If you’ve heard of fractions, then you know that they could be complex, confusing and frustrating for many students. However, mastering simple fractions is a prerequisite knowledge before moving on to more complex topics like decimals and percentages. One of the most commonly asked questions about fractions is “What is 9 out of 15?” In this article, we will provide a comprehensive guide on mastering simple fractions.

## Understanding Fractions

A fraction represents a part of a whole. Fractions are represented using two numbers; the top number is called the numerator, and the bottom number is called the denominator. The numerator represents the portion of the whole that is being considered, while the denominator represents the total number of equal parts in the whole.

For instance, if you were considering a pizza with eight slices and you ate three of those slices, the fraction of the pizza that you’ve consumed would be 3/8.

## Types of Fractions

There are four types of fractions; proper, improper, mixed and decimal.

### Proper Fractions

Proper fractions are those fractions where the numerator is less than the denominator. For example, 2/3 or 5/8

### Improper Fractions

Improper fractions, on the other hand, are those fractions where the numerator is greater than or equal to the denominator. Examples include 7/3 or 12/5.

### Mixed Fractions

Mixed fractions are a combination of whole numbers and proper fractions. For example, 2 1/2 or 4 3/4.

### Decimal Fractions

Decimal fractions are fractions that are expressed in decimal form. For instance, 0.75 or 0.3

## Converting Fractions

Converting fractions may seem difficult, but there are simple steps to follow for each type of conversion, as seen below:

### Proper Fractions to Decimals

To convert a proper fraction to a decimal fraction, divide the numerator (the top number) by the denominator (the bottom number). For instance, to convert 3/5 to a decimal form will be 3 ÷ 5 = 0.6.

### Improper Fractions to Mixed Fractions

To convert an improper fraction to a mixed fraction, you have to divide the numerator by the denominator, then write the remainder as the numerator of the fractional part. For example:

Improper Fraction | Mixed Fraction |
---|---|

7/2 | 3 1/2 |

12/4 | 3 |

### Mixed Fractions to Improper Fractions

To convert a mixed fraction to an improper fraction, you have to multiply the whole number by the denominator, then add the numerator to the result. The result will become your new numerator, while the denominator will remain the same. For instance:

Mixed Fraction | Improper Fraction |
---|---|

3 1/2 | 7/2 |

2 2/3 | 8/3 |

## Adding and Subtracting Fractions

### Adding and Subtracting Like Fractions

When adding or subtracting like fractions, you only need to add or subtract the numerators, leaving the denominators unchanged. If you’re adding fractions with different denominators, you need to find the common denominator first.

### Adding and Subtracting Unlike Fractions

When adding and subtracting unlike fractions, you need to get equivalent fractions with common denominators first. Once the denominators are equal, add or subtract the numerators, keeping the denominators unchanged.

## Multiplying and Dividing Fractions

### Multiplying Fractions

To multiply fractions, multiply the numerators together and the denominators together.

### Dividing Fractions

To divide fractions, turn the second fraction upside down, and then multiply.

## Percentages and Fractions

Percentages are fractions expressed as parts out of 100. For instance, 25% is the same as 25/100. To convert percentages to fractions, remove the percentage sign and divide by 100. To convert fractions to percentages, you simply multiply the fraction by 100.

## Conclusion

Mastering simple fractions is an essential skill for students to have. With the right guidance, learning how to add, subtract, multiply, and divide fractions can be a walk in the park.

## FAQs

**What is a fraction?**A fraction represents a part of a whole.**What are the four types of fractions?**The four types of fractions include proper, improper, mixed and decimal fractions.**How do I convert fractions?**Converting fractions involves various steps depending on the type of fraction being converted. For instance, to convert a proper fraction to a decimal fraction, divide the numerator by the denominator.**What is the formula for adding and subtracting fractions?**The formula for adding and subtracting fractions varies based on whether the fractions are like or unlike fractions.**How do I convert percentages to fractions?**To convert percentages to fractions, remove the percentage sign and divide by 100.

## References

Mathematics Exercises for National Curriculum Standards: Mathematics, Grade 6. Education, U.S. Department of. Washington, DC: National Academy Press, 1998.

Understanding Fractions. (n.d.). Retrieved from https://www.mathsisfun.com/fractions.html.