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Chapter 0: Problem 45

Write each improper fraction as a mixed number. $$ \frac{83}{11} $$

Short Answer

Expert verified
The mixed number is \(7 \frac{6}{11}\).

Step by step solution

01

Divide the numerator by the denominator

To convert the improper fraction \(\frac{83}{11}\) to a mixed number, divide 83 by 11. This will give the whole number part of the mixed number. \[ 83 梅 11 = 7 \]
02

Find the remainder

Calculate the remainder of the division to get the fractional part of the mixed number. The remainder when you divide 83 by 11 is \[ 83 - 7 \times 11 = 83 - 77 = 6 \]
03

Write the Mixed Number

Combine the whole number part and the remainder over the original denominator to form the mixed number. Therefore, the mixed number is \[ 7 \frac{6}{11} \]

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Key Concepts

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

Understanding Division
Division is a basic arithmetic operation that involves splitting a number, called the dividend, into equal parts. The number you are dividing by is called the divisor.
For example, in the problem given where we need to convert \(\frac{83}{11} \) into a mixed number, 83 is the dividend and 11 is the divisor.
When you perform the division, you get a quotient and sometimes a remainder.
The quotient represents how many times the divisor fits into the dividend completely.

Key points to remember about division:
  • Dividend: The number to be divided. (83 in our example)
  • Divisor: The number by which the dividend is divided. (11 in our example)
  • Quotient: The result of division, indicating how many times the divisor fits into the dividend. (7 in our example)
  • Remainder: What is left over after division. (6 in our example)
This basic understanding of division is crucial for converting improper fractions to mixed numbers.
What is a Remainder?
When dividing two numbers, sometimes the divisor does not fit perfectly into the dividend.
This leaves us with a remainder, which is the amount left after the division.
In our example of \(\frac{83}{11} \), the remainder is the part of the dividend that cannot be evenly divided by the divisor.

To find the remainder, we follow these steps:
  • Calculate the total amount the divisor fits into the dividend: \ 11 \times \ 7 = 77 \
  • Subtract this value from the original dividend: \ 83 - 77 = 6 \
So, the remainder here is 6. Remainders are crucial when dealing with mixed numbers as they become the numerator of the fractional part.
Converting to Mixed Numbers
Mixed numbers are combinations of a whole number and a fraction. They make it easier to understand quantities that are not whole.
To convert an improper fraction like \(\frac{83}{11} \) to a mixed number, follow these steps:
  • First, perform division: \( 83 \div 11 = 7 \) giving you a whole number do not delete.
  • Next, find the remainder: 6 in our case.
  • Lastly, write the mixed number: The quotient (7) is the whole number part and the remainder (6) over the original denominator (11) forms the fraction: \ 7 \frac{6}{11} \.
Mixed numbers are helpful in everyday math as they represent quantities more intuitively compared to improper fractions.

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