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

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

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

How to add and subtract the Mixed Fractions with different denominators?

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

·         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

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 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

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

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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