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Chapter 3: Problem 11

\((10)(3) \div 2=\) ?

Short Answer

Expert verified
15

Step by step solution

01

Calculate the Multiplication

First, we multiply the numbers inside the parentheses: \((10)(3) = 30\)This gives us the result of the multiplication as 30. This step simplifies our expression down to 30 divided by 2.
02

Perform the Division

Now, take the result from Step 1 and divide it by 2:\(30 \div 2 = 15\)This division step simplifies the expression to the final answer.

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Key Concepts

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

Multiplication
Multiplication is one of the basic arithmetic operations and involves finding the total of one number repeated a specified number of times. For example, when you see an equation like \((10)(3)\) this means you take the number 10 and add it to itself 3 times. This operation is succinctly expressed as: \[10 + 10 + 10 = 30\] With multiplication, every number is called a factor, and the result is called the product. In our example, 10 and 3 are the factors, and 30 is the product.

Remember:
  • Multiplication is a faster way to add consecutive numbers.
  • Using numbers in parentheses like \((10)(3)\) signifies multiplication.
  • Always compute expressions inside the parentheses first if they appear in an equation.
Division
Division is another core arithmetic operation, and it allows us to find out how many times one number is contained within another. In simpler terms, it is the process of distributing or splitting equally. When you complete the multiplication in our initial problem and get 30, the next task is to divide by 2: \(30 \div 2 = 15\). Here, 30 is called the dividend, 2 is the divisor, and 15 is the quotient.

Key points about division:
  • Division is the inverse operation of multiplication. If a number is multiplied, division will break it back down.
  • The result of division tells you how much one unit contains when divided equally.
  • The division sign can be represented as "\(\div\)" or "/". For example, 30 \(\div\) 2 or 30 / 2 both mean the same thing.
Order of Operations
The order of operations, often memorized through the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right)), is crucial for solving equations correctly. It tells you the correct sequence to approach solving complex mathematical expressions. Without it, the expression could be misinterpreted, leading to incorrect answers.

Applying **PEMDAS** to our problem \((10)(3) \div 2\), we first solve the multiplication part: \(10 \times 3\), which yields 30.
Then, you follow with division: \(30 \div 2\), resulting in the final number of 15.
  • Always handle any calculations inside parentheses first. Thus, multiplication within them should be managed initially.
  • When both multiplication and division are present in a sequence, process them in order from left to right.
  • This ensures uniformity and accuracy in solving equations.

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