 times, write it as: $$9 \times 3$$.
04

Simplify the Multiplication

Perform the multiplication: $$9 \times 3 = 27$$.

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Key Concepts

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

Repeated Addition
When facing an addition problem with the same number again and again, we talk about repeated addition. This is an important step to understand multiplication. For example, look at the problem: 9 + 9 + 9. Here, the number '9' occurs three times. This frequent addition of the same number can be easily and quickly expressed using multiplication.
Multiplication Process
The core idea behind multiplication is it simplifies repeated addition. To convert the repeated addition into multiplication, we count how many times the number is added, and then we multiply the number by this count. For our example, 9 is added thrice. So, we write this addition as a multiplication expression: 9 脳 3. This means adding 9 three times.
Simplifying Multiplication
After setting up our multiplication expression, the next step is to perform the multiplication operation. In our example, we have 9 脳 3. Performing the multiplication, we get the answer 27. So, 9 + 9 + 9 simplifies to 9 脳 3, which in turn simplifies to 27. This saves time and effort, showing how multiplication makes repeated addition simpler.

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