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Chapter 4: Problem 78

Divide. Write the quotient as a mixed number. $$921 \div 4$$

Short Answer

Expert verified
230 \( \frac{1}{4} \)

Step by step solution

01

- Divide the whole number

Divide 921 by 4. Calculate how many times 4 can go into 921 without exceeding it. \[ \frac{921}{4} \rightarrow 230 \text{ R } 1 \]
02

- Determine the quotient and remainder

The division results in a quotient of 230 and a remainder of 1.
03

- Write as a mixed number

To write the quotient as a mixed number, place the quotient as the whole number, the remainder as the numerator, and the original divisor as the denominator. \[ 230 \frac{1}{4} \]

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Key Concepts

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

Mixed Numbers
Mixed numbers combine a whole number with a fraction. They are useful for representing quantities that are not purely whole numbers. For example, the number 230.25 can be written as \(230 \frac{1}{4}\) in mixed number form.
To convert a division problem into a mixed number:
  • First, perform the division to find the whole number quotient.

  • Next, identify the remainder from the division.

  • Combine the whole number quotient and the remainder by placing the remainder over the original divisor.

This way, you get a clear representation of the result as both a whole and fractional part.
Long Division
Long division helps you to divide larger numbers by breaking the division process into smaller, manageable steps. Here鈥檚 how it works:
  • Write the dividend (the number being divided) and divisor (the number you鈥檙e dividing by).

  • Determine how many times the divisor fits into the digits of the dividend from left to right without exceeding it, and write that number above the dividend line.

  • Multiply the divisor by the number you wrote above the line, subtract this result from the relevant portion of the dividend, and bring down the next digit.

Continue this process until you have worked through all the digits of the dividend. The final number above the line is your quotient, and if any number remains, that is your remainder.
Quotients and Remainders
When dividing numbers, the quotient is the result of the division, while the remainder is what is left over when the division process is complete. Let鈥檚 break it down:
  • The quotient shows how many times the divisor fits fully into the dividend.

  • The remainder is the difference left when the divisor can no longer fully fit into the remaining part of the dividend.

To express a quotient with a remainder as a mixed number:
  • Take the quotient as the whole number part.

  • Place the remainder as the numerator of the fraction.

  • Use the divisor as the denominator of the fraction.

With this method, the final result from our exercise of dividing 921 by 4 transforms into the mixed number \(230 \frac{1}{4}\). This notation makes it easier to understand and use in practical contexts.

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