Problem 40 - Prealgebra

Question

Change to improper fractions. $$1 \frac{3}{5}$$

Step-by-Step Solution

Answer

\(1 \frac{3}{5}\) is \(\frac{8}{5}\) as an improper fraction.

Step 1: Understand the Mixed Number

A mixed number consists of a whole number and a fraction. In the given number \(1 \frac{3}{5}\), the whole number is 1 and the fraction is \(\frac{3}{5}\). Our goal is to convert this into an improper fraction.

Step 2: Multiply the Whole Number by the Denominator

To convert a mixed number to an improper fraction, multiply the whole number part by the denominator of the fraction. In this case, multiply 1 by 5, which gives 5.

Step 3: Add the Numerator

Add the result from Step 2 to the numerator of the fraction. So, 5 (result from Step 2) plus 3 (numerator) equals 8.

Step 4: Write the Improper Fraction

Write the result from Step 3 over the original denominator. Therefore, the improper fraction is \(\frac{8}{5}\).

Key Concepts

Mixed Numbers

Mixed numbers are a combination of a whole number and a fraction. For instance, in the number \(1 \frac{3}{5}\), 1 is the whole number and \(\frac{3}{5}\) is the fractional part. Mixed numbers are often used to show values greater than one in a more compact form.

They are quite handy in everyday measurements, such as recipes or measurements of materials. When you need to perform mathematical operations, like multiplication or division, it's often beneficial to convert mixed numbers into improper fractions.

Converting Fractions

Converting between mixed numbers and improper fractions is a valuable skill in prealgebra. This allows you to navigate and solve mathematical problems effectively.

To convert a mixed number into an improper fraction, follow the steps outlined:

• Multiply the whole number by the denominator of the fraction.
• Add the numerator of the fraction to this product.
• Place this sum over the original denominator.

This method transforms the combined whole number and fractional part into an improper fraction, which can be more straightforward to manipulate in equations and calculations.

Prealgebra

Prealgebra serves as a foundation for all future math learning. It introduces basic math concepts necessary for algebra and beyond.

A critical part of prealgebra is understanding fractions, including how to work with mixed numbers and improper fractions. Learning to convert between these forms simplifies many algebra problems. Prealgebra encompasses other important concepts, like:

• Basic arithmetic operations (addition, subtraction, multiplication, division).
• Understanding properties of numbers.
• Developing skills to solve equations.

Grasping these foundational skills helps students build confidence and succeed in more advanced mathematical subjects.