Question

Change the following mixed numbers to improper fractions. \(2 \frac{3}{5}=\) ______

Short answer

\(2 \frac{3}{5}\) as an improper fraction is \(\frac{13}{5}\).

Step-by-step solution

Understand the Mixed Number

A mixed number consists of a whole part and a fractional part. In this case, the mixed number is given as \(2 \frac{3}{5}\), where 2 is the whole number and \(\frac{3}{5}\) is the fractional part.

Convert the Whole Number to a Fraction

To convert the whole number to a fraction with the same denominator as the fractional part, multiply the whole number by the denominator of the fractional part. Here, 2 is multiplied by 5, giving \(\frac{10}{5}\).

Add the Fractional Part

Now, add the fractional part \(\frac{3}{5}\) to the fraction obtained from the whole number, which is \(\frac{10}{5}\). This can be written as: \(\frac{10}{5} + \frac{3}{5}\).

Perform the Addition

Add the two fractions together by adding their numerators, while keeping the denominator the same. Therefore, \(10 + 3 = 13\), and the denominator remains 5. The result is \(\frac{13}{5}\).

Key concepts

Mixed Numbers

A mixed number is like a two-part entity involving both a whole number and a fraction. Picture walking into a bakery and buying 2 and 3/5 of a cake. You have two whole cakes and a bit extra, precisely 3/5 of another cake. This combination forms a mixed number, which is written as \(2 \frac{3}{5}\). This format is excellent for expressing quantities larger than one in a clear way.

Understanding mixed numbers is vital in mathematics because they're often seen in real-world scenarios involving measurements or quantities. They offer a comfortable way to express numbers that aren't quite complete, making them easy to interpret. However, calculations are easier when numbers are purely fractional or whole. This is where converting mixed numbers into improper fractions becomes handy.

Fraction Conversion

Converting a mixed number to an improper fraction involves a few simple steps. Let's take \(2 \frac{3}{5}\) as an example. The first part is the whole number 2, and the fractional part is \(\frac{3}{5}\).

• First, multiply the whole number by the denominator. So 2 times 5 equals 10.
• Next, add the numerator of the fractional part, which is 3. So, 10 plus 3 equals 13.

This makes the converted fraction \(\frac{13}{5}\), where 13 is the numerator and 5 remains the denominator. This form is called an improper fraction because the numerator is larger than the denominator. The advantage is that improper fractions are easier to work with, especially in addition, subtraction, multiplication, and division tasks.

Mathematics Education

Understanding the transition from mixed numbers to improper fractions at an early stage is crucial for learners. It strengthens a foundational skill in mathematics that is useful in various advanced topics. Educators focus on teaching these concepts in ways that make them intuitive and relatable.

Visual aids can be remarkably effective. Using pie charts or objects can help students visualize the breakdown of whole numbers and fractions. Moreover, practicing this conversion builds a solid base, enabling students to tackle more complicated math problems with confidence. Essential skills like these are the stepping stones to higher mathematical learning, supporting not just academic success, but also practical everyday problem-solving.