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Chapter 4: Problem 29

In the following exercises, rewrite the improper fraction as a mixed number. $$\frac{5}{3}$$

Short Answer

Expert verified
\frac{5}{3} = 1 \frac{2}{3}

Step by step solution

01

Divide the Numerator by the Denominator

First, divide the numerator (5) by the denominator (3). This will give the whole number part of the mixed number. When we do the division, we get 1 as the quotient.
02

Find the Remainder

Next, find the remainder of the division. When 5 is divided by 3, the remainder is 2. This remainder becomes the new numerator of the fractional part.
03

Write the Mixed Number

Finally, write down the quotient from Step 1 as the whole number. Place the remainder from Step 2 over the original denominator to form the fractional part. Therefore, the improper fraction \(\frac{5}{3}\) can be written as the mixed number \(\frac{5}{3} = 1 \frac{2}{3}\).

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Key Concepts

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

Mixed Numbers
A mixed number is a combination of a whole number and a fraction. This type of number often makes it easier to understand quantities that are more than one but less than two, or in between any two whole numbers. In our example: \(\frac{5}{3}\). When we convert this improper fraction to a mixed number, we get \(1 \frac{2}{3}\).

Here鈥檚 why a mixed number is helpful: It tells you that there is 1 whole part and \(\frac{2}{3}\) of another part. This can be much easier to visualize and work with in various math problems. For example, if you bake 1 whole cake and then another \(\frac{2}{3}\) of a cake, you can quickly understand how many cakes you have in total.
Numerator and Denominator
In any fraction, the top number is called the numerator, and the bottom number is the denominator. The numerator represents how many parts we have, while the denominator indicates how many equal parts the whole is divided into. For example, in the fraction \(\frac{5}{3}\):
  • 5 is the numerator.
  • 3 is the denominator.
When converting an improper fraction to a mixed number, both the numerator and the denominator play crucial roles. In our case, the numerator 5 gets divided by the denominator 3. The quotient becomes the whole number part of the mixed number and the remainder becomes the new numerator of the fractional part, with the original denominator staying the same.
Division in Fractions
Understanding how to divide the numerator by the denominator is key to converting improper fractions to mixed numbers. Let's use the previous example, \(\frac{5}{3}\):
  • We divide 5 (numerator) by 3 (denominator).
  • The quotient is 1, which is our whole number.
  • The remainder is 2, which becomes our new numerator of the fraction part.
This process can be generalized for any improper fraction. Division helps us separate the fraction into an understandable whole number and a fractional part. For instance, in every fraction where the numerator is larger than the denominator, following these steps allows you to easily convert it into a mixed number format.

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Most popular questions from this chapter

In the following exercises, solve the equation. $$ -\frac{2}{3} c=18 $$

In the following exercises, simplify. $$ \frac{7}{11} \div\left(-\frac{7}{11}\right) $$

In the following exercises, evaluate the given expression. Express your answers in simplified form, using improper fractions if necessary. 8\(u^{2} v^{3}\) when \(u=-\frac{3}{4}\) and \(v=-\frac{1}{2}\)

In the following exercises, evaluate the given expression. Express your answers in simplified form, using improper fractions if necessary. \(\frac{5}{12}-w\) when (a) \(w=\frac{1}{4} \quad\) (b) \(w=-\frac{1}{4}\)

In the following exercises, perform the indicated operations and simplify. $$-\frac{11}{36}-\frac{11}{20}$$
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