day 39 subtracting mixed number fractions › wp...warning! our answer is an improper fraction. we...

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

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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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