Question

Change the following mixed numbers to improper fractions. \(6 \frac{5}{7}=\) ______

Short answer

\(6 \frac{5}{7} = \frac{47}{7}\)

Step-by-step solution

Understand the Components

The mixed number \(6 \frac{5}{7}\) is made up of a whole number 6 and a fraction \(\frac{5}{7}\).

Multiply the Whole Number by the Fraction's Denominator

Multiply the whole number 6 by the denominator of the fraction, which is 7. \[ 6 \times 7 = 42 \]

Add the Numerator

Add the product obtained in Step 2 to the numerator of the fraction. \[ 42 + 5 = 47 \]

Form the Improper Fraction

Write the sum from Step 3 over the original denominator to form the improper fraction. Hence, the improper fraction is:\[ \frac{47}{7} \]

Key concepts

Understanding Improper Fractions

Improper fractions are a type of fraction where the numerator is greater than or equal to the denominator. This may sound a bit confusing at first, but it's actually quite simple once you break it down. Think of improper fractions as fractions that have a value greater than or equal to one.
For example, in the improper fraction \( \frac{47}{7} \), 47 is the numerator and 7 is the denominator. Here, 47 is greater than 7, meaning the fraction's value is more than one whole.

• Improper fractions can represent mixed numbers, such as \(6 \frac{5}{7}\).
• They are great for use in mathematical calculations, particularly in division and multiplication.
• Be sure always to compare the numerator with the denominator to identify improper fractions.

Mastering improper fractions is key to progressing in understanding more complex fractions and mixed numbers.

Simplifying Fraction Conversion

Converting mixed numbers to improper fractions is a straightforward process once you get the hang of it. The key is to think of mixed numbers as composed of a whole part and a fractional part.
For example, the mixed number \(6 \frac{5}{7}\) consists of a whole number 6 and the fraction \( \frac{5}{7} \).

• Step 1: Multiply the whole number by the denominator of the fractional part. For \(6 \frac{5}{7}\), multiply 6 by 7, which equals 42.
• Step 2: Add the numerator to this product. Add 5 (numerator) to 42, resulting in 47.
• Step 3: Write the sum over the original denominator: \( \frac{47}{7} \).

This process transforms the mixed number into an improper fraction, making it easier to use in equations and other calculations. Practicing these steps will make fraction conversion a breeze.

Effective Math Problem-Solving Techniques

Approaching mathematical problems with a strategic mindset is crucial for successful resolution and understanding. Here are some techniques that can enhance your problem-solving ability, particularly when working with fractions.

• Understand the Problem: Grasp the situation by identifying key elements. In our exercise, you needed to understand what a mixed number is.
• Break It Down: Divide the problem into manageable steps or parts. For instance, separate the whole number operation from the fractional component.
• Verify Your Steps: Review each step to ensure accuracy, such as confirming the multiplication and addition steps are correct in fraction conversion.
• Practice Patience: Allow yourself time to process and understand each step, which is particularly important when converting fractions or performing complex calculations.

By using these techniques consistently, you'll build confidence and improve your problem-solving skills, making math a more enjoyable experience.