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Chapter 1: Problem 387

Divide. Then check by multiplying. $$72 \div 3$$

Short Answer

Expert verified
24

Step by step solution

01

- Set Up the Division Problem

Write down the division problem in long division form: \[72 \ 3\]
02

- Divide

Determine how many times 3 can go into 72 without exceeding it. For long division, start with the first digit of 72. Since 3 goes into 7 two times, write 2 above the 7. Then multiply 3 by 2 and subtract 6 from 7, bringing down the next digit (2), making it 12. Divide 12 by 3 to get 4. Write 4 above the next digit. Each division step looks like this: \[ \frac{72}{3} = 24 \]
03

- Multiply to Check

Multiply the result (24) by the divisor (3) to check your work. Calculate \(24 \times 3\). If the product is equal to the original dividend (72), the division is correct: \[24 \times 3 = 72\]

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Key Concepts

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

division
When we talk about division, we mean splitting a number into equal parts. In this example, we are dividing 72 by 3. Start by writing it out using the long division format.

  • Write 72 (the dividend) under the long division symbol.
  • Write 3 (the divisor) outside, to the left of the symbol.

Next, determine how many times 3 can be multiplied to stay within each portion of the number, starting from the leftmost digit. Since 3 fits into 7 two times (because 3 times 2 is 6), you place a 2 above the 7. Multiply 3 by 2 to get 6, and subtract 6 from 7, leaving 1. Bring down the next digit, which is 2, making it 12. Now, determine how many times 3 fits into 12. It fits perfectly 4 times, so you write a 4 above the digit 2. When you finish dividing 12 by 3, you complete the process with no remainder.
multiplication
Multiplication is essentially repeated addition. After you find the quotient (the result of division), you can multiply it by the divisor to verify that your division was done correctly.

  • Take the quotient (24) you got from dividing 72 by 3.
  • Multiply 24 by 3.
  • Express it as a straightforward multiplication problem: \(24 \times 3\).

Perform the multiplication: \(24 \times 3 = 72\). Since the product matches the original dividend, your division work is confirmed to be accurate.
checking division
Checking your division work ensures that your solution is correct. It's always good practice, especially when you're learning. To check your division:
  • Multiply the quotient by the divisor.
  • Compare the product to the original dividend.

If the product equates to the original dividend, your division is correct. In our example:
  • Quotient: 24
  • Divisor: 3
  • Multiplication: \(24 \times 3 = 72\)

The result, 72, matches our starting number, confirming that the solution is accurate. This step not only verifies your work but also deepens your understanding of the relationship between division and multiplication.

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