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
Final Answer 9 1/3
· 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
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
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.
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
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 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
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)
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)
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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