Question

Change the following mixed numbers to improper fractions. \(8 \frac{4}{10}=\) ______

Short answer

\(8 \frac{4}{10} = \frac{84}{10}\)

Step-by-step solution

Convert Mixed Number to Improper Fraction

To convert a mixed number to an improper fraction, multiply the whole number by the denominator of the fraction. Then, add the numerator of the fraction to this product.

Multiply Whole Number by Denominator

Multiply the whole number 8 by the denominator 10: \[ 8 \times 10 = 80 \]

Add the Numerator

Add the numerator 4 to the product obtained in the previous step: \[ 80 + 4 = 84 \]

Write the Improper Fraction

The improper fraction is formed by placing the sum from the previous step over the original denominator: \[ \frac{84}{10} \]

Key concepts

Mixed Numbers

A mixed number is a combination of a whole number and a fraction. It is a way to represent numbers that are somewhere between two whole numbers. Think of it like a whole pizza with some extra slices on the side. The whole number tells you how many whole items you have, while the fraction indicates the additional part of a whole. For example, in the mixed number \(8 \frac{4}{10}\), the "8" represents the whole number, and \(\frac{4}{10}\) is the fractional part. Mixed numbers are useful for simplifying the representation of quantities larger than one but less than the next whole number. They make understanding the magnitude and nature of the number more intuitive and align well with everyday counting.

Numerator and Denominator

The numerator and denominator are crucial components of any fraction. The numerator is the number above the line in a fraction, showing how many parts we have. The denominator is below the line and indicates how many of those parts make up a whole. In the fraction \(\frac{4}{10}\), "4" is the numerator and "10" is the denominator. The numerator tells us we have 4 parts out of the 10 parts that make up the whole. Understanding these two parts is integral to working with fractions and performing operations like addition, subtraction, multiplication, and division. They provide the foundational knowledge required to manipulate and convert different types of fractions effectively.

Fraction Conversion

Fraction conversion is the process of changing a fraction from one form to another, such as converting a mixed number to an improper fraction. Conversion is essential when performing arithmetic operations involving fractions, as it ensures numbers are compatible for calculation. Converting \(8 \frac{4}{10}\) to an improper fraction involves the following quick transformation:

• First, multiply the whole number (8) by the denominator (10), resulting in 80.
• Second, add the numerator (4) to this product, which gives 84.
• Finally, place this sum over the original denominator, forming \(\frac{84}{10}\).

This method allows all numbers in calculations to share a consistent format, making mathematical operations smoother and clearer.

Mathematical Steps

Math problems often require a series of steps to arrive at the correct answer. Breaking down problems into smaller, systematic steps can simplify complex operations and make them easier to understand. Let's explore the steps for converting a mixed number to an improper fraction, using the example of \(8 \frac{4}{10}\):

• Step 1: Identify the whole number "8" and the fraction \(\frac{4}{10}\).
• Step 2: Multiply the whole number (8) by the denominator (10), resulting in 80.
• Step 3: Add the numerator (4) to 80 to get 84.
• Step 4: Place the result over the original denominator, turning it into \(\frac{84}{10}\).

These clear, logical steps guide you through the process, ensuring that you achieve the correct conversion every time. Part of mastering math is becoming comfortable with following and executing these types of structured approaches.