**Fractions and Decimals**

## Lesson 2: Conversion

**Welcome to Lesson 2 Conversion.**

**Objective**: In this lesson we will learn what proper fraction, improper fraction and mixed fractions or mixed numbers are.

We will also learn how to convert improper fractions to mixed numbers and vice versa.

Fractions consist of two numbers. The top number is called the numerator. The bottom number is called the denominator.

__Numerator__

Denominator

**Proper fraction:**

Definition: When in the given fraction the numerator is smaller than the denominator the fraction is called the ‘Proper Fraction’.

Examples: 3/7, 2/3, 21/36, 107/109

**Improper fraction:**

Definition: An improper fraction is a fraction that has a numerator larger than or equal to its denominator.

E.g. 3/2, 5/4, 17/15, 105/100

**Mixed fraction or mixed number:**

When a given fraction contains an integer and a proper fraction it is called a mixed fraction or mixed number.

E.g. 2 ½, 3 4/7 , 12 110/115

**Conversion of an improper fraction to a mixed fraction:**

· You are given the Improper Fraction e.g. 9/2

· When you divide 9 by 2, you get quotient 4 and remainder 1

· Now 4 will be the integer and remainder 1 will be the numerator and 2 will be the denominator. So the equivalent mixed fraction will be 4 ½

**Conversion of a mixed fraction to an improper fraction:**

· You are given the Mixed Fraction e.g. 3 7/9

· Multiply the integer by the denominator and add the numerator to the product

· Write their total as the numerator and the original denominator as the denominator of the fraction.

· So the equivalent improper fraction will be : 34/9

## Practice Problems

Remember you will simply solve these problems on your own; It is

· Convert following Mixed Fractions to Improper Fractions

o 6 4/9

o 7 ¾

· Convert following Improper Fractions to Mixed Fractions

**not**needed to email the answers to the instructor.· Convert following Mixed Fractions to Improper Fractions

o 6 4/9

o 7 ¾

· Convert following Improper Fractions to Mixed Fractions

- 11/8
- 127/15

## Assignment 2

**Please email the answers to this Assignment 2 to the email address provided at the bottom of the page. Please do not forget to write the Assignment number.**

· Convert following Mixed Fractions to Improper Fractions

1. 15 3/5

2. 2 1/2

3. 8 3/5

· Convert following Improper Fractions to Mixed Fractions

- 9/7
- 15/4
- 27/6

## Assessment 2

**Please email the answers to this Assessment 2 to the email address provided at the bottom of the page. Do not forget to write the Assessment number.**

· Convert following Mixed Fractions to Improper Fractions

1. 3 4/5

2. 2 7/8

3. 4 6/5

4. 5 2/3

5. 6 3/4

· Convert following Improper Fractions to Mixed Fractions

1. 14/3

2. 18/7

3. 13/9

4. 20/3

5. 11/3

## Objectives of next lesson

Objectives of the next lesson : Lesson 3 is about Reducing Fractions, you will know how to Reduce the proper fractions.

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**Please email your assignments and assessments to: dskarkha@ncsu.edu**