Subtracting a proper fraction from a mixed number

$Subtracting a proper fraction from a mixed number fraction Success Criteria ü I can$

Subtracting a proper fraction from a mixed number fraction Success Criteria ü I can find the lowest common denominator ü I can identify a proper fraction ü I can subtract proper fractions from mixed number fractions DNA Complete this times table grid.

Retrieval practice Click on the speaker to hear Miss Odedina reading the retrieval questions 1 HP 2 HPs 3 HPs What is the lowest common multiple of 15 and 6? What is the product of 3 and 7? What is the lowest What is the product of common multiple of 3 9 and 7? and 6? What is the difference How many degrees is there in a full circle? between 500 cm and 1 km?

Retrieval practice 1 HP 2 HPs 3 HPs What is the lowest What is the product of common multiple of 3 and 7? 15 and 6? 21 30 What is the lowest What is the product of common multiple of 3 9 and 7? and 6? 63 6 What is the difference How many degrees is there in a full circle? between 500 cm and 1 km? 500 cm 360

Daily practice 1 to 12 times table for 10… Explain what mistakes people could make doing this and how we could avoid them

Daily practice Example: 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 Multiple Product Fraction Definition Example

$Subtracting a proper fraction from a mixed number fraction • Let’s dive straight into$

Subtracting a proper fraction from a mixed number fraction • Let’s dive straight into it!

Question One 18 7 3 5 = • Let’s attempt this question together.

$Step One – convert the mixed number fraction into an improper fraction 18 =$

Step One – convert the mixed number fraction into an improper fraction 18 = 7 My method (1 x 8) + 7 8 = • Let’s attempt this question together. 15 8

Step Two – Make our denominator the same 15 8 - 3 5 = 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).

Step Three – Set the question out like this 15 8 - 3 5 = 40 - 40 = 40 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.

Step Four – Fill out the 1 st Blank Fraction numerator 1 st Fraction 15 8 - 2 nd Fraction 3 5 = 1 st Blank Fraction 75 40 - 2 nd Blank Fraction 40 = Let us make the 1 st Fraction equivalent to the 1 st Blank Fraction. I multiplied 8 by 5 to get 40. So I have to multiple 15 by 5 to get 75. 15 8 x 5 = x 5 75 40 40

Step Four – Fill out the 2 nd Blank Fraction numerator 1 st Fraction 15 8 - 2 nd Fraction 3 5 = 1 st Blank Fraction 75 40 - 2 nd Blank Fraction 24 40 = Let us make the 2 nd Fraction equivalent to the 2 nd Blank Fraction. I multiplied 5 by 8 to get 40. So I have to multiple 3 by 8 to get 24. 3 5 x 8 = x 8 24 40 40

Step Five – Subtract the numerators 1 st Fraction 15 8 - 2 nd Fraction 3 5 = 1 st Blank Fraction 75 40 - 2 nd Blank Fraction 24 40 = 51 40 I can now subtract my numerators, 75 – 24 = 51 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.

51 40 =1 40 11 • How many 40 s go into 51? 1 time right, so I have to write 1 whole. • The denominator stays the same (40). • Multiply 1 whole by 40 to get 40. How much do I add to 40 to get to 51? 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 times table 40 x 1 = 40 40 x 2 = 80 40 x 3 = 120 40 x 4 = 160 40 x 5 = 200

Step Six – the finale! 18 7 3 5 = 1 40 11 I have placed my answer with the original question.

Reflection • How did you get on with working through this example? • Use your red hat to express your emotions. Write three full sentences.

Let’s go through another example. Keep persisting! You can do it!

Question One 38 4 9 10 = • Let’s attempt this question together.

$Step One – convert the mixed number fraction into an improper fraction 38 =$

Step One – convert the mixed number fraction into an improper fraction 38 = 4 My method (3 x 8) + 4 8 = • Let’s attempt this question together. 28 8

Step Two – Make our denominator the same 28 8 - 9 10 = 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 10. • The multiples of 8 are: 8, 16, 24, 32, 40, 48, 56, 64, 72, 80 • The multiples of 10 are: 10, 20, 30, 40, 50, 60, 70, 80 The numbers are in both 40 and 80, but let’s choose the lowest number (40).

Step Three – Set the question out like this 28 8 - 9 10 = 40 - 40 = 40 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.

Step Four – Fill out the 1 st Blank Fraction numerator 1 st Fraction 28 8 - 2 nd Fraction 9 10 = 1 st Blank Fraction 140 40 - 2 nd Blank Fraction 40 = Let us make the 1 st Fraction equivalent to the 1 st Blank Fraction. I multiplied 8 by 5 to get 40. So I have to multiple 28 by 5 to get 140. 28 8 x 5 = x 5 140 40 40

Step Five – Fill out the 2 nd Blank Fraction numerator 1 st Fraction 28 8 - 2 nd Fraction 9 10 = 1 st Blank Fraction 140 40 - 2 nd Blank Fraction 36 40 = Let us make the 2 nd Fraction equivalent to the 2 nd Blank Fraction. I multiplied 10 by 4 to get 40. So I have to multiple 9 by 4 to get 36. 9 10 x 4 = x 4 36 40 40

Step Five – Subtract the numerators 1 st Fraction 28 8 - 2 nd Fraction 9 10 = 1 st Blank Fraction 140 40 - 2 nd Blank Fraction 36 40 = 104 40 I can now subtract my numerators, 140 – 36 = 104 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.

104 40 =2 40 24 • How many 40 s go into 104? 2 time right, so I have to write 1 whole. • The denominator stays the same (40). • Multiply 2 wholes by 40 to get 80. How much do I add to 80 to get to 104? 24, so this is my numerator. • Can I simplify this answer/fraction? What are the factors of both 24 and 40? • 24 has factors that 1, 2, 3, 4, 6, 8, 12 and 24. • 40 has factors that are 1, 2, 4, 5, 8, 10, 20 and 40. • The number 8 is within both, let’s divide the proper fraction by 8. 40 times table 40 x 1 = 40 40 x 2 = 80 40 x 3 = 120 40 x 4 = 160 40 x 5 = 200

Simplifying time! 2 40 24 ÷ 8 2 3 5

Step Six – the finale! 38 4 9 10 =2 3 5 I have placed my answer with the original question.

$Make yourself a flow map to remember how to subtract proper fractions from mixed$

Make yourself a flow map to remember how to subtract proper fractions from mixed number 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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