**Fractions and Decimals**

## Lesson 4 continued

Mathematical operations on Mixed Fractions

Mathematical Operations on Improper Fractions/Mixed Fractions.

Mixed Fraction consists of an integer followed by a fraction.

For addition and subtraction when Improper Fractions are involved,

· First convert Improper Fraction to Mixed Fraction.(Refer Lesson 2 Conversion )

· Then perform the operation

· Add the numerators of the two fractions

· Place that sum over the common denominator.

· If this fraction is Improper (numerator larger than or equal to the denominator) then convert it to a Mixed Fraction

· Add the Integer portions of the two Mixed Fractions

· If adding the fractional parts created a Mixed Fraction then add its integer portion to the sum.

For Example: 3 2/3 + 5 2/3

Add the fractional part of the mixed numbers 2/3 + 2/3 = 4/3

Convert 4/3 to a mixed number 4/3 = 1 1/3

Add the integer portions of the mixed numbers 3 + 5 = 8

Add the integer from the sum of the fractions 8 + 1 = 9

Final Answer 9 1/3

· Follow same steps for Subtraction of two Mixed Fractions with same denominator.

· Rename the fractions to have the LCD

· Add/Subtract the numerators of the Mixed Fractions

· Add/Subtract the integers of the Mixed Fractions

o Add the integer from the sum/subtraction of the fractions

· Reduce/Simplify the Fraction

For Example: 2 ¾ - 1 ½

Subtract the fractional part of the mixed numbers 3/4 - 2/4

Convert it to mixed Fraction (If needed) 1/4

Subtract the integer portions of the mixed numbers 2 – 1 = 1

Add the integer from the sum/subtraction of the fractions 1 1/4

Final Answer 1 1/4

· Convert each mixed number to an improper fraction.

· Multiply the two numerators together.

· Multiply the two denominators together.

· Convert the result back to a mixed number if it is an improper fraction.

· Simplify the mixed number.

Example: 6 2/3 * 3 1/4 =

Convert each mixed number to an improper fraction. 20/3 * 13/4

Multiply the two numerators together. 20 * 13 = 260

Multiply the two denominators together. 3 * 4 = 12

Convert the result to a mixed number. 260/12 = 21 8/12

Simplify the mixed number. 21 2/3

· Convert each Mixed Fraction to an Improper Fraction.

· Invert the Improper Fraction that is the divisor.

· Multiply the two numerators together.

· Multiply the two denominators together.

· Convert the result back to a Mixed Fraction if it is an improper fraction.

· Simplify the Mixed Fraction.

Example: 6 2/3 ÷ 3 1/4 =

Convert each mixed number to an improper fraction. 20/3 ÷ 13/4

Invert the improper fraction that is the divisor and multiply. 20/3 * 4/13

Multiply the two numerators together. 20 * 4 = 80

Multiply the two denominators together. 3 * 13 = 39

Convert the result back to a mixed number. 80/39 = 2 2/39

Simplify the mixed number. 2 2/39

Mixed Fraction consists of an integer followed by a fraction.

For addition and subtraction when Improper Fractions are involved,

· First convert Improper Fraction to Mixed Fraction.(Refer Lesson 2 Conversion )

· Then perform the operation

**How to add and subtract the Mixed Fractions with same denominators?**· Add the numerators of the two fractions

· Place that sum over the common denominator.

· If this fraction is Improper (numerator larger than or equal to the denominator) then convert it to a Mixed Fraction

· Add the Integer portions of the two Mixed Fractions

· If adding the fractional parts created a Mixed Fraction then add its integer portion to the sum.

For Example: 3 2/3 + 5 2/3

Add the fractional part of the mixed numbers 2/3 + 2/3 = 4/3

Convert 4/3 to a mixed number 4/3 = 1 1/3

Add the integer portions of the mixed numbers 3 + 5 = 8

Add the integer from the sum of the fractions 8 + 1 = 9

Final Answer 9 1/3

· Follow same steps for Subtraction of two Mixed Fractions with same denominator.

**· Find the Least Common Denominator (LCD) of the fractions**

**How to add and subtract the Mixed Fractions with different denominators?**· Rename the fractions to have the LCD

· Add/Subtract the numerators of the Mixed Fractions

· Add/Subtract the integers of the Mixed Fractions

o Add the integer from the sum/subtraction of the fractions

· Reduce/Simplify the Fraction

For Example: 2 ¾ - 1 ½

Subtract the fractional part of the mixed numbers 3/4 - 2/4

Convert it to mixed Fraction (If needed) 1/4

Subtract the integer portions of the mixed numbers 2 – 1 = 1

Add the integer from the sum/subtraction of the fractions 1 1/4

Final Answer 1 1/4

**How to perform multiplication and division on Mixed Fractions?****Multiplying two Mixed Fractions**· Convert each mixed number to an improper fraction.

· Multiply the two numerators together.

· Multiply the two denominators together.

· Convert the result back to a mixed number if it is an improper fraction.

· Simplify the mixed number.

Example: 6 2/3 * 3 1/4 =

Convert each mixed number to an improper fraction. 20/3 * 13/4

Multiply the two numerators together. 20 * 13 = 260

Multiply the two denominators together. 3 * 4 = 12

Convert the result to a mixed number. 260/12 = 21 8/12

Simplify the mixed number. 21 2/3

**Dividing two Mixed Fractions**· Convert each Mixed Fraction to an Improper Fraction.

· Invert the Improper Fraction that is the divisor.

· Multiply the two numerators together.

· Multiply the two denominators together.

· Convert the result back to a Mixed Fraction if it is an improper fraction.

· Simplify the Mixed Fraction.

Example: 6 2/3 ÷ 3 1/4 =

Convert each mixed number to an improper fraction. 20/3 ÷ 13/4

Invert the improper fraction that is the divisor and multiply. 20/3 * 4/13

Multiply the two numerators together. 20 * 4 = 80

Multiply the two denominators together. 3 * 13 = 39

Convert the result back to a mixed number. 80/39 = 2 2/39

Simplify the mixed number. 2 2/39

## Solve the following runaway puzzle.

Friends, you will find it interesting to solve this puzzle. Try it, is fun!!

## Practice Problems

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

Solve the following:

1. 1/5 + 2/5

2. 4/7 – 3/7

3. 3/10 - 3/20

4. 2/8 + 5/7

5. 12/ 15 * 21 / 24

6. 13 /27 divided by 11/54

**not**needed to email the answers to the instructor.Solve the following:

1. 1/5 + 2/5

2. 4/7 – 3/7

3. 3/10 - 3/20

4. 2/8 + 5/7

5. 12/ 15 * 21 / 24

6. 13 /27 divided by 11/54

## Assignment 4

**Please email the answers to this Assignment**

**4**

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

Solve the following

Addition

o ¾ + 2/3

o ¼ + 3/5

Subtraction

o 2/3 -1/3

o 3/5-2/8

Multiplication

o 4/9 * 2

o 5/12 * 8/15

Division

o (2/7 ) / (4/5)

o (14/3) / (12/7)

## Assessment 4

**Please email the answers to this Assessment 4 to the email address provided at the bottom of the page. Do not forget to write the Assessment number.**

Solve the following

Addition

o 2/7 + 3/8

o 1/6 + 2/4

Subtraction

o 3/5-2/8

o 4/5 – ¾

Multiplication

o 4/5 * 3/8

o 2 ½ * 2 1/7

Division

o (3/5) /(4/9)

o (12/7) / (11/3)

Miscellaneous

3 3/5 – 2 1/10

(2 4/7 ) / (1 2/3)

## Objectives

Objective of next Lesson: In the next lesson we will study How to solve Real World Problems applying concepts and rules we studied so far.

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