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Chapter 0: Problem 41

Write each improper fraction as a mixed number. $$ \frac{12}{7} $$

Short Answer

Expert verified
1 \( \frac{5}{7} \)

Step by step solution

01

Divide the numerator by the denominator

Divide 12 (the numerator) by 7 (the denominator) to determine how many whole numbers are in the fraction. The result is 1 with a remainder of 5.
02

Write down the whole number

The quotient from the division in Step 1 is 1, which represents the whole number part of the mixed number.
03

Formulate the remainder as a fraction

The remainder from the division is 5. Place this remainder over the original denominator of 7 to form the fractional part of the mixed number. Thus, the fractional part is \( \frac{5}{7} \).
04

Combine the whole number and the fraction

Combine the whole number from Step 2 and the fraction from Step 3 to form the mixed number. Therefore, \( \frac{12}{7} \) as a mixed number is \( 1 \frac{5}{7} \).

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Key Concepts

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

improper fractions
Understanding improper fractions is crucial for converting them into mixed numbers. An improper fraction has a numerator larger than or equal to its denominator.
This means it represents a value equal to or greater than 1.
For example, \[\frac{12}{7}\] is an improper fraction because 12 (numerator) is greater than 7 (denominator).
To handle improper fractions, often we need to convert them into mixed numbers for easier comprehension.
division in fractions
To change an improper fraction into a mixed number, start with division.
Divide the numerator by the denominator to figure out how many whole numbers fit into the fraction.
In our example, divide 12 by 7.
The result is 1 with a remainder.
This quotient (1) tells us the whole number part of our mixed number.
Always remember that the division step lays the foundation for finding the mixed number.
remainder in fractions
Next, the remainder plays a significant role in forming the fractional part of the mixed number.
After dividing 12 by 7, we get a remainder of 5.
Unlike in typical division where the remainder might become less relevant, here it becomes the numerator of the fractional part.
The original denominator (7) remains the same.
Therefore, the fractional part of our mixed number is \[\frac{5}{7}\], derived directly from the remainder and the original denominator.
fraction to mixed number
Combining the whole number and the fractional parts gives us the final mixed number.
From our steps earlier, 1 is the whole number and \[\frac{5}{7}\] is the fractional part.
When put together, the improper fraction \[\frac{12}{7}\] converts to the mixed number \[\text{1} \frac{5}{7}\].
This mixed number represents both the whole units and the remaining fraction more intuitively.
Mixed numbers make it easier to visualize quantities larger than one.

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Most popular questions from this chapter

Gary earns \(\$ 15\) per hour at his job. He recently received a \(7 \%\) raise. How much per hour was his raise? What is his new hourly rate?

Decide whether each statement is true or false. If it is false, explain why. The mixed number equivalent of the improper fraction \(\frac{31}{5}\) is \(6 \frac{1}{5}\)

\(23.29 \div 1000\)

\(1.62 \div 10\)

Find each product or quotient, and write it in lowest terms as needed. $$ \frac{2}{5} \div 30 $$
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