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Chapter 0: Problem 46

Write each improper fraction as a mixed number. $$ \frac{67}{13} $$

Short Answer

Expert verified
5 \(\frac{2}{13}\)

Step by step solution

01

Divide the numerator by the denominator

To convert the improper fraction \(\frac{67}{13}\), start by dividing 67 by 13. The division gives a quotient and a remainder. Perform the division: 67 梅 13 = 5 with a remainder of 2.
02

Write the mixed number

The quotient from Step 1 becomes the whole number part of the mixed number. The remainder becomes the numerator of the fraction part, and the original denominator stays the same. Therefore, \(\frac{67}{13}\) as a mixed number is 5 \(\frac{2}{13}\).

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Key Concepts

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

mixed numbers
When dealing with improper fractions, we often convert them to mixed numbers for easier understanding and readability. A mixed number combines a whole number and a fraction. For example, the improper fraction \(\frac{67}{13}\) is converted into the mixed number 5 \(\frac{2}{13}\).
  • The whole number part (5) represents how many times the denominator can fit into the numerator fully.

  • The remaining part (\(\frac{2}{13}\)) is what we still have left over after taking out the whole number part.
Mixed numbers are especially useful in real life, like when measuring in cooking or dividing things into portions. They help us grasp the concept of parts greater than one in a more intuitive way.
division
Division is a mathematical operation where we determine how many times one number (the divisor) can be contained within another (the dividend). In converting improper fractions to mixed numbers, division is the core process. Let's take another look at the problem: \(\frac{67}{13}\).
  • Perform the division: 67 梅 13 = 5 with a remainder of 2. Here, 67 is the dividend and 13 is the divisor.

  • The whole number part of the mixed number comes from the quotient (5).

  • The numerator of the fraction part comes from the remainder (2).
Understanding division helps break down larger parts into manageable pieces, which is helpful for various mathematical problems and real-life applications.
numerator and denominator
Fractions consist of two parts: the numerator and the denominator. The numerator is the top number, showing how many parts we have. The denominator is the bottom number, showing how many equal parts the whole is divided into. For the improper fraction \(\frac{67}{13}\),
  • The numerator is 67, indicating 67 parts.
  • The denominator is 13, indicating each part is one-thirteenth of the whole.
When converting to a mixed number, we keep the denominator the same and adjust the numerator based on the remainder. Thus, in the mixed number 5 \(\frac{2}{13}\), 13 remains the denominator, making it clear the fraction part is still based on the original partitioning.

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Most popular questions from this chapter

A cookie recipe calls for \(2 \frac{2}{3}\) cups of sugar. How much sugar would be needed to make four batches of cookies?

A cake recipe calls for \(1 \frac{3}{4}\) cups of sugar. A caterer has \(15 \frac{1}{2}\) cups of sugar on hand. How many cakes can he make?

Find each sum or difference, and write it in lowest terms as needed. $$ \frac{7}{12}-\frac{1}{9} $$

Find each sum or difference, and write it in lowest terms as needed. $$ 3 \frac{4}{5}-1 \frac{4}{9} $$

Write each improper fraction as a mixed number. $$ \frac{16}{9} $$
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