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Chapter 2: Problem 11

Evaluate each expression. $$45 \div 5$$

Short Answer

Expert verified
45 divided by 5 equals 9.

Step by step solution

01

Understanding Division

The expression to solve is a division problem: \( 45 \div 5 \). Division involves finding how many times the divisor (5) fits into the dividend (45).
02

Performing the Division

Now, divide 45 by 5. To do this, consider how many 5's can fit into 45. There are 9 distinct groups of 5 in 45, as 5 times 9 equals 45.
03

Reviewing the Calculation

After dividing, we find that 45 divided by 5 equals 9. This step confirms that the answer makes sense since \( 9 \times 5 = 45 \) checks out with the original dividend.

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Key Concepts

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

Understanding Division Concepts
Division is one of the fundamental operations in math. It is essentially the process of determining how many times one number is contained within another. In the expression \( 45 \div 5 \), the number 45 is called the 'dividend', and the number 5 is called the 'divisor'. The result of the division is called the 'quotient'. It answers the question, "How many groups of the divisor can we make with the dividend?"
  • The dividend: This is the number you want to divide into equal parts. Here, it's 45.
  • The divisor: This number tells us how many equal parts you are dividing the dividend into. Here, it's 5.
  • The quotient: This is the number of equal groups or "parts" we get, which in this example is 9.

Understanding these terms helps us grasp the division process more intuitively.
Approaching Math Problem-Solving
Math problem-solving can sometimes feel like cracking a puzzle. Here, the goal is clear鈥攆ind out how many times the number 5 can "fit" into 45. Problem-solving involves carefully thinking about numbers and their relationships.
  • Identify what you're being asked to find. In this case, "How many groups of 5 are in 45?"
  • Think about multiplication and division as inverse operations. If you know \( 9 \times 5 = 45 \), then you can quickly recognize that \( 45 \div 5 = 9 \).
  • Use logic and previous knowledge to find the answer. Leverage things like multiplication tables that you may already know.

When you approach division problems with a step-by-step thought process, they become much easier to solve.
Following a Division Step-by-Step Process
Using a structured approach to division ensures accuracy. Let's walk through the step-by-step process:
  • **Step 1: Identify the dividend and the divisor.** Here, \( 45 \) is the dividend and \( 5 \) is the divisor.
  • **Step 2: Estimate how many times the divisor goes into the dividend.** You might recognize that \( 5 \times 9 = 45 \), thus quickly concluding that it fits 9 times.
  • **Step 3: Perform the division operation.** Break down 45 by seeing how many groups of 5 make up 45. Exactly 9 groups of 5 make up 45.
  • **Step 4: Check your work.** Multiply the quotient (9) by the divisor (5) to ensure it equals the dividend (45). Since \( 9 \times 5 = 45 \), everything checks out.

Step-by-step division is not just about obtaining the answer but understanding why the answer is correct.

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