Problem 72 Convert the improper fraction to... [FREE SOLUTION]

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Prealgebra

Julie Miller, Molly O鈥橬eill, Nancy Hyde

$Math Studyset 91影视 Explanations$ Math

1 Edition

Chapter 4: Problem 72

Convert the improper fraction to a mixed number. $$\frac{67}{12}$$

Short Answer

Expert verified

5 $\frac{7}{12}$

Step by step solution

- Divide the Numerator by the Denominator

First, divide the numerator (67) by the denominator (12). You鈥檒l find that 67 divided by 12 equals 5 with a remainder.

- Find the Quotient

The quotient is the whole number part of the mixed number. In this case, the quotient is 5.

- Determine the Remainder

Next, determine the remainder of the division. When 67 is divided by 12, the remainder is 7.

- Form the Mixed Number

The mixed number is formed by combining the quotient, the remainder, and the original denominator. So, \[\frac{67}{12} = 5 \frac{7}{12}\].

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Key Concepts

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

fraction division

To convert an improper fraction to a mixed number, begin by understanding fraction division. Dividing fractions involves dividing the numerator (the top number) by the denominator (the bottom number). This process is similar to regular division. For instance, taking $\frac{67}{12}$, you need to see how many times 12 fits into 67. Divide 67 by 12 to identify an integral part and obtain the remainder. This foundational concept drives all steps following.

quotient and remainder

When you divide 67 by 12, you get a quotient and a remainder. Here鈥檚 how that looks:

Quotient: The quotient is the resultant whole number from the division. For example, 67 divided by 12 is 5.
Remainder: After identification of the quotient, the leftover part of 67 that is not wholly divisible by 12 is the remainder. For this example, 67 divided by 12 results in a remainder of 7.

The quotient and remainder are crucial in converting the improper fraction to a mixed number.

mixed number conversion

After understanding quotient and remainder, let鈥檚 perform the mixed number conversion. For $\frac{67}{12}$, the quotient is 5, and the remainder is 7. To convert:

Start with the quotient as the whole number part.
Use the remainder as the new numerator.
Keep the original denominator.

So, $\frac{67}{12} = 5 \frac{7}{12}$. This mixed number includes a whole number and a fraction part. The fraction part always carries the same denominator from the original improper fraction. This is how you transition from working with improper fractions to mixed numbers.

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91影视

Convert the improper fraction to a mixed number. $$\frac{67}{12}$$

Short Answer

Step by step solution

- Divide the Numerator by the Denominator

- Find the Quotient

- Determine the Remainder

- Form the Mixed Number

Key Concepts

fraction division

quotient and remainder

mixed number conversion

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