Introduction to Fractions: Understanding the Division of 3/5 by 3

Fractions are a fundamental concept in mathematics, representing parts of a whole. The fraction 3/5 specifically denotes three parts of a whole divided into five equal parts. This article delves into the process of dividing 3/5 by 3 and explores other conversions involving 3/5.

Dividing 3/5 by 3

To divide 3/5 by 3, we can rewrite the division as multiplication by the reciprocal of 3, which is 1/3:

Step-by-step Explanation:

Step 1: Rewrite the division as a multiplication:

3/5 ÷ 3 3/5 × 1/3

Step 2: Multiply across the top and the bottom:

3/5 × 1/3 (3 × 1) / (5 × 3) 3/15

Step 3: Simplify the fraction:

3/15 1/5 (both 3 and 15 are divisible by 3)

Therefore, 3/5 divided by 3 equals 1/5.

Equivalent Fractions for 3/5

The fraction 3/5 can be expressed in various equivalent forms. Here are some examples:

3/5 6/10 9/15 12/20 Another set of equivalent fractions for 3/5 includes: 15/25 18/30 21/35 24/40 30/50 90/150

Mixed Numbers and Improper Fractions

A mixed number is a combination of a whole number and a fraction. For example, three and five-tenths (3 5/10) can be written as a mixed number. This mixed number can also be expressed as an improper fraction:

3 x 10 5 35 (this is the numerator, and 10 is the denominator: 35/10 7/2)

When writing it as a mixed number, it could be 7 1/2.

Converting 3/5 to Decimal and Percentage

The fraction 3/5 can also be represented as a decimal and a percentage. Here's how to convert it:

Decimal Conversion:

3/5 0.60

Percentage:

3/5 60%
Therefore, the fraction 3/5 is equivalent to 60/100, which simplifies to 6/10 or 0.60.

Summary

Converting and manipulating fractions can be straightforward once you understand the principles. Here are the key points:

3/5 ÷ 3 1/5 Equivalent fractions: 3/5 6/10 9/15 12/20 and so on. Decimal equivalent: 3/5 0.60 Percentage equivalent: 3/5 60%

Understanding these conversions and manipulations is crucial for solving more complex mathematical problems and applications.