1. Adding and Subtracting Mixed Numbers
Grade 6

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Warm up
19/7 x 37/7
77/108 ÷ 6/56
3/7 ÷ 2/3
3/7 x 21/18
84/7 ÷ = 126
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3. Lets review what we have learned
Multiplying fractions
To multiply two fractions multiply the numerators and then multiply the denominators
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Division of Fractions
To divide fractions , multiply by its multiplicative inverse
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5. Properties of Multiplication
Property
Examples
Commutative-The product of two fractions is the same regardless of the way in which they are ordered
Associative- The sum or product of three or more fractions is the same regardless of the way in which they are grouped
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6. Properties of Multiplication
Property
Examples
Identity- The product of any fraction and 1 is the fraction itself
Inverse Reciprocal- The product of a fraction and its inverse is 1
Distributive -The sum of two fractions multiplied by a number is equal to the sum of products of each fraction and the number
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Mixed Number
A mixed number has a whole number part and a fraction part. Such as
We connect the whole-number name to the fraction name with the word “and.” This mixed number is read as three AND two fifths
2/5 : Fraction Part
3: Whole Number Part
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8. Pictorial Representation of Mixed Numbers
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9. Conversion from a mixed fraction to an improper fraction
To add or subtract any mixed number we first need to convert the mixed number to an improper fraction…..
Multiply the whole number times the denominator
Add your answer to the numerator
Put your new number over the denominator
The improper fraction will be written as
(Whole number x Denominator) + Numerator
Denominator
Remember : Add and subtract these fractions the same way as we do for the proper fractions by making a common denominator to solve the fractions
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10. Lets change a mixed number to an improper fraction
Example:
Multiply whole number 3 with denominator 6
Add the product (18) to the numerator 1
Divide the sum (19) by the denominator 6
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Try Some!
Write the mixed number in the simplest form.
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Adding Mixed Numbers
Method 1:
Step 1: Convert all the mixed numbers to improper fractions
Step 2: Then perform the addition.
Step 3: The final answer can be expressed as an improper fraction or as a mixed number.
Method 2:
Step 1: Add the whole number parts and the fractional parts separately.
Step 2: When this method is used, however, sometimes the fractional part is itself an improper fraction. In this case, that improper fraction must be changed to a mixed number.
Step 3: Then the whole number parts must again be added.
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Method 1
Lets see an example of each method
Improper fraction 7 9 4 11 43 9 15 11 + = 4 1 + = = 99 99 14 99
= 6
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14. Method 2 + 14 + 2 5 3 5 4 5 3 5 4 5 Example: 6 7 = 6 7 3 + 4 5 = 6 + 7
Equal
denominators 7 5
= 13 2 5 2 14 = = 5
Add the fractions together and the whole numbers together
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15. Same example solved with the two methods7 40 3 8 4 5 = =
327 40 4 + 3 + =
= 8 40
Method 2 3 8 4 5 4 + + 3 =
4 + 3 = 7 40 7 40 47 40 7 40 =7 =
7 + 1
= 8
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Try some!
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17. Addition of Mixed fractions with different denominators
When the denominators are co-prime, we need to multiply the two denominators to get the common denominator
When the two denominators have a common factor we find the least common denominator by factoring
When one denominator is a multiple of the other denominator the multiple is the denominator
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Addition with different denominators
Prime denominators
In this case, (after making improper fractions) we need to first convert them into equivalent fraction with the same denominator
Example: + 2 3
An easy choice for a common denominator is 3×5 = 15 x x x x = = = = 11 15 + + = = 5 2 3 =
Therefore,
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19. Examples of each type of denominators
Multiple Denominators 1 8 = 23 4 17 8 8 +
23 x 2
4 x 2 63 8 + = = + 5 2 = =
8 is multiple of 4
Prime Denominators 9 7 + 13 5
13 x x 5
5 x x 5 + = 2 1 + = = + = =
5 and 7 are both prime
Common Factor 25 6 31 9
25 x x 2
6 x x 2 + 75 18 62 18
137 18 + = + + = 4 3 = =
Taking LCM of 6 and 9 which is 18
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Try some!
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21. Subtracting mixed numbers
Method 1 :
One way to subtract one mixed number from another is to change both numbers to improper fractions.
When this method is used, it is never necessary to “borrow” from the whole number part of the minuend
Method 2 :
It is also possible to subtract one mixed number from another by subtracting the whole number parts and the fractional parts separately.
However if the fractional part of the number being subtracted is larger than the fractional part of the number it is being subtracted from the minuend, it is necessary to “borrow” 1 from the whole-number part of the minuend.
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22. Subtracting mixed numbers
Method 1 7 12 5 12 - 5 6 12 19 12
= 1 3 1 = - = =
Method 2 7 8 5 8 2 8 1 4 10 - 6 = = 4 =4
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23. Subtracting mixed numbers
Denominators that are multiple of each other 1 4 1 4 - - 1 2 1 2
Example:
Example: 5 5 3
4 is a multiple of 2
Since 1/4 is not enough to be subtracted by 1/2, we have to convert all mixed numbers into improper fractions first then compute 1 4 1 2
5 x x 2 + 1 - - 5 3 = - = = - 7 4 3 4 = = 1
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Lets see some examples
Equal Denominators 4 - 2 = =
Different denominators
x x
x x
341 - 7 - 2 = = =
Do same as in Addition
Multiple Take the multiple
Common Factors Take LCM
Prime Multiply the two
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Try some!
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26. Addition/ Subtraction of mixed numbers
Convert the mixed fraction in to an improper fraction or add the whole numbers and fractions separately
Find a common denominator
Add/Subtract as required
Simplify, then if it is an improper fraction then again convert in to a mixed fraction
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27. Break Time

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Assessment 1 3 1 5
1) 6 + 2 = 7 2 1 2 2 + 5 2) = 11 3 + = 3) 11 3 3 6 2 3 + = 4) 1 3 1 2 1 2 + = 5) 1 3
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Assessment 2 9 3 9 4 - 2 6. = 2 13 4 7 - = 5 3 7. 1 8 3 8 - = 6 9 8. 7 12 - 2 4 = 9. 2 2 1 18 4 9 =
10. 2 - 1
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Assessment
At the geologists convention 1/4 of the people are students, 1/6 are professors and 1/6 are industry representatives. The rest are employees of the convention centre. If there are 336 people at the convention, how many are employees of the centre?
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Assessment
Jeffrey is baking brownies. So far he has put in 2 ¼ cups of flour and 1 2/3 cups of sugar. What is the total amount of ingredients that he already has in his bowl?
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Assessment
All of Sharon’s school books weigh a total of eleven and one-sixth pounds. If you take away her math book, the total weight drops to ten and a third pounds. How much does Sharon’s math book weigh?
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34. A mixed number has a whole number part and a fraction part
Lets review what we have learned in this lesson
A mixed number has a whole number part and a fraction part
To add or subtract any mixed number we first need to convert the mixed number to an improper fraction then proceed further…..
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35. + Adding Mixed Fractions with equal denominators + + + 3 7 5 7 3 7 5 74 2
= 4 2
3 + 5 7 =
Equal
denominators 8 7
= 6 + 8 5
= 6
Add the fractions together and the whole numbers together
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36. Addition of Mixed fractions with different denominators
When the denominators are co-prime, we need to multiply the two denominators to get the common denominator
When the two denominators have a common factor we find the least common denominator by factoring
When one denominator is a multiple of the other denominator the multiple is the denominator
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37. Subtraction of Mixed Numbers
Denominators that are multiple of each other
Example: 1 4 1 2 - 5 3
4 is a multiple of 2
Since 1/4 is not enough to be subtracted by 1/2, we have to convert all mixed numbers into improper fractions first then compute 1 4 1 2
5 x x 2 + 1 - - 5 3 = - - = = 7 4 3 4 = = 1
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Lets see some more examples
Equal Denominators 4 - 2 = =
Different denominators
x x
x x
341 - 7 - 2 = = =
Do same as in Addition
Multiple Take the multiple
Common Factors Take LCM
Prime Multiply the two
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39. Steps: Addition/Subtraction of mixed numbers
Convert the mixed fraction in to an improper fraction or add the whole numbers and fractions separately
2. Find a common denominator
3. Add/Subtract as required
4. Simplify, then if it is an improper fraction then again convert in to a mixed fraction
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40. You had a Great Lesson Today!