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Chapter 4: Problem 28

In the following exercises, rewrite the improper fraction as a mixed number. $$\frac{3}{2}$$

Short Answer

Expert verified
1 \(\frac{1}{2}\)

Step by step solution

01

Identify the Whole Number

Determine how many times the denominator fits into the numerator completely. For the fraction \(\frac{3}{2}\), 2 fits into 3 one time. Therefore, the whole number part of the mixed number is 1.
02

Find the Remainder

To find the remainder, subtract the product of the whole number and the denominator from the numerator: \(3 - 2 \times 1 = 1\). This remainder will be the numerator of the fractional part of the mixed number.
03

Form the Mixed Number

Combine the whole number and the new fraction. The mixed number is \(1 \frac{1}{2}\).

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Key Concepts

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

Improper Fraction
Before we dive into our core concepts, let's grasp what an improper fraction is. An improper fraction is a fraction where the numerator (the top number) is greater than or equal to the denominator (the bottom number). In the given exercise, \(\frac{3}{2}\) is an improper fraction. Here, the numerator (3) is bigger than the denominator (2). Improper fractions often represent a value greater than or equal to one.
Understanding improper fractions helps in converting them into mixed numbers smoothly.
Whole Number
Identifying the whole number is the first crucial step in converting an improper fraction into a mixed number. The whole number comes from dividing the numerator by the denominator without considering the remainder.
In the example \(\frac{3}{2}\), 2 goes into 3 one time without exceeding it. So, the whole number part of the mixed number becomes 1. This tells us how many full parts we have.
Remember, the whole number helps in simplifying and interpreting the value of improper fractions.
Remainder
Once you've figured out the whole number, the next step is to find the remainder. The remainder is what's left of the numerator after the whole number calculation.
For \(\frac{3}{2}\), after fitting 2 into 3 one time, we subtract the product of the whole number and the denominator from the numerator: \[3 - 2 \times 1 = 1.\]
The remainder becomes the numerator of the fractional part in the mixed number.
Numerator and Denominator
In fractions, the numerator and denominator play definitive roles. The numerator is the top part, indicating how many parts we have, and the denominator is the bottom part, specifying the total parts in a unit.
In \(\frac{3}{2}\), 3 (numerator) indicates parts we have, and 2 (denominator) shows the whole's parts. When converting an improper fraction to a mixed number, the remainder (1 here) becomes the new numerator. We keep the original denominator (2 in this case) the same in the fractional part.
Therefore, our mixed number for \(\frac{3}{2}\) is \[1 \frac{1}{2}.\]

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Most popular questions from this chapter

In the following exercises, perform the indicated operations and simplify. $$\frac{\left(\frac{2}{3}\right)^{2}}{\left(\frac{5}{8}\right)^{2}}$$

Evaluate. $$ x+\frac{1}{3} $$ $$ (a)x=\frac{2}{3} $$ $$ (b)x=-\frac{5}{6} $$

In the following exercises, find the least common denominator. $$\frac{3}{4}, \frac{1}{6}, \text { and } \frac{5}{10}$$

In the following exercises, simplify. $$\frac{2}{5}+\frac{5}{8}-\frac{3}{4}$$

In the following exercises, simplify. $$ \frac{1}{3} \cdot \frac{3}{4} $$
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