Day 39 – Subtracting mixed number fractions
Success Criteria
I can find the lowest common denominator
I can identify a mixed number fraction
I can subtract mixed number fractions
DNATry to complete this times table grid in under 1 minute 30 seconds. Set a timer.
Retrieval practice
What is the lowest common multiple of
15 and 1?
What is the product of 9 and 7?
What is the lowest common multiple of 3
and 2?
What is the product of 8 and 7?
How many degrees is there in a full circle?
What is the difference between 720cm and
1km?
1 HP
2 HPs
3 HPs
Retrieval practice answers
1 HP
2 HPs
3 HPs
What is the lowest common multiple of
15 and 1?15
What is the product of 9 and 7?
63
What is the lowest common multiple of 3
and 2?6
What is the product of 8 and 7?
56
How many degrees is there in a full circle?
360
What is the difference between 720cm and
1km?180cm
Explain what mistakes people could make doing this and how we could avoid them
Daily practice
0 to 12 times table for 16…
Daily practiceExample: People could not partition properly and add incorrectly
Write the definitions for the words we will come across today – can you think of an example question for the word?
Word Definition Example
Partition
Quotient
Whole number
Subtracting mixed number fractions
• Let’s dive straight into it!
Question One
• Let’s attempt this question together.
7
8- =
3
53 1
Step One – convert the first mixed number fraction into an improper fraction
7
8=3
My method(3 x 8) + 7
8= 31
8
Step Two – convert the second mixed number fraction into an improper fraction
3
5=1
My method(1 x 5) + 3
5= 8
5
Step Three – Make our denominator the same
We have to make our denominator (bottom numbers) the same. We need to get the lowest common multiple. Let’s write out the multiples of both 8 and 5.
• The multiples of 8 are: 8, 16, 24, 32, 40, 48, 56, 64, 72, 80
• The multiples of 5 are: 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, 65, 70, 75, 80
The numbers are in both 15 and 30, but let’s choose the lowest number (40).
31
8- =
8
5
Step Three – Set the question out like this
The lowest common denominator is 40. Above, I have made the original question equal to blank fractions (where there is no numerator for now).
Please note that I have kept the operation the same, the subtraction sign is constant.
31
8- =8
5 40-
40=
40
Step Four – Fill out 1st Blank Fraction numerator
Let us make the 1st Fraction equivalent to the 1st Blank Fraction. I multiplied 8 by 5 to get 40. So I have to multiple 31 by 5 to get 155.
31
8- =8
5 40-
40=
40
1st Fraction 2nd Fraction 1st Blank Fraction 2nd Blank Fraction
31
8= 40
x 5
x 5
155
155
Step Five – Fill out 2nd Blank Fraction numerator
Let us make the 2nd Fraction equivalent to the 2nd Blank Fraction. I multiplied 5 by 8 to get 40. So I have to multiple 8 by 8 to get 64.
31
8- =8
5 40-
40=
40
1st Fraction 2nd Fraction 1st Blank Fraction 2nd Blank Fraction
8
5= 40
x 8
x 8
64
155 64
Step Six – Subtract the numerators
I can now subtract my numerators, 155 – 64 = 91 and I can place this as the total numerator.
WARNING! Our answer is an improper fraction. We need to convert this improper fraction into a mixed number fraction.
31
8- =8
5 40-
40=
40
1st Fraction 2nd Fraction 1st Blank Fraction 2nd Blank Fraction
155 64 91
• How many 40s go into 91? 2 times right, so I have to write 2 whole.
• The denominator stays the same (40).
• Multiply 2 whole by 40 to get 80. How much do I add to 40 to get to 91? 11, so this is my numerator.
• Can I simplify this answer/fraction? What are the factors of both 11 and 40?
• 11 has factors that 1 and 11.
• 40 has factors that are 1, 2, 4, 5, 8, 10, 20 and 40.
• The number 1 is within both, but there is no need in dividing the numerator and the denominator by 1 because our answer will remain the same.
40
91
=40 times table
40 x 1 = 40 40 x 2 = 80
40 x 3 = 12040 x 4 = 16040 x 5 = 200
402 11
Step Six – the finale!
I have placed my answer with the original question.
= 402 117
8- =
3
53 1
Reflection
• How did you get on with working through this example?
• Use your red hat to express your emotions. Write three full sentences.
Make yourself a flow map to remember how to subtract mixed numbers fractions
Answer these questions
Mark your work
Try these questions
Mark your work
Exit ticket
What went well today?
What errors did you make or avoid today?
What do you feel this lesson has made you want to learn about next?
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